AND FOUR DIMENSIONAL DEVICES

PRIORITY CLAIM

[0001] This application claims priority from Singapore Patent Application No. 10201802828U filed on 04 April 2018 and Singapore Patent Application No. 10201803689X filed on 02 May 2018.

TECHNICAL FIELD

[0002] The present invention generally relates to three-dimensional (3D) printing, and more particularly relates to 3D printing systems capable of fabricating soft composite actuators and four-dimensional devices.

BACKGROUND OF THE DISCLOSURE

[0003] Shape memory alloys (SMAs) are a class of active materials that can perform reversible actuation upon thermomechanical training. Shape memory alloys (SMAs) have been widely used to fabricate soft actuators by embedding SMA wires into various soft matrices manufactured by conventional moulding methods or novel three- dimensional (3D) printing techniques. However, soft matrices of SMA based actuators are typically fabricated from only one or two different materials.

[0004] Although SMAs are manufactured in a variety of shapes, including plates, springs, wires, and ribbons, the most widely used shape is the one-dimensional SMA wire which can be integrated into soft matrices to fabricate actuators that transform one dimensional deformation of the SMA wires into a broad range of three-dimensional deformations. For instance, conventional soft actuators comprised of a polydimethylsiloxane (PDMS) matrix embedded with Nitinol (Nickel-Titanium) SMA wires arranged in different configurations to create a variety of bending, twisting, and extensional actuators which have potential applications in soft robotics, aerospace, and biomedical fields.

[0005] Most research efforts to develop SMA-powered soft actuators rely on time- consuming moulding and casting based manufacturing methods which typically consist of the following steps: (i) fabricating a polymeric or metallic mold based on the desired geometry of the soft actuator; (ii) embedding a pre-strained SMA wire into the mold and fixing the two ends of the SMA wire on both ends of the mold; (iii) casting liquid polymer resin into the mold, and thermally curing the resin; and (iv) finally removing the actuator from the mold. A major limitation of this method is that each actuator design requires fabricating a different mold adopting the actuator geometry. Further, this method can only produce simple structures.

[0006] Recent advancements in multimaterial three-dimensional (3D) printing technologies have significantly improved the capability to fabricate complicated 3D structures with intricate details through micron-scale placement of various materials with different properties. In particular, multimaterial inkjet 3D printing provides high design freedom to produce complex composite structures by selectively depositing photopolymer droplets on a build tray followed by UV illumination to trigger photopolymerization, which transforms the droplets of various constituents and compositions into solids with different mechanical properties. Using this technology, the spatial arrangement of different materials over multiple length scales can be easily achieved in a single printing job and the desired stiffness variation can be realized. Multimaterial inkjet 3D printing has the potential to automate the fabrication process of the body of the soft actuators and replace conventional manufacturing methods.

[0007] Although some recent studies have used 3D printing in fabricating SMA based actuators, they have not tried to tailor the actuator deformation using different printing materials. Also, developing a predictive model to simulate the actuator deformation and study the effect of printing material properties on its performance is of critical importance.

[0008] Three-dimensional (3D) printing technologies have been increasingly used to create mechanism components for robots, flight vehicles, and other applications. However, to date, the motions of these mechanisms are only driven by external actuators (i.e. traditional motors). Integrating chunky and often heavy motors into printed mechanism components significantly increases the manufacturing complexity and limits the design flexibility. Therefore, developing a novel approach based on 3D printing to combine mechanisms and actuators as a single unity is highly desired.

[0009] The emerging 4D printing technology, which adds a fourth dimension“time” to 3D printed structures, offers a practical solution to integrating actuation into printed mechanisms. 4D printing can be realized by 3D printing structures with soft active materials (SAMs) which exhibit large-deformation in response to environmental stimuli such as heat, moisture, voltage, magnetic field, and others. Among the existing SAMs, the thermally-responsive shape memory polymers (SMPs) are regarded as one of the most promising candidates for 4D printing, due to their compatibility with 3D printing, relatively large recovery force and fast responding rate. However, despite great progress in 4D printing, the relatively low actuation force of the 4D printed structures often impedes their engineering applications. [0010] In recent years, many efforts have been made to demonstrate 4D printing using thermal responsive SMPs. Examples include self-assembly coiling, twisting and wavy- shape strips, sequential recovering structures, and active origami. However, the 4D printed structures became soft when the free recovery was triggered at high temperatures, as the SMPs entered the low stiffness rubbery state. This low stiffness in the free recovery process significantly impedes the application of the 4D printed parts to practical engineering structures. In addition, the thermal actuation of the 4D printed SMP structures is mostly triggered through a change of ambient temperature by placing the printed structures into hot water or thermal chambers, which cannot be used for real applications that require precise and timely control of temperature.

[0011] Thus, there is a need in the art for an SMA-based actuator fabrication process using a multimaterial 3D printing system which tailors the actuator deformation to the multimaterials used. Also, there is a need for a SMP-based 4D printing system where time for actuation of the fabricated device can be controlled by heat or other environmental stimuli in a scalable fabrication system. Furthermore, other desirable features and characteristics will become apparent from the subsequent detailed description and the appended claims, taken in conjunction with the accompanying drawings and this background of the disclosure.

SUMMARY

[0012] According to at least one aspect of present embodiments, a method for fabrication of shape memory alloy (SMA) based actuators is provided. The method includes multimaterial fabrication of a three-dimensional (3D) printed actuator structure comprising at least soft matrix elastomer material and rigid polymer material, the actuator structure having a SMA wire channel formed therein. The method also includes pre-straining a SMA wire, inserting the pre-strained SMA wire into the SMA wire channel in the actuator structure, and firmly affixing the SMA wire to the printed actuator structure. The method further includes heating the SMA wire until it exceeds its austentite transition temperature and contracts, the contracted SMA wire transferring contraction to the actuator structure, and cooling the SMA wire to release elastic strain energy in the actuator structure.

[0013] According to another aspect of the present embodiments, a method for fabrication of shape memory polymer (SMP) based four-dimensional (4D) structures is provided. The method includes multimaterial fabrication of three-dimensional (3D) printed portions of the 4D structures comprising one or more active hinges and one or more flexible hinges, each of the one or more active and flexible hinges comprising soft and rigid shape memory polymers, the active hinges having one or more resistive wire channels formed therein. The method also includes inserting a resistive wire into the one or more resistive wire channels in the active hinges and assembling the SMP-based 4D structures. Finally, the method includes programming the SMP-based 4D structure to achieve a fixed temporary shape; and thereafter actuating the SMP-based 4D structure to trigger a free recovery of a pre programmed shape of the SMP-based 4D structure.

BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The accompanying figures, where like reference numerals refer to identical or functionally similar elements throughout the separate views and which together with the detailed description below are incorporated in and form part of the specification, serve to illustrate various embodiments and to explain various principles and advantages in accordance with present embodiments.

[0015] FIG. 1 , comprising FIGs. 1A and 1 B, depicts illustrations of basic designs of shape memory alloy based (SMA-based) 3D printed soft multimaterial actuators in accordance with present embodiments, wherein FIG. 1A depicts an illustration of a bending actuator with an eccentrically embedded SMA wire and a rigid layer printed at the midplane and FIG. 1 B depicts an illustration of an extensional actuator with a concentrically embedded SMA wire and alternating rigid reinforcement segments printed on the top and bottom surfaces.

[0016] FIG. 2, comprising FIGs. 2A to 2D, depicts graphs of results of characterization test of 3D printed materials fabricated in accordance with present embodiments, wherein FIG. 2A depicts a graph of stress-strain curves of the soft materials used to print the soft matrix of the actuators, FIG. 2B depicts a graph of Young’s modulus of the soft materials, FIG. 2C depicts a graph of stress-strain curves of the rigid materials used to print the rigid reinforcement segments of the actuators, and FIG. 2D depicts a graph of Young’s modulus of the rigid materials.

[0017] FIG. 3 depicts a flow diagram of a fabrication process for SMA-based 3D printed soft multimaterial bending actuators in accordance with the present embodiments.

[0018] FIG. 4, comprising FIGs. 4A, 4B and 4C, depicts designs of SMA-based 3D printed soft multimaterial bending and twisting actuators in accordance with the present embodiments, wherein FIG. 4A is a schematic illustration of a top view and a cross- sectional view of a bending actuator with a uniform cross section over the entire effective length of the actuator, FIG. 4B is a schematic illustration of a top view and two cross- sectional views of a bending actuator having five segments with equal lengths, including two soft segments acting as hinges, and FIG. 4C is schematic illustrations of a top view and a bottom view of a twisting actuator composed of a soft matrix with rigid fibers diagonally printed on its bottom surface to create a twisting deformation.

[0019] FIG. 5 depicts a schematic illustration of a SMA-based 3D printed extensional actuator in accordance with present embodiments including two magnified views of the extensional actuator.

[0020] FIG. 6, comprising FIGs. 6A to 6C, are photographic illustrations depicting the effect of thickness of the rigid mid-layer on the maximum deformation of a bending actuator as shown in FIG. 4A in accordance with present embodiments, wherein FIG. 6A depicts a bending actuator having no rigid mid-layer, FIG. 6B depicts a bending actuator having a 0.3mm rigid mid-layer, and FIG. 6C depicts a bending actuator having a 0.5mm rigid mid-layer.

[0021] FIG. 7, comprising FIGs. 7A and 7D, are photographic illustrations and a graph depicting a comparison of experimental and modelling results of maximum deformation of bending actuators with varying lengths in accordance with the present embodiments, wherein FIG. 7A depicts maximum deformation of a 40mm long bending actuator, FIG. 7B depicts maximum deformation of a 60mm long bending actuator, FIG. 7C depicts maximum deformation of a 80mm long bending actuator, and FIG. 7D depicts a graph of tip displacement versus actuator length.

[0022] FIG. 8, comprising FIGs. 8A to 8D, are photographic illustrations and a graph depicting a comparison of experimental and modelling results of matrix stiffness effect on maximum deformation of 80mm long bending actuators with soft matrix in accordance with present embodiments, wherein FIG. 8A depicts maximum deformation of a bending actuator printed from FLX9940, FIG. 8B depicts maximum deformation of a bending actuator printed from FLX9970, FIG. 8C depicts maximum deformation of a bending actuator printed from FLX9995, and FIG. 8D depicts a graph of tip displacement versus matrix stiffness.

[0023] FIG. 9, comprising FIGs. 9A to 9D, are photographic illustrations and a graph depicting a comparison of experimental and modelling results of maximum deformation of two similar bending actuators based on the design of FIG. 4B in accordance with present embodiments, wherein FIG. 9A depicts maximum deformation of a bending actuator printed from FLX9950, FIG. 9B depicts maximum deformation of a bending actuator printed from FLX9970, FIG. 9C depicts maximum deformation of a bending actuator printed from FLX9995, and FIG. 9D depicts a graph of tip displacement versus matrix stiffness.

[0024] FIG. 10, comprising FIGs. 10A to 10F, depicts photo illustrations of experimental results and simulation modelling results of maximum deformation of bending actuators with two dissimilar hinges based on the design of FIG. 4B in accordance with present embodiments, wherein FIG. 10A depicts maximum deformation of a two-hinged bending actuator having a first hinge printed from FLX9995 and a second hinge printed from FLX9950, FIG. 10B depicts maximum deformation of a two- hinged bending actuator having a first hinge printed from FLX9985 and a second hinge printed from FLX9950, FIG. 10C depicts maximum deformation of a two-hinged bending actuator having a first hinge printed from FLX9970 and a second hinge printed from FLX9950, FIG. 10D depicts maximum deformation of a two-hinged bending actuator having a first hinge printed from FLX9960 and a second hinge printed from FLX9950, FIG. 10E depicts maximum deformation of a two-hinged bending actuator having a first hinge printed from FLX9970 and a second hinge printed from FLX9985, and FIG. 10F depicts maximum deformation of a two-hinged bending actuator having a first hinge printed from FLX9950 and a second hinge printed from FLX9985.

[0025] FIG. 1 1 , comprising FIGs. 1 1 A to 1 1 E, depicts photo illustrations of a soft gripper including multiple actuators fabricated in accordance with the present embodiments grasping and releasing a fifteen gram cylindrical object, wherein FIG. 1 1 depicts the grasping and releasing procedure at the start (t = 0), FIG. 1 1 B depicts the grasping and releasing procedure at time t = 2 seconds, FIG. 1 1 C depicts the grasping and releasing procedure at time t = 6 seconds, FIG. 1 1 D depicts the grasping and releasing procedure at time t = 10 seconds, and FIG. 1 1 E depicts the grasping and releasing procedure at time t = 15 seconds.

[0026] FIG. 12, comprising FIGs. 12A and 12B, are photographic illustrations depicting a twisting actuator fabricated according to the design of FIG. 4C in accordance with present embodiments, wherein FIG. 12A is a top view and FIG. 12B is a front view.

[0027] FIG. 13, comprising FIGs. 13A and 13B, depicts configurations of an extensional actuator as depicted in FIG. 5 in accordance with present embodiments, wherein FIG. 13A depicts an as-fabricated compact shape of the actuator with embedded SMA wires and FIG. 13B depicts an extensional deformed shape of the actuator.

[0028] FIG. 14, comprising FIGs. 14A to 14D, depicts schematic illustrations of four dimensional (4D) printed shape memory structures with active and flexible hinges in accordance with present embodiments, wherein FIG. 14A depicts an as-printed morphing wing flap consisting of three hinges, including two active hinges and one flexible hinge, FIG. 14B depicts a programmed shape of the morphing wing flap after thermomechanical training, FIG. 14C depicts an as-printed deployable structure with four hinges, including two active hinges and two flexible hinges, and FIG. 14D depicts a programmed shape of the deployable structure after thermomechanical training. [0029] FIG. 15, comprising FIGs. 15A to 15C, depicts graphs of dynamic mechanical analysis (DMA) testing of ten different printing materials in accordance with the present embodiments, wherein FIG. 15A depicts a graph of storage modulus versus temperature for the ten printing materials, FIG. 15B depicts a graph of Tan<5 versus temperature for the ten printing materials, and FIG. 15C depicts a graph of glass transition temperatures (7 _gS ) of the ten printing materials.

[0030] FIG. 16, comprising FIGs. 16A to 16D, depicts tensile test results of the printing materials in accordance with present embodiments, wherein FIG. 16A depicts a graph of stress versus strain curves of VeroClear at different temperatures, FIG. 16B depicts a graph of failure strain and Young’s modulus of VeroClear at different temperatures, FIG. 16C depicts a graph of stress versus strain curves of the elastomeric materials at room temperature, and FIG. 16D depicts a graph of Young’s modulus of the elastomeric digital materials at room temperature.

[0031] FIG. 17, comprising FIGs. 17A and 17B, depicts the as-fabricated and assembled configurations of two 4D printed structures in accordance with the present embodiments, wherein FIG. 17A depicts a morphing wing flap structure including stationary and moving rigid parts and FIG. 17B depicts a deployable structure also including stationary and moving rigid parts.

[0032] FIG. 18, comprising FIGs. 18A to 18D, depicts photographic illustrations of programming and actuating steps of the morphing wing flap structure in accordance with the present embodiments, wherein FIG. 18A depicts a first step in the programming process of heating the active hinges of the structure, FIG. 18B depicts a second step in the programming process of applying a load after the heating step, FIG. 18C depicts the third step in the programming process after removal of the load remains relatively stable in the new programmed shape, and FIG. 18D depicts the actuation step where the recovered shape of the structure is resumed after the structure is reheated.

[0033] FIG. 19, comprising FIGs. 19A to 19F, depict photographic illustrations taken over time during the actuation process of the deployable structure in accordance with the present embodiments, wherein FIG. 19A is a photo taken at the start of the actuation process (t = 0 seconds), FIG. 19B is a photo taken at t = 15 seconds, FIG. 19C is a photo taken at 20 seconds, FIG. 19D is a photo taken at t = 30 seconds, FIG. 19E is a photo taken at 40 seconds, and FIG. 19F is a photo taken at t = 60 seconds.

[0034] FIG. 20, comprising FIGs. 20A to 20D, depicts photographic illustrations demonstrating the effect of the stiffness of the flexible hinges on the load-bearing capacity of the 4D printed structures in accordance with the present embodiments, wherein FIG. 20A depicts a photo of the recovered shape of the morphing wing flap with a 10g weight hung from the tip of the moving part where the flexible hinges were printed from Agilus30, and FIG. 20B depicts a photo of the recovered shape of the morphing wing flap with a 10g weight hung from the tip of the moving part where the flexible hinges were printed from FLX9995, FIG. 20C depicts a photo of the recovered shape of the deployable structure with a 50g weight placed on the actuator where the flexible hinges were printed from Agilus30, and FIG. 20D depicts a photo of the recovered shape of the deployable structure with a 50g weight placed on the actuator where the flexible hinges were printed from FLX9995.

[0035] FIG. 21 , comprising FIGs. 21 A to 21 F, depicts illustrations, simulations and graphs of results of heat transfer simulation in the active hinge in accordance with the present embodiments, wherein FIG. 21 A depicts an illustration a repeating unit cell of the active hinge representing heat transfer mechanisms, including conduction and convection, FIG. 21 B depicts simulation results of temperature change in the representative unit cell over time, FIG. 21 C depicts a graph of experimental measurements and finite element method (FEM) predictions of temperature change on the outer surface (Point A of FIG. 21 A), FIG. 21 D depicts a graph comparing temperature distribution on the outer surface (Point A in FIG. 21 A) and the inner surface (Point B in FIG. 21 A), FIG. 21 E depicts a graph of the effect of the natural and forced convections on temperature distribution on the outer surface (Point A in FIG. 21 A), and FIG. 21 F depicts a graph of heating time versus applied voltage.

[0036] FIG. 22, comprising FIGs. 22A to 22D, depicts strain contours in the active hinges in accordance with present embodiments, wherein FIG. 22A depicts strain contours in the as-printed active hinges used in the morphing wing flap of FIGs. 14A and 14B, FIG. 22B depicts strain contours in the programmed active hinges used in the morphing wing flap, FIG. 22C depicts strain contours in the as-printed active hinges used in the deployable structure of FIGs. 14C and 14D, and FIG. 22D depicts strain contours in the programmed active hinges used in the deployable structure.

[0037] FIG. 23, comprising FIGs. 23A to 23D, depicts finite element predictions of the morphing wing flap configurations during programming and actuating steps in accordance with the present embodiments, wherein FIG. 23A depicts an initial configuration of the flap, FIG. 23B depicts a deformed shape of the flap under a combination of mechanical and thermal loads, FIG. 23C depicts a programmed shape of the flap at T< T _g , and FIG. 23D depicts a recovered shape of the flap at T> T _g .

[0038] FIG. 24, comprising FIGs. 24A to 24D, depicts graphs of experimental measurements and finite element predictions of the shape memory and shape fixity of the morphing wing flap with flexible hinges printed from various elastomeric digital materials in accordance with the present embodiments, wherein FIG. 24A is a graph comparing experimental measurements and finite element predictions of the recovery ratio of the morphing wing flap with no external load, FIG. 24B is a graph comparing experimental measurements and finite element predictions of the recovery ratio of the morphing wing flap with a 10g external load, FIG. 24C is a graph comparing shape fixity of the morphing wing flap with no external load, and FIG. 24D is a graph comparing shape fixity of the morphing wing flap with a 10g external load.

[0039] And FIG. 25 depicts a flow diagram of a fabrication process for SMP-based 4D printed shape memory structures in accordance with the present embodiments.

[0040] Skilled artisans will appreciate that elements in the figures are illustrated for simplicity and clarity and have not necessarily been depicted to scale.

DETAILED DESCRIPTION

[0041] The following detailed description is merely exemplary in nature and is not intended to limit the invention or the application and uses of the invention. Furthermore, there is no intention to be bound by any theory presented in the preceding background of the invention or the following detailed description. It is the intent of present embodiments to present a design and manufacturing approach to fabricate shape memory alloy (SMA) powered soft actuators with tunable functionalities and various deformations by following two different strategies to create various deformation modes including bending, twisting and extensional deformations. First, the stiffness of the soft and rigid segments of the multimaterial actuators are modulated by printing various compositions of two base materials having different properties. Second, spatial variations of soft and rigid segments are controlled to achieve the desired structural performance.

[0042] It is the intent of the present embodiments to also present a design and fabrication methodology for enhanced multimaterial 4D printing in which shape memory polymer (SMP) active hinges are produced using a high-resolution, multimaterial inkjet 3D printing technology. Recovery force is enhanced by combining active hinges with elastic flexible hinges which store elastic strain energy during programming, then release it during actuation to increase the recovery force.

[0043] A major advantage of multimaterial 3D printing for fabricating soft actuators is the ability of multimaterial 3D printing to precisely control spatial arrangements of distinctive soft and rigid segments without complicating the manufacturing process or increasing fabrication time. Such precise control cannot be easily achieved in conventional fabrication methods. For example, in order to optimize bending actuation of SMA-embedded soft actuators, a rigid thin layer is commonly placed in the mid-plane of the actuator to increase the axial stiffness, and reduce axial contraction caused by contraction of the SMA wire. Moreover, both ends of the actuator must be fabricated from a rigid material to ensure that during the actuation process, metal connections fixing the SMA wire to the actuator body do not damage the soft matrix at elevated temperatures. These requirements add steps to conventional manufacturing processes, therefore increasing time and cost of fabrication. In accordance with present embodiments, these challenges can be easily addressed using a multimaterial inkjet 3D printing technology to simplify complexity of fabricating soft actuators by directly printing 3D multimaterial structures where materials with different stiffnesses are precisely placed at desired locations.

[0044] Referring to FIGs. 1A and 1 B, schematic illustrations 100, 150 depict basic designs of multimaterial soft actuators 102, 152 which achieve bending and extensional deformations in accordance with present embodiments. Each actuator 102, 152 includes a multimaterial structure which includes a polymeric soft matrix 104, 154 and several rigid reinforcement segments 106, 156 which are fabricated using a multimaterial inkjet 3D printer. After the actuators 102, 152 are printed, shape memory allow (SMA) wires 1 10, 160 are inserted into the printed polymeric structure and fixed externally at both ends using crimp connections 1 15, 165 to prevent sliding between the embedded wire and the printed structure. During actuation, the small linear axial deformation of the SMA wires 1 10, 160 is transformed into a large out-of-plane deformation of the actuators 102, 152.

[0045] By changing the location of the SMA wire 1 10, 160 within the actuator 102, 152 as well as the geometry and spatial arrangement of the rigid reinforcing segments 106, 156, actuators can be created in accordance with the present embodiments exhibiting different complex 3D deformations. As shown in the schematic illustration 100, in order to create a large-deformation bending actuator 102, the SMA wire 1 10 is eccentrically embedded into a 3D printed structure having a thin layer of the rigid material 106 printed along a midplane of the actuator 102. The schematic illustration 150 depicts another actuator 152 created to transform the axial deformation of the SMA wire 160 into bending deformation through concentrically inserting the SMA wire 160 into the printed structure which has the rigid thin layers 156 printed alternatively on the top and bottom surfaces. Incorporating a number of these actuators as repeating unit into a larger structure, actuators exhibiting net extensional deformation can be fabricated.

[0046] Mechanical properties of the printed materials are required in the design process of the actuators to achieve a desired performance. Such mechanical properties are also required in finite element modelling of the printed materials to simulate deformation of the actuators. The printing materials used for the polymeric soft matrix 104, 154 include a rubber-like elastomer, referred to as Agilus30, and the printing materials used for the rigid reinforcement segments 106, 156 include a rigid polymer, such as VeroClear. In order to test the properties of the elastomers and the rigid polymers, a number of digital materials which were mixtures of VeroClear and Agilus30 were also tested. The soft printed materials include Agilus30 and digital materials with Agilus30 as the base material (identified with prefix FLX). The rigid printed materials include VeroClear and digital materials with VeroClear as the base material (identified with prefix RGD).

[0047] Referring to FIGs. 2A, 2B, 2C and 2D, graphs 200, 230, 260 280 depict characterization tests of the various soft and rigid materials. The graph 200 depicts stress-strain behavior for the soft material Agilus30 202 and the digital materials with Agilus30 as the base material 204, 206, 208, 210, 212, 214, while the graph 230 depicts the Young’s modulus for the same materials 232, 234, 236, 238, 240, 242, 244. The graph 260 depicts stress-strain behavior for the rigid material VeroClear 262 and two digital materials with VeroClear as the base material 264, 266, while the graph 280 depicts the Young’s modulus for the same materials 282, 284, 286. From the graphs 230, 280, it can be seen that the Young’s modulus of VeroClear 282 (E = 1.4 GPa) is about four orders of magnitudes larger than the Young’s modulus of Agilus30 232 (£=0.43 MPa). The moduli E 232, 234, 236, 238, 240, 242, 244, 286, 284, 282 of the digital materials are between 0.43 MPa and 1 .4 GPa. Since the Young’s modulus 286, 284, 282 of the rigid materials is significantly larger than the Young’s modulus 232, 234, 236, 238, 240, 242, 244 of the soft materials, the stiffness of the printed structures 102, 152 can be controlled by adjusting the thickness of the rigid reinforcements segments 106, 156.

[0048] Referring to FIG. 3, a flow diagram 300 depicts a process for fabrication of a soft actuator in accordance with present embodiments. The process starts 302 by 3D printing 304 multimaterial structures 102, 152 containing soft segments 104, 154 and rigid segments 106, 156. Then, the SMA wire 1 10, 160 is inserted 306 into the printed multimaterial body of the actuator. In accordance with the present embodiments, the SMA wire 1 10, 160 can be any wire which functions as a tendon actuator to generate bending, twisting, or extensional deformation based on the spatial layout of the SMA wire and the rigid reinforcement segments within the soft matrix. In accordance with one embodiment, the SMA wire 1 10, 160 is formed of a nickel-titanium alloy and has a diameter of 0.25mm.

[0049] In each multimaterial structure, a channel or hole slightly larger than the diameter of the SMA wire 1 10, 160 is formed 304 along the length of the actuator 102, 152 for positioning the SMA wire 1 10, 160. For example, when the SMA wire has a diameter of 0.25mm, the channel diameter should be approximately 0.4mm. Before insertion 306, the SMA wire 1 10, 160 is pre-strained 308 by at least 5%. Then, depending on the type of the actuator 102, 152, the SMA wire 1 10 is embedded eccentrically, with a fixed off-centre distance of approximately 0.7mm, into the printed structure 102 or the SMA wire 160 is embedded concentrically into the printed structure 152. In accordance with present embodiments, the embedding process can be done manually. After inserting the SMA wire 1 10, 160, it can be fixed at both ends 310 using, for example, copper crimp connections 1 15, 165, to ensure there is no slack between the embedded SMA wire 1 10, 160 and the actuator body.

[0050] In accordance with the present embodiments, an electric current (of, for example, approximately 1 .0 A) is then applied to the pre-strained SMA wire 1 10, 160 embedded within the actuator 102, 152 to raise 312 a temperature of the pre-strained SMA wire 1 10, 160 via Joule heating until it exceeds its austenite transition temperature (approximately ten to twelve seconds). After exceeding its austenite transition temperature, the SMA wire 1 10, 160 contracts to recover its original undeformed shape. Since the SMA wire 1 10, 160 is fixed to the printed multimaterial structure 102, 152 at both ends using the crimp connections 1 15, 165, the contraction of the SMA wire 1 10, 160 is transferred to the multimaterial structure 102, 152 and produces a large deformation. After the electric current is switched off, the SMA wire 1 10, 160 cools down 314 by natural convection below the austenite transition temperature and the elastic strain energy stored in the deformed actuator results in the recovery of its original shape.

[0051] FIGs. 4A, 4B and 4C depict schematic illustrations 400, 440, 470 of details bending and actuators following the basic designs of the actuators 102, 152 in accordance with present embodiments. Referring to the illustration 400, an actuator 402 has a uniform cross section 404 over its effective length, with a thin rigid layer 406 printed from VeroClear, and two soft layers 408, 410 with equal thicknesses symmetrically printed on the top and bottom of the rigid layer 406, as indicated in the cross-section 404 across A-A of the actuator 402. Also, rigid segments 412 (approximately 2mm) at both ends of the soft matrix are printed from VeroClear to prevent direct contact between the crimp connection 414 and the soft matrix 408, 410. The SMA wire 416 in the actuator 402 is embedded into the top soft layer 408 to create a bending deformation of the structure upon actuation. While actuators in accordance with the present embodiments are not limited to specific dimensions, those pictured in FIGs. 4A, 4B and 4C have dimensions of 60 mm in length (unless otherwise mentioned), 15 mm in width, and 3 mm in thickness. In accordance with the present embodiments, an extra rigid feature 418 (approximately 35 mm long) is printed at the end of the actuator 402 to facilitate a secure connection between the actuator and a rigid surface. A distance 420 between the SMA wire 416 and the midplane of the actuator (A-A) is approximately 0.7 mm. [0052] Referring to FIG. 4B, the schematic illustration 440 depicts a second design of a bending actuator 442 having two hinges 444, 446 which can be printed from two different elastomeric digital materials having properties similar to those shown in the graphs 200, 230 to achieve dissimilar bending angles at each hinge. The actuator 442 has five segments 448, 444, 450, 446, 452 with equal lengths, including the two soft segments 444, 446 acting as hinges. The three sections 448, 450, 452 have two layers, including one rigid layer 454, and one soft layer 456, 458, as shown in cross-sections 460 (B-B) and 462 (C-C). The hinges 444, 446 can be printed from dissimilar elastomeric digital materials 456, 458 to create different deformations in each hinge 444, 446. Similar to the actuator 402, a thin rigid layer 464 was printed along the midplane over the entire length of the actuator to avoid axial contraction and buckling of the soft matrix during actuation. The layer on the top of the thin rigid layer is always printed from a soft digital material 456, 458, while the layer on the bottom is printed from a rigid material 454 to create rigid sections, or from a soft digital material such as the soft digital materials 456, 458 to create the soft hinges 444, 446, as depicted in the cross-sections 460, 462.

[0053] Referring to FIG. 4C, the schematic illustration 470 depicts a twisting actuator 472 realized in accordance with the present embodiments by printing thin rigid fibers 474 from VeroClear on the bottom surface of the actuator 472 at an angle Q with respect to the actuator longitudinal direction. The angle Q can be changed in accordance with the present embodiments to generate a broad range of twisting deformations. It should be noted that this multimaterial structure in accordance with the present embodiments is highly scalable while it is very difficult to create using conventional manufacturing methods. The thickness of the rigid fibers 474 as well as their spacing 476 from one another can be modified to control twisting deformation.

[0054] FIG. 5 depicts a schematic illustration 500 of an extensional actuator 512 and two magnified views 502, 504 of portions of the extensional actuator 512. The extensional actuator 512 is a multi-segment structure consisting of four basic linear elements 514, 516, 518, 520 based on the design of the actuator 152 (FIG. 1 B). A single SMA wire 522 passes through the two layers of the actuator 512. The alternative placement of the rigid layers 524 in each basic element results in a wavy shape of the actuation. Once actuated, the actuator 512 expands in a transverse (vertical) direction and contracts in longitudinal (horizontal) direction.

[0055] It should be noted that the SMA-based 3D printed actuators 102, 152, 402, 442, 472, 512 require complicated arrangement of various materials which are very difficult to achieve through conventional manufacturing methods. The superior manufacturing flexibility offered by multimaterial 3D printing to fabricate geometries with delicate details is essential to successful implementation of the present embodiments.

[0056] Deformation of the bending multimaterial actuators was simulated using a two- dimensional finite element model created in the software ABAQUS (Simulia, Providence, Rl, USA). In the experiments, a 0.25 mm thick SMA wire was inserted into the actuator wire channel whose diameter (0.4 mm) was larger than the wire thickness to ensure that it can be easily embedded into the actuator. The actuator channel was initially filled with support material before the SMA wire was manually embedded into it. Therefore, the gap between the SMA wire and the channel wall was filled with support material. However, for simplicity, in the modeling it was assumed the hole diameter and the wire thickness are both 0.25 mm, meaning there was no gap between the SMA wire and the hole wall.

[0057] A surface to surface frictionless contact was considered at the interface between the channel wall and the SMA wire 1 10, 160. In addition, both ends of the SMA wire 1 10, 160 were fixed to the actuator 102, 152 using rigid connections (e.g., the crimped connections 1 15, 165). Further simulations using different values of the friction coefficient showed that the friction coefficient has a negligible effect on the actuator tip displacement. For example, by increasing the friction coefficient from zero to 0.6, the tip displacement changed by less than 0.2 % evidencing that there is negligible tangential (friction) force between the SMA wire 1 10, 160 and the channel wall.

[0058] The soft and rigid segments of the matrix were assumed to have linear elastic behavior with the material properties reported in the graph 230 (FIG. 2B). Furthermore, a coupled thermo-mechanical material model was used for the shape memory alloy, which was developed and implemented as a user-defined material subroutine. Table 1 presents the material constants of the SMA used in the finite element model.

Table 1

[0059] To simulate loading conditions, the SMA wire 1 10, 160 was first extended 5% at room temperature, while the material was in its martensitic phase. Then, the SMA wire 1 10, 160 was unloaded while still at room temperature. These two steps led to detwinning in the martensitic phase and induced 5% strain to the SMA wire 1 10, 160. Finally, the contact between the SMA wire 1 10, 160 and the soft matrix material (e.g., the material 104, 154) was activated and the temperature of the SMA wire 1 10, 160 was increased to a temperature higher than the austenitic finish temperature (A _s =341 K, Table 1 ). As a result, the SMA wire 1 10, 160 contracted to recover its original length. The final length of the SMA wire 1 10, 160 depends on the bending stiffness of the soft matrix material 104, 154, which acts as a resistant force to limit deformation of the SMA wire 1 10, 160.

[0060] Inherent low stiffness of soft actuators often results in a small actuation force which limits their effective applications. In accordance with the present embodiments, efficient stiffness modulation of soft actuators with predefined general dimensions is accomplished either by changing the geometry and layout of the rigid segments 106, 156 within the structure or by printing the soft matrix 104, 154 from various digital materials with different tensile moduli. A broad range of bending, twisting, and extensional deformations can be realized through accurate placement of different printing materials by multimaterial 3D printing in accordance with the present embodiments.

[0061] Bending soft actuators are developed by embedding the thin SMA wires 1 10, 416 eccentrically into a polymeric soft matrix 104, 408, 456, 458, as shown schematically in the illustrations 100 (FIG. 1A), 400 (FIG. 4A), 440 (FIG. 4B). FIGs. 6A to 6C, 7A to 7D and 8A to 8D depict the effect of parameters such as the mid-layer thickness, the actuator length, and the matrix stiffness on actuator performance. Referring to FIGs. 6A to 6C, photographs 600, 630, 660 depict the effect of thickness of the rigid mid-layer 406 (FIG. 4A) on actuator maximum deformation. In all three samples tested, the soft polymeric matrix was printed from FLX9940 with £=0.74 MPa (bar 2234 (FIG. 2B)). The photo 600 (FIG. 6A) indicates that when there is no rigid layer, the low stiffness of the matrix causes the actuator 602 to buckle under the axial contraction force applied by the SMA wire. However, the photo 630 (FIG. 6B) reveals that incorporation of a thin rigid layer printed from VeroClear with a thickness of 0.3mm increases the stiffness of an actuator 632 and results in a larger bending deformation. As seen in the photo 660 (FIG. 6C), further increase of the thin rigid layer thickness to 0.5mm increases bending stiffness of an actuator 662 significantly, limits the recovery of the SMA wire, and reduces the maximum deformation of the actuator 662. For consistency, all the bending actuators depicted in FIGs. 7A to 7C and 8A to 8C were fabricated with a 0.3mm thick rigid mid-layer.

[0062] FIGs. 7A, 7B and 7C depict photos 700, 730, 760 of experimental results and numerical simulation results 710, 740, 770 of actuator length effect on maximum deformation in accordance with the present embodiments. The photo 700 and the simulation results 710 depict maximum deformation of a 40mm long bending actuator 702. The photo 730 and the simulation results 740 depict maximum deformation of a 60mm long bending actuator 732. And the photo 760 and the simulation results 770 depict maximum deformation of a 40mm long bending actuator 762. The arrangement of soft and rigid segments is schematically shown in FIG. 4A, the soft matrix was printed from FLX9940 and the 0.3mm thick rigid midlayer was printed from VeroClear. The longer actuators 732, 762 show a larger tip deformation as shown in the photos 730, 760, the simulation results 740, 770 and a graph 780 (FIG. 7D) which plots tip displacement 782 versus actuator length 784. The good agreement between the experimental results 786 and the simulation results 788 in the graph 780 show the efficiency of the developed finite element model in predicting actuator performance indicating that the verified model can advantageously be used to design printed actuators with more complex deformations. It can also be employed to estimate the force and energy generated by the actuator.

[0063] The multimaterial printing method used in this work enables the fabrication of the soft matrix from various digital materials with properties reported in the graphs 200, 230. Referring to FIGs. 8A to 8D, photographic illustrations 800, 830, 860, simulation results 810, 840, 870 and a graph 880 depict a comparison of experimental and modelling results of matrix stiffness effect on maximum deformation of 80mm long bending actuators with a soft matrix in accordance with present embodiments. The arrangement of soft and rigid segments is schematically shown in FIG. 4A and a 0.3mm thick rigid midlayer 406 was printed from VeroClear rigid polymer material. The photo 800 and the simulation results 810 depict maximum deformation of a bending actuator 802 printed from FLX9940 soft polymeric matrix. The photo 830 and the simulation results 840 depict maximum deformation of a bending actuator 832 printed from FLX9970 soft polymeric matrix. And the photo 860 and the simulation results 870 depict maximum deformation of a bending actuator 862 printed from FLX9995 soft polymeric matrix. The graph 880 plots tip displacement 882 versus matrix stiffness 884. The experimental results 886 and the numerical results 888 of the deformed shape of the actuators 802, 832, 862 with soft matrix printed from different digital materials show actuators with soft matrix printed from more flexible digital materials demonstrate a larger deformation, although at the sacrifice of stiffness, as shown quantitatively in the graph 880. This enables tunable functionality of the actuator based on structural and performance requirements

[0064] FIGs. 9A to 9D depict photographic illustrations 900, 930, 960of experimental results, simulation modelling results 910, 940, 970 and a graph 980 depicting a comparison of experimental and simulation results of maximum deformation of two similar bending actuators in accordance with present embodiments and based on the design of FIG. 4B, where the two-hinged bending actuator consisted of five segments with equal lengths and the total length of the actuator was 100mm.

[0065] The photo 900 and the simulation results 910 depict maximum deformation of a bending actuator 902 printed from FLX9950 and VeroClear material to form the two similar bending actuator design 442 (FIG. 4B). The photo 930 and the simulation results 940 depict maximum deformation of a bending actuator 932 printed from FLX9970 and VeroClear material to form the two similar bending actuator design 442. And the photo 960 and the simulation results 970 depict maximum deformation of a bending actuator 962 printed from FLX9995 and VeroClear material to form the two similar bending actuator design 442. The graph 980 plots tip displacement 982 versus matrix stiffness 984 and demonstrated that by varying the material of the soft hinges, a variety of bending angles and stiffnesses can be generated. For gripper applications, higher stiffness of the hinges provides the necessary rigidity to generate effective grasping force. The values of tip displacement seen in the graph 980 show a good agreement between the experimental results and finite element predictions.

[0066] Multimaterial 3D printing method used in processes in accordance with the present embodiments allows for fabrication of the two hinges 444, 446 of the bending actuator 442 from different soft digital materials to independently control the deformation of each hinge. This adds another dimension to design freedom and enables the fabrication of finger actuators mimicking human fingers with dissimilar deformation at each hinge. Referring to FIGs. 10A to 10F, photo illustrations 1000, 1010, 1020, 1030, 1040, 1050 of experimental results and simulation modelling results 1005, 1015, 1025, 1035, 1045, 1055 of maximum deformation of bending actuators with two dissimilar hinges 444, 446 based on the design of 442 (FIG. 4B) depict comparison of experimental and simulation results of maximum deformation of two dissimilar bending actuators in accordance with present embodiments where the two-hinged bending actuator consisted of five segments with equal lengths and the total length of the actuator was 100mm.

[0067] The photo 1000 and the simulation results 1005 depict maximum deformation of a two-hinged bending actuator 1002 having a first hinge printed from FLX9995 and a second hinge printed from FLX9950. The photo 1010 and the simulation results 1015 depict maximum deformation of a two-hinged bending actuator 1012 having a first hinge printed from FLX9985 and a second hinge printed from FLX9950. The photo 1020 and the simulation results 1025 depict maximum deformation of a two-hinged bending actuator 1022 having a first hinge printed from FLX9970 and a second hinge printed from FLX9950. The photo 1030 and the simulation results 1035 depict maximum deformation of a two-hinged bending actuator 1032 having a first hinge printed from FLX9960 and a second hinge printed from FLX9950. The photo 1040 and the simulation results 1045 depict depicts maximum deformation of a two-hinged bending actuator 1042 having a first hinge printed from FLX9970 and a second hinge printed from FLX9985. And the photo 1050 and the simulation results 1055 depict maximum deformation of a two-hinged bending actuator 1052 having a first hinge printed from FLX9950 and a second hinge printed from FLX9985. The stiffness variations of the various materials can be determined form the graph of Young’s modulus 230 (FIG. 2B).

[0068] From the experimental and simulations results it can be seen that various combinations of hinge deformations can be obtained by using different digital soft materials for the two hinges. As observed in the photo 1000 and the simulation result 1005, when the first hinge 444 (FIG. 4B) is highly stiffer than the second hinge 446, only the second hinge deforms. With increase of the flexibility of the first hinge 444, it also starts to bend. This deformation sequence can be fully reversed by printing the second hinge from a much stiffer material, as seen in the photo 1050 and the simulation result 1055.

[0069] The basic designs proposed for bending deformation have many potential applications in soft robotics. To show the functionality of this approach, a soft gripper has been designed and printed in accordance with present embodiments which is composed of three identical fingers. Each finger followed the design of the bending actuators of 152 (FIG. 1A) and 402 (FIG. 4A) with the difference that each finger had two rows of embedded SMA wires with a distance of 10mm from each other and an extra rigid section printed at the end of the finger actuator to mimic a finger nail. Three identical fingers are mounted on a base to create the robotic soft gripper, the base being printed from VeroClear. The SMA wires embedded in the three figures are connected in series to ensure simultaneous actuation of all three fingers. Alternatively, each finger can be actuated with a separate SMA wire to activate each finger independently. [0070] FIGs. 1 1 A to 1 1 E show a series of photo illustrations 1 100, 1 1 10, 1 120, 1 130, 1 140 of effective and stable grasping of a fifteen gram cylindrical object. The whole grasping and releasing process was done in almost fifteen seconds. The photo 1 100 depicts the grasping and releasing procedure at the start (t = 0), the photo 1 1 10 depicts it at time t = 2 seconds, the photo 1 120 at time t = 6 seconds, the photo 1 130 at time t = 10 seconds, and the photo 1 140 at release, time t = 15 seconds. It is possible to generate more complex deformations by changing the soft matrix material for each hinge, or fabricating each finger with two hinges, similar to the design 442 (FIG. 4B) and the experimental and simulation results of the previous figures, with the stiffness of each hinge independently changed by printing various digital materials with different mechanical properties.

[0071] One particularly useful application of multimaterial 3D printing for fabrication of SMA-based soft actuators in accordance with the present embodiments involves creating complex 3D shapes from structures with a simple 2D original shape. For example, an actuator capable of twisting deformation can be fabricated in accordance with the present embodiment by printing thin rigid fibres within the soft matrix along a diagonal direction, as specified by angle Q in the actuator 472 (FIG. 4C). Referring to FIGs. 12A and 12B, photographic illustrations 1200, 1250 depict separate views of twisting deformation of the actuator 472 for an angle Q = 15°. The photo 1200 is a top view of the twisting deformation and the photo 1250 is a front view of the twisting deformation. Rigid and soft segments 474, 476 of the twisting actuator 472 (FIG. 4C) were printed from VeroClear and Agilus30, respectively, where one millimeter thick rigid fibers 474 were printed from VeroClear on a bottom surface of the actuator 472 at an angle q= 15° with respect to the actuator longitudinal direction In accordance with the present embodiments, the maximum deformation and twisting angle of the actuator 472 can be controlled by changing Q.

[0072] There is a growing demand for packable lightweight deployable structures, with an initial compact shape, that can be deployed into an extended shape under a certain external stimulus. These structures are increasingly used to deploy solar panels, antennas, and masts of satellites. Flowever, most existing deployable structures rely on time-consuming traditional manufacturing methods and consist of complex linkage mechanisms with numerous mechanical components resulting in complicated and expensive assembly processes. In accordance with the present embodiments, a scalable SMA powered actuator that advantageously includes a deployable structure capable of a large extensional deformation without complex linkage mechanisms or numerous mechanical components is provided based on the actuator 512 (FIG. 5) configuration. The actuator 512 uses the basic design 152 (FIG. 1 B) as a repeating unit 514, 516, 518, 520 with rigid segments 524 printed on opposite sides to create two hollow pockets upon actuation. The final printed actuator is shown in FIGs. 13A and 13B where photographic illustrations 1300, 1350 depict a combination of two configurations 512a, 512b placed on each other. The illustration 1300 shows an initial as-fabricated shape of the actuators 512a, 512b and the illustration 1350 depicts a deployed configuration of the actuators 512a, 512b with five hollow pockets. The soft matrix was printed from FLX9960 with a Young’s modulus of £=2.6 MPa (238 (FIG. 2B)) and the rigid reinforcements from VeroClear with £=1.4 GPa (280 (FIG. 2D)). The initial height of a single hollow pocket of the actuators 512a, 512b was 6mm which on average increased to 25.5mm after actuation. This advantageously indicates an increase of approximately 425% in the height of the actuator from the initial as-fabricated configuration depicted in the photo 1300 to the deployed configuration depicted in the photo 1350. Also, the width of a single pocket (in horizontal direction) changed from 75mm to 65mm, indicating a decrease of 14% in the width. A larger number of basic actuators can be assembled in accordance with the present embodiments to form large- scale extensional structures. Compared with the conventional deployable structures, self-actuating structures in accordance with the present embodiments are easy to fabricate, assemble, and deploy.

[0073] Incorporation of SMA wires into multimaterial fully 3D printed parts in accordance with the basic fabrication process of the flowchart 300 (FIG. 3) can generate three-dimensional shapes and more complex shapes can be accomplished by rearrangement of rigid and soft segments within actuators to achieve a desired functionality. In addition, actuators have been presented which provide pure bending, twisting, or extensional deformation. A combination of these basic deformations can be realized by utilizing the flexibility of multimaterial 3D printing to combine the basic designs shown in FIGs. 4A, 4B, 4C and 5.

[0074] In accordance with a second fabrication process leveraging on 3D multimaterial printing, active hinge structures can be fabricated in accordance with present embodiments using shape memory polymer (SMP). A conventional method to increase recovery force of SMPs is to increase their stiffness through the addition of reinforcements such as carbon fibers or silicon carbide (SiC) nano-particles. This technique, however, greatly increases fabrication time and requires additional manufacturing steps and may negatively influence the shape memory behavior. In accordance with the present embodiments, an alternative approach is proposed which utilizes designing and 3D printing actuators consisting of active hinges reinforced by elastic flexible hinges to increase the recovery force. [0075] Referring to FIGs. 14A to 14D, schematic illustrations 1400, 1430, 1450, 1480 depict two-representative four-dimensional (4D) printed shape memory structures with active and flexible hinges in accordance with present embodiments. The schematic illustrations 1400, 1430 depict a morphing wing flap 1405 that exhibits large bending deformation and the schematic illustrations 1450, 1480 depict a deployable structure 1455 that exhibits large extensional deformation. The morphing wing flap 1405 includes two active hinges 1410, 1412 and one flexible hinge 1414 and was initially fabricated in a bent shape as depicted in the schematic illustration 1400. Following a thermomechanical training process, the morphing bent wing flap 1405 was programmed into a temporary straight shape as shown in the illustration 1430. The programming and actuating were performed using localized Joule heating by applying current to resistive wires (not shown) that were embedded into channels 1420 formed in the active hinges 1410, 1412 as shown in the magnified inset 1425.

[0076] Similarly, the schematic illustration 1450 depicts an as-printed deployable structure 1455 with four hinges, including two active hinges 1460 and two flexible hinges 1465. Localized Joule heating by resistive wires embedded in channels 1470 was used to program the deployable structure as shown in the magnified inset 1475 from the as- fabricated a standing 3D shape as shown in the schematic illustration 1450 into a compact, nearly 2D shape as shown in the schematic illustration 1480. The thickness of all hinges 1410, 1412, 1414, 1460, 1465 was 3mm.

[0077] Programming and actuating the 4D printed structures is performed at temperatures related to a glass transition temperature (T _g ) of the SMP used to print the active hinges. Also, the allowable strain of the 3D printing materials used to fabricate the active 1410, 1412, 1460 and flexible hinges 1414, 1465 must be sufficient to accommodate the large deformation induced during the programming and actuating steps. In addition, the stiffness of the flexible hinges 1414, 1465 must be sufficient to deliver the desired recovery force and increase the load-bearing capacity of the structure 1405, 1455.

[0078] A dynamic mechanical analysis (DMA) tester (Q800 DMA, TA Instruments, New Castle, DE, USA) was used to measure thermomechanical properties of base materials, VeroClear and Agilus30, as well as eight digital materials which are a mixture of the two base materials. Rectangular samples with dimensions of 15mm c 5mm c 1 mm were dynamically strained at a frequency of 1 Hz with a peak-to-peak amplitude of 0.1 %. Each sample was first equilibrated at a temperature at least 30°C higher than its glass transition temperature (T _g ) for ten minutes, then cooled down to a low temperature at which the sample was at its glassy state. [0079] FIGs. 15A, 15B and 15C depict graphs 1500, 1530, 1560 of dynamic mechanical analysis (DMA) testing of ten different printing materials in accordance with the present embodiments. The ten different printing materials tested were Agilus30 1510, 1540, 1570, FLX9940 1512, 1542, 1572, FLX9950 1514, 1544, 1574, FLX9960 1516, 1546, 1576, FLX9970 1518, 1548, 1578, FLX9985 1520, 1550, 1580, FLX9995 1522, 1552, 1582, RGD8630 1524, 1554, 1584, RGD8625 1526, 1556, 1586, and VeroClear 1528, 1558, 1588. The graphs 1500, 1530 show changes of storage modulus 1502 and Tan<5 1532 with temperature 1504, 1534 for the ten different printing materials. The glass transition temperatures ( T _g s) 1562 of the ten printing materials were identified as the temperature where Tan<5 reaches its maximum and are plotted in the graph 1560.

[0080] Based on the graphs 1530, 1560, it can be concluded that three of the tested materials, RGD8630 1554, RGD8625 1556 and VeroClear 1558, potentially exhibit shape memory behaviour because their T _g s are higher than room temperature and they transit from the glassy state to the rubbery state when heated from room temperature to a temperature higher than their T _g . Based on these findings, VeroClear ( T _g = 58 °C) 1588 was selected to print the active hinges because it has the highest rubbery modulus and, thus, the highest recovery stress.

[0081] In order to better understand the mechanical behavior of the ten 3D printing materials and to determine the material parameters required in the simulation of the active and flexible hinges, a series of uniaxial tensile tests were performed at different temperatures. In accordance with conventional tensile testing of plastics, three samples of each polymer were tested using a universal testing machine (Criterion Model 43, MTS Systems Corporation, Eden Prairie, MN, USA) equipped with a thermal chamber and a video extensometer. The strains were measured using a digital image correlation (DIC) technology and the tensile samples were loaded at a testing speed of two millimeters per minute until fracture.

[0082] FIGs. 16A, 16B, 16C and 16D depict graphs 1600, 1620, 1640, 1660 of tensile test results of the printing materials in accordance with present embodiments. The graph 1600 of stress 1602 versus strain 1604 of VeroClear tested at different temperatures 1606, 1607, 1608, 1609, 1610, 161 1 , 1612, 1613, 1614, 1615, VeroClear being the 3D printing material used to print the SMP active hinges 1410, 1412, 1460. Consistent with previous studies on polymer characterization, the stress-strain behavior shows a high temperature dependency. From 25°C 1606 to 40°C 1609, VeroClear exhibits an elastoplastic behavior and its maximum elastic strain is less than its failure strain (strain at the moment of fracture). Also, within this temperature range, the Young’s modulus gradually decreases with the increase of the testing temperature as seen in the graph 1620. Once the testing temperature reaches 50 °C or higher 161 1 , 1612, 1613, 1614, 1615, VeroClear exhibits linear elastic behavior.

[0083] Moreover, as the 4D printed active hinges undergo a large deformation during programming and actuating at temperatures higher than T _g , it is important to understand the effect of temperature on failure strain of VeroClear. The graph 1620 depicts temperature dependent failure strain of VeroClear extracted from the graph 1600 (i.e., failure strain 1622 versus temperature 1624) as well as Young’s modulus 1626 versus temperature 1624. The failure strain of VeroClear 1630 changes rapidly with temperature, starting from 25% at T= 25°C, increasing with temperature, and reaching a maximum value of 59% at T = 35°C. Above 35°C, the failure strain of VeroClear 1630 decreases continuously and reaches 26% at T = 80°C and a minimum of 19% at T = 90 °C. The Young’s modulus of VeroClear 1635 decreases throughout the heating process.

[0084] In accordance with the present embodiments, Joule heating is used to heat the active hinges 1410, 1412, 1460 printed from VeroClear while the flexible hinges 1414, 1465 printed from the elastomeric digital materials remain at room temperature. Referring to the graph 1640, stress 1642 versus strain 1644 behavior at room temperature for the candidate elastomeric digital materials including the base elastomer Agilus30 1646 and the mixtures of Agilus30 and VeroClear (denoted with the prefix FLX in their names) FLX9940 1648, FLX9950 1650, FLX9960 1652, FLX9970 1654, FLX9985 1656, and FLX9995 1658. As the T _g s of all the elastomers are below room temperature, they all exhibit an elastic stress-strain behavior with a large failure strain and a low tensile strength. With the increase of VeroClear concentration (the elastomers vary from Agilus30 1646 to FLX9995 1658), an increase in the tensile strength (from 0.7 MPa to 4.2 MPa) and a decrease in the failure strain (from 175% to 53%) are observed. Referring to the graph 1660, the Young’s modulus 1662 of these materials used to print the flexible hinges 1414, 1465 of the 4D printed structures (i.e., Agilus30 1666, FLX9940 1668, FLX9950 1670, FLX9960 1672, FLX9970 1674, FLX9985 1676, and FLX9995 1678) was measured at 1% strain of the stress-strain curves of the graph 1640. A flexible hinge printed with a stiffer material can store a higher elastic strain energy during programming and generate a higher recovery force in actuation. On the other hand, stiffer elastomers have a lower failure strain, which restricts their deformability during the programming step. A finite element model is used to find the maximum strain in the deformed hinges and ensure it is lower than the failure strain of the digital materials used to print the flexible hinge.

[0085] Both active structures, the morphing wing flap 1405 (FIGs. 14A and 14B) and the deployable structure 1455 (FIGs. 14C and 14D), were first 3D printed and then assembled to the configurations shown in the photographic illustrations 1700, 1750 in FIGs. 17A and 17B. The as-fabricated morphing wing flap 1705 depicted in the photo 1700 was assembled from a moving rigid part 1710 and a stationary rigid part 1715 connected using three hinges, including two active hinges 1720, 1722 and one flexible hinge 1724. The rigid parts (i.e., the moving flap part 1710 and the stationary part 1715) were produced using a fused deposition modeling (FDM) printer from a high- performance thermoplastic, acrylic-styrene-acrylonitrile (ASA), whereas both the active hinges 1720, 1722 and the flexible hinges 1724 were fabricated using an inkjet multimaterial 3D printer in accordance with the present embodiments. The morphing wing flap 1705 was then assembled by joining together the moving flap part 1710 and the stationary part 1715 using the two active hinges 1720, 1722, printed from a shape memory polymer (SMP) (e.g., VeroClear), and the flexible hinge 1724 whose middle section 1726 was printed from a elastomeric digital material (e.g., a mixture of VeroClear and Agilus30) and two end sections 1728, 1730 were printed from a rigid material (e.g., VeroClear). Finally, resistive wires 1732 for Joule heating in accordance with the present embodiments is inserted through channels in the active hinges 1720, 1722.

[0086] A similar procedure was followed to fabricate the deployable structure 1752 in the photo 1750. The deployable structure 1752 is comprised of eight rigid rods 1754, 1756, 1758, 1760, 1762, 1764, 1766, 1768, two active hinges 1770, 1775 and two flexible hinges 1780, 1785. All parts were printed in a single printing job using a multimaterial inkjet printer and then assembled together to create the deployable structure 1752. It is important to note that using the one-step inkjet 3D printing process considerably reduces fabrication time and complexity, and such time and complexity reduction is not possible with conventional manufacturing methods based on molding and casting.

[0087] Localized joule heating, which precisely controls the free recovery of active hinges in both structures of Fig. 4, was achieved using resistive wires (e.g., the resistive wires 1732) which were embedded into the equally-spaced holes designed for each active hinge. The resistive wires were composed of Constantan, a copper-nickel alloy, and had a resistance of 3.90 W/m and a diameter of 0.4mm. The programming and actuating temperatures of the active hinges were assumed to be 68°C, which is 10°C higher than the 7 _g of VeroClear (1588 in the graph 1560). Coupled thermal-electrical finite element simulations suggest that this temperature can be achieved by applying a unit voltage of 12.7 V/m (Volts per unit length of the resistive wire 1732) for fifteen seconds, which corresponds to the application of 3.3 A electrical current. The two active hinges in each 4D printed and assembled structure (active hinges 1720, 1722 and active hinges 1770, 1775) were connected in series to ensure the electrical current, and hence the temperature, is identical in both hinges.

[0088] Thermal programming and actuating a SMP include four typical thermomechanical steps. These steps are: (i) deform the SMP at a temperature higher than the phase transition temperature (T _trans ) of the SMP, e.g. the glass transition temperature (T _g ) in the cross-linked thermosets, (ii) decrease the temperature below T _trans while maintaining an external load, (iii) remove the external load at a low temperature to achieve a fixed temporary shape, and (iv) increase the temperature above T _trans again to trigger the free recovery.

[0089] Details of the thermomechanical programming and actuating of the assembled morphing wing flap with the active SMP hinges are shown in the photographic illustrations 1800, 1820, 1840, 1860 of FIGs. 18A, 18B, 18C and 18D respectively. In the photo, O _max shows the angle 1802 between the moving part 1804 and the stationary part 1806 of the as-fabricated morphing wing flap 1808. The morphing flap angle 1802 Q _max was 70 ^e . A voltage of 12.7 V/m was applied to the resistive wires for fifteen seconds, which increased the temperature on the surface of the active hinges to 68°C. Referring to the photo 1820, a 200g weight 1822 was left on the moving part 1804 of the hinge 1808 for three minutes to fix the hinge in the programmed (flat) shape. The as- printed bent active hinge was then programmed into a straight hinge as pictured in the photo 1840. As noted in the photo 1840, when the 200g weight was removed, the moving part 1804 of the hinge 1808 slightly recovered and remained stable in the new programmed shape, DQ indicating the bounce back angle 1842 after unloading. The middle flexible hinge followed the same deformation as the active hinges, and stored elastic strain energy.

[0090] In the recovery step (i.e., the actuation step) shown in the photo 1860, the same voltage as the programming step (i.e., 12.7 V/m for 15 seconds) was applied again to the resistive wires. The active hinges deformed from the flat shape to the bent original shape and the stored elastic strain in the flexible hinge is released to increase the recovery force. Referring to the photo 1860, O ₆ o _s is the recovery angle 1862 sixty seconds after the voltage was applied, which is slightly lower than 0 _max .

[0091] A similar process was followed to program and actuate the deployable structure. Referring to FIGs. 19A, 19B, 19C, 19D, 19E and 19F, photos 1900, 1910, 1920, 1930, 1940, 1950 show the actuation process over time of the printed deployable structure showing stages of the recovery of the deployable structure. The deployable structure in accordance with present embodiments can thus be seen from the photos 1900, 1910, 1920, 1930, 1940, 1950 to have the potential to be used as an extensional stage, which can be compacted and, upon actuation, can be extended in one direction. In accordance with present embodiments, the multimaterial inkjet printing technology used also enables the fabrication of the two flexible hinges from various elastomers having different stiffnesses. Such fabrication results in the rotational deformation during the actuation process in addition to the extensional deformation.

[0092] A key desire in the application of the SMP actuators is to enhance their actuation force and load-bearing capacity. In order to assess the effect of the stiffness of the flexible hinges on the load-bearing capacity of the printed structures, an external load was applied during the recovery step. To this end, a 10g load was hung from the tip of the moving part of the morphing wing flap during the recovery step and a 50g load was placed on the deployable structure during the recovery step. The active hinges for both structures were printed from VeroClear while the middle section of the flexible hinges was printed from Agilus30 and FLX9995, which have Young’s moduli of £=0.43 MPa and £=14.8 MPa, according to the characterization data shown in the graph 1660 (FIG. 16D). The total weight of the three hinges of the morphing wing flap was 14g and the four hinges of the deployable structure 29g. This can be seen in FIGs. 20A to 20D where the photos 2000, 2020 depict the morphing wing flap 2010 during the recovery step with the 10g load 2015 hung from the tip of the moving part 2012 of the morphing wing flap 2010 and where the photos 2040, 2060 depict the deployable structure 2050 during the recovery step with the 50g load 2055 thereon. The photo 2000 depicts the morphing wing flap 2010 where the middle section of the flexible hinge was printed from Agilus30, while the photo 2020 depicts the morphing wing flap 2010 where the middle section of the flexible hinge was printed from FLX9995. Similarly, the photo 2040 depicts the deployable structure 2050 where the middle section of the flexible hinges was printed from Agilus30, while the photo 2060 depicts the deployable structure 2050 where the middle section of the flexible hinges was printed from FLX9995.

[0093] Comparing the photos 2000, 2040 to the photos 2020, 2060 indicates that the flexible hinges printed from FLX9995 in the photos 2020, 2060 significantly and advantageously increase the load-bearing capacity of both 4D printed structures in accordance with the present embodiments because they have a higher stiffness and can store a larger strain energy during the programming steps.

[0094] Shape training and actuating the active hinges of the 4D printed structures were achieved by localized Joule heating during which the heat flux generated by electrical current in the resistive wires embedded in the hinge holes was transferred to the SMP to increase its temperature. The heat flux generated by Joule heating (qr _Joute ) is applied to the inner surface of each hole within the active hinge. It then moves through the SMP hinge via conduction ( q _Cond ) Part of the transferred heat increases the hinge temperature, and part of it is dissipated into the surrounding environment at the boundary between the hinge and air through convection ( q _Conv ) Time-dependent 3D temperature distribution in the SMP is governed by the partial differential Equation (1 ):

where a is thermal diffusivity, indicating the rate of heat transfer from the high- temperature side of the material to the low-temperature side, i.e. from the hinge inner surface to the outer surface. The Joule heat flux (q _ouie ) applied to the hole inner surface as well as the heat flux dissipated from the hinge free surface via convection ( q _Com ) are considered as the boundary conditions to solve Equation (1). This equation with the mentioned boundary conditions has no analytical solution for the geometry of the active hinges described in FIGs. 14A to 14D. Therefore, finite element simulations were utilized to calculate temperature distributions in the active hinges during Joule heating. To this end, a coupled thermal-electrical analysis was performed in the commercial finite element package ABAQUS. Both the resistive wire and the SMP were modeled.

[0095] Thermal and electrical properties of the resistive wire and the SMP were used in the finite element model to simulate heat transfer. The 0.4mm diameter resistive wire had an electrical resistivity of 490 x10 ⁹ W-rn. Natural convection with the coefficient of heat convection h= 10 W/(m ² K) was applied at the free surface of the hinge. Density, specific heat, and thermal conductivity of the resistive wire were 8900 kg/m ³ , 390 J/K, and19.5 W/mK, respectively. The values of these parameters for the SMP were 1 190 kg/m ³ , 1470 J/K, 0.2 W/mK, respectively.

[0096] Detailed finite element analysis (FEA) simulations were also conducted to model the entire programming and activation steps, and capture time and temperature dependent large deformation of the morphing wing flap. To this aim, we used a multi branch viscoelastic constitutive model to simulate the shape memory behavior of the morphing wing flap. The FEA simulations were performed using the FEA software

ABAQUS.

[0097] In order to accurately simulate the shape recovery behaviour of the morphing flap, the four steps used to program and actuate the flap were modelled following the steps illustrated in the photos 1800, 1820, 1840, 1860. First, the active hinges were heated up to 68 ^e C to model the Joule heating step illustrated in the photo 1800. Then a small bending moment was applied to the flap tip to mimic the programming step illustrated in the photo 1820, which was realized in practice by leaving a 200g weight on the flap. It was found that the magnitude of the bending moment had negligible effect on the stress and strain state of the hinge in the programmed straight shape. [0098] In the next step, the active hinge temperature was reduced to 25 ^e C, then the bending load was removed. As a result, the flap slightly recovered as illustrated in the photo 1840. Finally, the temperature of the active hinges was increased again to 68 ^e C to simulate the recovery step illustrated in the photo 1860. The recovery angles after the programming step (e.g., the photo 1840) and the activating step (e.g., the photo 1860) were measured using the developed finite element model, and were compared with the experimental data.

[0099] FIGs. 21 A to 21 F depict illustrations, simulations and graphs of results of heat transfer simulation in the active hinge in accordance with the present embodiments. Referring to FIG. 21 A, an illustration 2100 depicts a repeating unit cell 2102 of the active hinge representing heat transfer mechanisms, including conduction and convection, modeled by the coupled thermal-electrical finite element model. FIG. 21 B depicts contours 21 12, 21 14, 21 16, 21 18, 2120, 2124, 2126 of temperature distributions derived from simulation results of temperature change in the representative unit cell 2102 over time. At time t= 0 (the contour 21 12), a voltage of 12.7 V/m (volts per unit length of the wire) was applied. By applying the voltage, the thermal energy is transferred from the wire outer surface to the inner surfaces of the holes and the temperature of the SMP active hinge starts to increase. At time t= 15 seconds (the contour 2122), the voltage was disconnected. Five seconds after voltage disconnection (the contour 2126, time t= 20 s), the temperature distribution becomes quite uniform in the hinge.

[00100] To verify the finite element model, a thermal multimeter with an integrated infrared camera was used to measure the temperature on the free surface of the active hinges. FIG. 21 C depicts a graph 2130 of experimental measurements 2136 and finite element method (FEM) predictions 2138, 2139 of temperature change 2132 on the hinge outer surface (Point A) of the unit cell 2102 over time 2134 after applying a voltage of 12.7 V/m for fifteen seconds.

[00101] Joule heating in the active materials is typically modelled using a thermal analysis, i.e. by applying temperature or heat flux directly to the finite element model. In the graph 2130, besides thermal-electrical analysis 2138, finite element simulation was also conducted using thermal analysis 2139 in which the resistive wire was not modeled and instead the heat flux generated in the wire was directly applied to the inner surfaces of the holes as a boundary condition. The graph 2130 shows that the thermal-electrical analysis 2138 has good agreement with the experimental data 2136, while thermal analysis 2139 overestimates temperature because it ignores the time required to heat up the wire. Also, part of the heat is used to increase the wire temperature itself. Since the thermal-electrical analysis 2138 estimates the temperature distribution in the active hinge more accurately, it was used to investigate the effect of different parameters such as convection coefficient on temperature distribution in the active hinge.

[00102] Referring to FIGs. 21 D and 21 E, graphs 2140, 2150 study the temperature change of the hinge with time more closely. In the graph 2140, temperatures 2142 on the inner and outer surfaces of the active hinge (Points A and B in the unit cell 2102) over time 2144 were extracted and plotted 2146, 2148. Two important trends can be observed. First, the temperature on the inner surface 2148 increases much faster than the outer surface 2146. This results in a non-uniform temperature distribution in the active hinge before t = 20 seconds, with the maximum temperature difference between the inner surface 2148 and the outer surface 2146 being 25°C at time t = 15 seconds. This is because the inner surface 2148 is closer to the heat source, while the outer surface 2146 is at the vicinity of the ambient temperature. The heat flux generated by the resistive wire first heats the inner surface of the channel/hole then is transferred to the outer surface via conduction and dissipated via convection to the ambient environment.

[00103] Shape recovery will not start until the temperature on the outer surface of the unit cell is also high enough. Therefore, temperature on the outer surface dominates the shape recovery. The second important result from the graph 2140 is that, although after voltage disconnection the temperature increases on the outer surface 2146 due to the heat flux from the hotter inner surface 2148 to the colder outer surface 2146, temperature on the inner surface 2148 drops immediately at time t = 15 seconds. For this reason, after t = 15 seconds the temperature difference decays rapidly and almost vanishes after time t = 20 seconds

[00104] On the free surface of the hinge, the heat is dissipated through convection. In natural (free) convection, the air molecules in contact with the hinge hot surface separate and scatter, causing the air at the vicinity of the hinge surface to be less dense. Consequently, the air is displaced and replaced with cooler air, and this way heat transfer between the hinge surface and the surrounding air continues.

[00105] In contrast to natural convection, in forced convection the surrounding air is forced to flow over the surface, e.g. using fans. This increases the heat transfer, because it generates an artificially induced convection current. When the morphing wing flap is in operation, e.g. in a flying unmanned aerial vehicle (UAV), the forced convection increases heat dissipation. Assuming a maximum speed of 15 m/s for the flying UAV, the convection coefficient will be h =50 W/(m ² K), much higher than h =10 W/(m ² K) for natural convection. The graph 2150 (FIG. 21 E) plots temperature 2152 versus time 2154 and demonstrates the effect of forced convection 2156 (as opposed to natural convection 2158) on the temperature distribution at the inner and outer surfaces of the active hinge. The forced convection 2156 had negligible effect on the maximum temperature on the inner surface because the inner surface is not in direct contact with the surrounding air. However, as shown the graph 2150, the forced convection 2156 reduces the maximum temperature on the outer surface by 10°C. This necessitates applying a larger actuation voltage or applying the same voltage for a longer time to achieve the required actuation temperature.

[00106] The recovery of the SMP is dominated by two factors: heat transfer and material intrinsic recovery. A faster heat transfer can be achieved by the increase of the applied voltage. To assess the effect of the voltage on heat transfer, the heating time is defined as the time at which the temperature at Point A on the outer surface reaches a target temperature of 68°C. FIG. 21 F depicts a graph 2160 of heating time 2162 versus applied voltage 2164. The plotted heating time vs. voltage 2166 shows that as the applied voltage 2164 increases, the heating time 2162 reduces rapidly, then converges to an extreme value of approximately seven seconds.

[00107] A practical parameter limiting the maximum voltage is ampacity, i.e. the maximum electrical current the wire can carry before burning. Ampacity is an important parameter that needs to be considered, because the electrical current increases almost linearly with voltage. The ampacity of the wire used in this study was 5 A, equivalent to a voltage of approximately 17 V/m. For this voltage, a heating time of almost 10 seconds could be achieved according to the graph 2160.

[00108] The material selection for active and flexible hinges was based on the local strain distribution from FEA simulations and the experimental data of failure strain from the characterization tests (FIGs. 16A, 16B, 16C and 16D). Referring to FIGs. 22A to 22D, the FEA simulations depict strain contours 2200, 2220, 2240, 2260 in the active hinges 2210 of the morphing wing flap and the active hinges 2250 of the deployable structure in accordance with present embodiments. The strain contours 2200, 2240 are strain contours of as-printed active hinges and the strain contours 2220, 2260 are strain contours of programmed active hinges. The highest principal engineering strain on the active hinges 2210, 2250 of the morphing wing flap and the deployable structure were about 14.6% and 21.2%, respectively, which are lower than the failure strain of VeroClear at the programming and actuating temperature (68 °C). Therefore, all the active hinges were printed from VeroClear

[00109] The implemented multi-branch viscoelastic model was used to simulate the shape memory behavior of the morphing wing flap. FIGs. 23A, 23B, 23C and 23D depict finite element predictions 2300, 2320, 2340, 2360 demonstrating the morphing wing flap 2305 configurations during a typical thermomechanical programming and recovery cycle obtained from the finite element simulations. Comparison with the experimental observations (the inset photos 2310, 2330, 2350, 2370 correspond to FIGs. 18A, 18B, 18C, 18D) show that the model is able to predict the deformation of the structure in each step with good accuracy, where the finite element prediction 2300 depicts an initial configuration of the flap, the finite element prediction 2320 depicts a deformed shape of the flap under a combination of mechanical and thermal loads, the finite element prediction 2340 depicts a programmed shape of the flap at T< T _g , and the finite element prediction 2360 depicts a recovered shape of the flap at T> T _g .

[00110] To characterize the shape memory of a SMP, the shape fixing ratio (R _f ) is used to measure its ability to fix a temporary shape, and the shape recovery ratio (R _r ) is used to measure its ability to recover its original shape upon heating. Specifically, for the shape memory morphing wing flap, R _f and R _r are calculated using the Equations (2) and (3):

where © _max denotes the angle between the stationary and moving parts of the as- fabricated flap, DQ is the bounce back angle after unloading at low temperature, and © _60s measures the recovery angle after applying the voltage for 60 seconds.

[00111] FIGs. 24A, 24B, 24C and 24D depict graphs 2400, 2420, 2440, 2460 shows the recovery ratio and shape fixity of the morphing wing flap with flexible hinges printed from various digital materials exhibiting different stiffnesses in accordance with the present embodiments measured experimentally and compared with the finite element predictions. In the graphs 2400, 2440, the weight of the moving part of the flap (15g) was the only applied load, while in the graphs 2420, 2460, a 10g load was additionally hung at the end of the flap, as shown in FIGs. 20A and 20B. The horizontal axis 2402 in the graphs 2400, 2420, 2440, 2460 plots the Young’s modulus of the elastomeric digital material used to print the flexible hinges and starts with a value of zero (E= 0) on the origin, corresponding with a control sample that does not contain any flexible hinge. The vertical axis 2404 in the graphs 2400, 2420 plots the experimental and simulation recovery ratios, while the vertical axis 2442 in the graphs 2440, 2460 plots the experimental and simulation shape fixity. The graphs 2400, 2420, 2440, 2460 show that the FEA simulations are able to reproduce the recovery ratio and shape fixity of the morphing wing flap with reasonable accuracy. They confirm that the use of a flexible hinge can significantly increase the recovery ratio of the morphing wing flap. For example, in the case 2410 where no external load is applied and no flexible hinge is used, the recovery ratio is only about 0.86. In comparison, in the case 2412 of a flexible hinge, printed from FLX9995 with Young’s modulus of 14.8 MPa, the recovery ratio increases to 0.97, confirming the enhanced actuation performance in accordance with the present embodiments which is a necessity for active structures. This effect is even more significant when an external load is applied. For instance, when a 10g load is hung at the tip of the flap in the graph 2420, FLX9995 flexible hinge increases the recovery ratio from 0.75 to 0.94 as shown at the points 2430, 2432 in the graph 2420.

[00112] On the other hand, the graphs 2440, 2460 show that the use of stiffer materials to print the flexible hinges reduces the shape fixity, because the stiffer hinges store a larger elastic energy in the programming step and tend to create a larger bounce back angle. Flowever, all the specimens printed with different digital materials were able to realize a shape fixity of at least 95%.

[00113] These results show that the multimaterial inkjet 3D printing technology used in systems and methods in accordance with the present embodiments provides high tailorability of the mechanical properties of the flexible hinges to control fixity and recovery of the printed active structures, thus allowing remarkable design flexibility. The good agreement between the finite element simulations and experimental results confirms that the developed multi-branch model in accordance with the present embodiments can advantageously be used to design sophisticated 4D printed structures undergoing complex large deformations.

[00114] The abovementioned structures show that incorporation of active and flexible hinges into fully 3D printed parts is able to generate three-dimensional shapes. More complex shapes can be accomplished by rearrangement of active and passive segments to achieve desired functionality. The 4D printed active structures presented here exhibited pure bending or extensional deformation. A combination of these deformations can be achieved by utilizing the flexibility of multimaterial 3D printing to combine the basic designs used here

[00115] In summary, FIG. 25 depicts a flow diagram 2500 of a fabrication process for SMP-based 3D printed shape memory structures in accordance with the present embodiments. The process starts 2502 by 3D printing 2504 multimaterial shape structure portions including active and flexible hinges (e.g., flap stationary part 1715, flap moving part 1710, active hinges 1720, 1722 and flexible hinge 1724 (FIG. 17A)) form rigid and flexible polymers, including forming equally spaced resistive wire channels in the active hinges. Then, the resistive wire 1732 is inserted 2506 into channels formed in the printed active hinges. The shape memory structure is then assembled 2508. In accordance with the present embodiments, a programming process 2510 and an actuation process 2512 is the performed to program the shape memory and thereafter trigger recovery of the programmed shape. [00116] Thermal programming 2510 the SMP includes deforming 2514 the SMP at a temperature higher than the phase transition temperature (T _trans ) of the SMP, e.g. the glass transition temperature ( T _g ) in the cross-linked thermosets, by heating the resistive wire until the temperature of the SMP exceeds the T _trans , then decreasing 2516 the temperature below T _trans while maintaining an external load on the structure, and, finally, removing 2518 the external load at a low temperature to achieve a fixed temporary shape (i.e., the programmed shape). Thermal actuation 2512 of the SMP after the programming 2510 includes increasing 2520 the temperature above T _trans again to trigger the free recovery.

[00117] Thus, it can be seen that the present embodiments provide methods and systems for providing a foundation for effective design and performance of SMA powered 3D-printed soft actuators and effective design and performance of SMP-based 4D structures. The results show the efficiency and flexibility of multimaterial 3D printing in tailoring the deformed shape of the SMA based soft actuators and enhancing the shape memory capability of active and flexible hinges in SMP-based structures, which cannot be accomplished using conventional fabrication methods.

[00118] In accordance with the present embodiments, design and fabrication methods are presented for soft actuators capable of tailorable large deformations. The manufacturing methods rely on a combination of materials and geometry that can be precisely controlled to achieve desired functionality.

[00119] In addition, novel approaches to increase the actuation force of 4D printed structures demonstrate the combined use of active and flexible hinges in an effective approach to increase the recovery ratio and the load-bearing capacity of the 4D printed structures.

[00120] A finite element model was demonstrated which effectively predicts the actuator performance. The verified model can be used as a helpful tool to design actuators capable of complex 3D deformations, and reduce time and cost of manufacturing. In addition, a viscoelastic multi-branch model incorporated into a finite element model was able to effectively simulate the thermomechanical behavior of the 4D printed structures and accurately predict their shape fixity and recovery ratio. Thus, these models can also be used to design complex active structures for specific performance and deformation and help select the materials with appropriate thermomechanical properties while reducing the time and expense required for experimentation.

[00121] While exemplary embodiments have been presented in the foregoing detailed description of the present embodiments, it should be appreciated that a vast number of variations exist. It should further be appreciated that the exemplary embodiments are only examples, and are not intended to limit the scope, applicability, operation, or configuration of the invention in any way. Rather, the foregoing detailed description will provide those skilled in the art with a convenient road map for implementing exemplary embodiments of the invention, it being understood that various changes may be made in the function and arrangement of steps and method of operation described in the exemplary embodiments without departing from the scope of the invention as set forth in the appended claims.