Description

Field of the art

The present invention generally regards metamaterials and more particularly a metamaterial "of mechanical type" i.e. with particular mechanical characteristics, susceptible of being applied in many different fields.

Prior art

A part of the prior art comprises the following references, cited multiple times in the following description.

1. Nan Hu and Rigoberto Burgueno, "Buckling-induced smart applications: recent advances and trends", Smart Mater. Struct. 24 (2015).

2. Dixon M. Correa, Carolyn Conner Seepersad and Michael R. Haberman, "Mechanical design of negative stiffness honeycomb materials", Integrating Materials and Manufacturing Innovation, 4, July 2015.

3. Kaikai Che, Chao Yuan, Jiangtao Wu, H. Jerry Qi and Julien Meaud, "Three- Dimensional-Printed Multistable Mechanical Metamaterials With a Deterministic Deformation Sequence", J. App. Mech. 84, January 2017.

4. R. S. Lakes, "Extreme damping in compliant composites with a negative-stiffness phase", Phil. Mag. Letters, 81, No. 2, pp. 95-100 (2001).

5. Liang Dong and Roderic Lakes, "Advanced damper with high stiffness and high hysteresis damping based on negative stiffness", International Journal of Solids and Structures 50 (2013) 2416-2423

6. https://youtu.be/LfzynfJjfC8 Quasi-zero stiffness to isolate vibrations

7. https://youtu.be/m9J8-YAMQKo An introduction to Minus K Technology's negative- stiffness isolators 8. https://youtu.be/Jie4r4tcU3Q Tunable Variable Stiffness HRL Laboratories, LLC

9. Gunnar Tibert, "Deployable Tensegrity Structures for Space Applications", Doctoral Thesis Stockholm, Royal Institute of Technology, Department of Mechanics (2002)

10. Mark Schenk, Andrew D. Viquerat, Keith A. Seffen and Simon D. Guest, "Review of Inflatable Booms for Deployable Space Structures: Packing and Rigidization", Journal of Spacecraft and Rockets, (2014)

11. Mark Schenk and Simon D Guest, "On Zero Stiffness", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 228, 10, pp. 1701-1714 (2013).

12. Alessandro Carrella, "Passive Vibration Isolators with High-Static-Low-Dynamic- Stiffness", Thesis for the degree of Doctor of Philosophy, University of Southampton, April 2008.

13. Jin Qiu, Jeffrey H. Lang, and Alexander H. Slocum, "A Curved-Beam Bistable Mechanism", Journal of Microelectromechanical Systems, 13, 2, April 2004.

Metamaterials: a definition thereof

Metamaterials (from the Greek μετά which signifies "beyond") are materials with artificial structure that are engineered so as to have properties that sometimes are not found in nature. The term was coined in 1999 by Rodger M. Walser, then of the University of Texas in Austin. Some points in common could be found with previously-made materials: fibrous compounds - mixtures of carbon fibers or glass fibers with polymers - already existed for decades and were widely used for creating structures that were simultaneously strong and light. Nevertheless, Walser along with many others deemed that such concept involved much more, i.e. effects that were not yet completely exploited, especially in the fields outside structural engineering. In fact, the arrival of metamaterials forced a re-examination of concepts underlying optics and many other fields (see Snell's law with negative refraction index, inverse Doppler effect, and still others).

Metamaterials have been used for controlling and manipulating electromagnetic waves, sound, heat transmission and many other physical phenomena. They are formed by sets/complexes of many different elements obtained from composite materials, metals or plastics. The materials usually have repeated structures/configurations (patterns). The elements that compose the metamaterials can be considered as molecules of this artificial material. In the case of the present invention, it will be seen that several of such elements have the role of mediating force between the "molecules" i.e. between the other elements of the same metamaterial.

In general, the properties of the metamaterials are derived not only from the intrinsic properties of the materials of the elements thereof, but also by the geometric arrangement of such elements.

Many structures can be qualified as metamaterials. The most common consists of the arrangement of elements whose size and mutual distance are much smaller than the size of the spatial variation (variation scale) of the exciting field. Within this limit, the responses of the single elements and their interactions can often be incorporated (or "made uniform") in effective continuous parameters of the material; the set of the discrete elements is then conceptually substituted by a hypothetical continuous material.

It is difficult to reach a definition of metamaterial that is both rigorous and lacking ambiguity, as well such to avoid excluding many other structure types that should fully be considered part of the field/category of metamaterials. For such reason, the previously provided definition is deliberately left a little vague.

Nevertheless, currently, most of the metamaterials are constituted by repeated structures/configurations (patterns), with size scales much smaller than the wavelengths of the electromagnetic waves or of the sound waves with which they interact. Consequently, they are engineered on sufficiently small-size scales in order to be able to manipulate said waves, blocking them, absorbing them, increasing the amplitude thereof or orienting them towards other directions.

For such reason, metamaterials have often been produced on nanometric or micrometric scale.

At the microwave frequencies (wavelengths on the order of 10 cm) it is possible to apply a rather simple process for modeling the elements of the metamatenal. According to a general rule, the "unit cell" must be at most equal to a tenth of the wavelength of the exciting field. Even if in past years most of the metamaterials were conceived for interacting with electromagnetic waves, today an increasingly greater number of mechanical metamaterials are being proposed - i.e. metamaterials capable of manifesting their particular properties when subjected to mechanical stimuli. The metamatenal that is the object of this invention is in fact one of these.

Intelligent applications of the "buckling" (deformation) and "snapping" (snap in position) phenomena

Beyond metamaterials, also known in the art is the snap in position phenomenon, better known as "snapping", of thin structures in one, two or three dimensions, such as beams, struts or supports, sheets, strips/belts, cylinders, etc. A recent article [ref. 1] collected many interesting examples, relative to numerous useful applications of such phenomenon, which were classified as "pertaining to energy" or "pertaining to movement". The applications pertaining to energy comprise energy sensors, dampers, absorbers, isolators and accumulators; the applications relative to movement comprise actuators, so-called "morphing" structures, and deployable structures. The growing number of articles published in recent years demonstrates a conesponding strongly-increasing interest for this argument, which includes various and multiple disciplines.

In addition, there is also a clear increasing interest for such phenomena in the world of the abovementioned metamaterials, where several examples of cells have already been demonstrated that exploit the phenomenon of "snapping" between two stable states [ref. 2]. Such interest in metamaterials cunently benefits even more from the new possibilities offered by AM (additive manufacturing) technologies.

More recently, a multistable metamaterial was proposed that was obtained by means of 3D printing ("3D-printed"), which exploits the phenomenon of "buckling", according to a deterministic sequence, in order to control the elastic waves [ref. 3]. Indeed, in a multistable material with deterministic sequence of the deformations, it is possible to apply a preload in order to cause a deterministic switching/transition towards another stable configuration; such switching or transition in the geometry of the micro-architecture affects the propagation of the sound waves by virtue of a predictable change between two frequency bands of the metamaterial. The deterministic deformation is obtained by means of varying the thickness of a membrane of each single cell between one layer (line) and the next, in the various layers or lines that constitute the metamaterial (Fig. 6 of ref. 3), or by means of the introduction of a proportional imperfection (factor a ₃ ) to the third buckling mode (equation (4) ref. 3), where also in this case the value of a ₃ is varied between one layer and the next of cells, while in the same layer a ₃ is a constant (Fig. 7 of ref. 3).

Problems that the invention intends to solve

Notwithstanding the great amount of work already performed in the field of metamaterials, and notwithstanding the variety of modes for exploiting the phenomena of "buckling" and of "snapping" by making multistable and reusable energy absorbers/dampers, or even deployable structures and actuators, there apparently still remains much space for improvement in the field of materials that are crushable/compactible (due to an impact or "crash"). Indeed, most of the materials used today as energy absorbers perform their function by sustaining plastic deformations, so that, once the impact has been sustained, they must be replaced. It would instead be useful to be able to provide materials capable of accumulating potential energy and restoring it when required, retaking their initial form, such that they can be reused.

Among the possible applications in the aerospace field, for example, the latter materials could be used for attenuating or damping the peaks of the acceleration at the time of landing of a spacecraft, protecting the payload thereof. The vent valve balloons constitute one of the ways for protecting an entire spacecraft during landing, but these are disadvantageous if one intends to protect only part of the payload.

In many cases, foam materials are instead used, or metal materials, or metals with honeycomb structure. Nevertheless, the foams and the metals with honeycomb structures:

1) cannot be easily made to size for a given mass, a given impact speed and a given stop distance;

2) occupy considerable space within the housing for equipment (housing of the payload) during the launch and cruise phases. It would instead be useful to make a damping structure which reaches its final size (necessary for protection) only during landing, i.e. only when said protection is required, so to save space in housing for spacecraft equipment.

Also "3D-printed" materials have been proposed for the aforesaid uses. Nevertheless, presently such materials have a compression ratio (length after the crush / length in the non- compressed state) on the order of 0.5, or even more disadvantageous; there is therefore a considerable need for a material that can easily reach an improved compression ratio. Indeed, a lower compression ratio signifies more space available for reducing the acceleration during impact, which is given by the known formula: a = v ² /(2s), where v is the impact speed and s the deceleration path (travel).

In addition, a lower compression ratio involves a lower volume where energy can be stored and hence a greater energy density.

Hence, one object of the present invention consists of providing a "3D-printed" metamaterial that can be easily made to size for a given mass of the spacecraft, a given impact speed and a given stop travel, which can reach the final use dimensions preferably only in landing phase, and which has an improved compression ratio.

Another useful application for the space field, which the present invention addresses, regards the deployable structures. To mention only one of these, telescopic structures (or telescopic supports) are considered.

One solution available in the state of the art is the extension by means of helical springs. In this case, the smaller the compression ratio (length in the compression state/length in the extension state) of the telescopic structure, the greater the F ₁ /F ₂ ratio between initial force (closed spring) and final force (extended spring). If Fi is large, it can be difficult to keep the structure closed, and then it will be necessary to devise appropriate locking-unlocking mechanisms, as well as shock absorbers or dampers that allow a soft/regular as well as slow deployment.

In some other cases, the gas springs can perform the function of telescopic structure. But even this latter solution had several drawbacks. Indeed, in the vacuum of extraterrestrial space, the evaporation of the lubricants can be a problem, and the exposure to high temperatures can compromise the effectiveness of the gaskets of the gas spring.

Other solutions such as the tensegrity structures, see [ref. 9], or the inflatable structures, see [ref. 10], could be too weak, or be more suitable when great extensions of the telescopic structure are required and if it is necessary to support low loads, but said solutions are not specifically designed for storing mechanical energy of considerable intensity.

Hence, it would be desirable to be able to provide a lightweight device, capable of being expanded in a sufficiently slow manner, without requiring external dampers, without lubrication and airtight seal problems, capable of providing a considerable force at the end of its travel, and simultaneously without requiring considerable energy for remaining in a locked position and for being activated, while being adapted to accumulate a great amount of mechanical energy in a limited space.

The object of the present invention thus also consists of providing a metamaterial that can be exploited as a technological instrument for manufacturing these and other devices.

A further object of the present invention consists of making a metamaterial that can also be used as a vibration isolator. Indeed, the metamaterial that is the object of the present invention, after an appropriate preloading, is such that most of its remaining compression travel is carried out in a condition of negative stiffness. Now, by coupling one such metamaterial to another external elastic element with positive stiffness or by rendering it interlaced or interconnected with an elastic array or another lattice with positive stiffness, in a condition of said suitable preload, the metamaterial, object of the present invention, is capable of operating as vibration isolator with high static stiffness and low dynamic stiffness (HSLDS vibration isolator: High Static Low Dynamic Stiffness vibration isolator). See also [ref. 12].

Another object of the present invention regards a simple adaptation of the metamaterial, object of the invention, in order to allow a large-scale industrial application, i.e. to vehicle bumpers, or even to guardrails and to the impact absorption barriers used on road systems. Hence, a particular object of the present invention specifically consists of providing a bumper for road vehicles based on the metamaterial concept of the invention, whose initial condition can be restored after the impact has been sustained - at moderate speed - by the vehicle. In a few seconds time, the initial form of the bumper can be restored without requiring interventions by a repair shop/person.

The objects of the invention will be obtained by means of the characteristics contained in the characterizing part of claim 1 and in the other independent claims enclosed with the present description.

Several advantageous embodiments and variants of the invention are defined in the enclosed dependent claims, which depend on the independent claims.

Brief description of the drawings

The object of the present invention, along with its advantages, functions and applications, will be better understood after reading the following detailed description of several preferred embodiments thereof, provided only as a non-limiting example. The drawings illustrate several practical embodiments of the invention as well as the theoretical aspects underlying the same invention. Such drawings show in:

Figure la, a two-dimensional representation of the structure of the metamaterial of the present invention, in a currently-preferred possible embodiment thereof, in the non-stressed condition, i.e. without a load;

Figure lb, the metamaterial of the preceding figure, in the condition of maximum extension of the elastic elements and of mutual alignment of the rigid elements or "struts"; Figure lc, the metamaterial of the preceding figures, in another stable state;

Figure 2, a qualitative representation of the potential energy of the metamaterial, object of the present invention, as a function of the crushing or compression of the metamaterial lattice;

Figure 3a, an articulation hinge or joint in two separate parts, according to a first embodiment of such hinge in the metamaterial according to figures la-lc;

Figure 3b, an articulation hinge or joint in a single body, based on a second possible embodiment of such hinge in the metamaterial according to figures la-lc;

Figure 4, a possible embodiment of the elastic connecting element in the metamaterial according to the present invention, shown in Fig. 1, obtained with an additive multi-jet manufacturing process;

Figure 5, (taken from ref. 6) the principle of an alternative embodiment of the metamaterial of the invention in which the elastic connecting elements work in compression, instead of with traction, in order to be able to obtain also in this case a configuration with negative stiffness and multiple stable states;

Figure 6, (taken from ref. 13) the first three modes of "buckling" of a beam constrained at the ends ("clamped-clamped beam") and of normalized length;

Figure 7, (taken from ref. 13) a qualitative and schematic representation of the deflection curve (or inflection curve) f-d for the inflection of a beam forced to be bent in the first mode, the second mode being constrained;

Figure 8, a representation of the curve f-d relative to a single cell of the metamaterial, object of the present invention; the deflection or inflection is normalized to the length of the struts; the elastic connecting elements are taken with stiffness equal to k = INm ^"1 and are not deformed (length equal to the free length) when the angle of the struts (rigid elements) with respect to the horizontal is equal to 45°;

Figure 9a, (taken from ref. 6) the known principle of the negative stiffness (negative stiffness design);

Figure 9b, (taken from ref. 6) the known principle of the quasi-zero stiffness (quasi-zero stiffness design).

Detailed description of several currently preferred embodiments of the invention

The present invention will be illustrated hereinbelow in a rather detailed manner, considering several possible embodiments and variants thereof, but the inventive concept underlying the present invention is wider such that the same is not limited to such embodiments and variants. One of the basic concepts of the invention in fact consists of having conceived a metamaterial in which the deformations of the structural elements are not plastic, but rather exclusively elastic and the bending moments generated in the compression of the metamaterial are zero or negligible for all parts of its constituent structure. The elements of the metamaterial of the present invention are distinguished for the fact that they belong to four distinct categories: the elastic elements (which work with traction), which during the macroscopic deformation of the metamaterial only undergo an elastic deformation and hence can retake their original form; the rigid connecting elements (also termed struts in the shown and described embodiment) which rotate around hinges without undergoing practically any bending moment; the joints, also rigid; and finally the hinges, which allow said rotation of the struts on the rigid joints, without transmitting bending moments to the struts themselves. In an alternative embodiment of the invention, which is however based on the same operating principle, the elastic connecting elements (e.g. helical springs) can also work in compression, as in Figure 9a. The fact of having introduced actual mechanical hinges in a metamaterial allows the present invention to trap the kinetic energy of an impact (e.g. in the landing phase of a spacecraft or other item) in the same material, without dissipating it, in order to then possibly transfer it again (in some applications), completely recovering the initial form.

Other aspects of the invention will be clearer from the following description.

With reference now in particular to figure la, this shows a possible basic configuration of an embodiment of the invention, in which such representation is - merely by way of a simplifying example - two-dimensional, even if of course the object of the present invention is also extended - or even mainly extended - to three-dimensional structures. The generalizations regarding three dimensions can be of various type; these are evident to a man skilled in the art of the field who reads the present description, so that it is not necessary to discuss this in further detail.

Hence, in detail, Fig. 1 shows a two-dimensional lattice formed by four base elements: the joints 1, the beams or struts 2 (also termed rigid connecting elements), the elastic elements 3 (which here work with traction), and the hinges 4. The latter are simple mechanical hinges which allow the rotation of the struts 2 around the joints 1. The shape of such hinges can be variable and will be illustrated hereinbelow, in two possible alternative embodiments, with reference to Fig. 3. These are in any case ideated for being made with additive manufacturing processes or 3D printing processes, the expressions "3D printing" and "additive manufacturing" being equivalents for the purpose of this discussion. The joints 1 are as rigid as the struts 2, and perform the function of constraints during the compression deformation of the metamaterial of the present invention. The elastic elements 3 are formed herein by way of a non-binding example by flat elements 3 with strip or belt form, which when laterally observed (as in Fig. 1) naturally take on the shape of a straight line with suitable thickness.

It is also observed (see Fig. la) that the metamaterial of the invention, like most of the other metamaterials of the prior art, has a structure with superimposed layers and with repeated "cells", in which each single "cell" essentially consists of - in the present two-dimensional shape - a quadrilateral with relative elastic element 3 that diagonally traverses it, being fixed at its ends (see also the subsequent description of Fig. 4) to the respective joints 1 of the cell. Hinges 4 are fixed to each joint 1.

Still with reference to figure 1, the operation of this metamaterial, of mechanical type, will now be illustrated according to the present invention.

By applying a vertical load of compression to the lattice, said struts 2, which are articulated to the joints 1, rotate without bending thanks to the hinges 4. The elastic connecting elements 3 oppose the compression with their elastic return force, until said struts 2 reach the horizontal alignment position (Fig. lb). From this moment on, the further compression produces a return contraction of the elastic connecting elements 3, the accumulated stress is relaxed/reduced and facilitates or promotes the compression. There is a negative reaction force that blocks the system in a compressed but stable state. From an energy standpoint, while the lattice is compressed it accumulates potential energy; nevertheless, when each layer is compressed beyond the point where its elastic connections 3 begin to be contracted, it falls in a potential energy well (Fig. 2).

Specifically, from the graph of Fig. 2 one sees that such metamaterial of mechanical type has a plurality of stable states, one for each energy well 5, and that as such it can act, for example, as a crushable material effective in absorbing the kinetic energy of a mass that hits a rigid surface. The difference and the advantage with respect to other crushable or compactible materials (e.g. the honeycomb structures, the foam materials, or the like) lies in the fact that the metamaterial of the invention does not sustain any type of plastic deformation: it will be sufficient to add or provide the small amount of energy necessary for filling the potential wells of Fig. 2 and the material will recover its original form. It is observed that since there is no plastic deformation, the kinetic energy is absorbed and trapped in the material instead of being dissipated. Such characteristic is important for some applications since most of the trapped energy can generally be reused.

The metamaterial of the present invention can in particular be made with the technique of additive manufacturing (AM). If multiple materials are used, the metamaterial of the represented embodiment could be obtained from the 3D printing technique ("3D printed") by means of a multi-jet 3D printer device, capable of operating under the control of a computer simultaneously with other materials, in a single process. Nevertheless, the invention is not limited to this case and also covers the metamaterials of the same type, which could require a sequence of different production steps for their attainment.

In a particular example, the joints 1 and the struts 2 are made of rigid plastic while the elastic connecting elements 3 are made with an elastomer. Nevertheless, the invention also includes other structures in which the "struts" or "beams" - or the rigid connecting elements 2 -, the rigid joints 1, and the elastic connecting elements 3 are obtained from other materials, characterized by a higher modulus of elasticity for the struts/beams 2 and the joints 1 with respect to the elastic connections 3.

The invention also comprises other structures in which the struts 2, the joints 1 and the elastic connecting elements 3 are all made of the same material, where the different stiffness of the elements with respect to each other derives from the specific morphology of each element type, in a manner rather similar to the example of the steel helical spring whose stiffness is rather different from the stiffness of a solid body/block, made of the same steel as the spring. Fig. 3b hereinbelow will analyze one aspect relative to this point.

A central element of the present invention is of course the hinge 4 that connects the struts 2 to the joints 1. Due to these hinges 4, the struts or beams 2 (rigid connecting elements) can complete an actual mechanical rotation practically without modifying their state of internal tension, remaining constantly loaded or stressed only axially, where most of the stress is concentrated in the elastic connections 3 which are suitably designed in order to withstand high variable loads.

The present invention among other things implements two possible types (non-binding) of hinges, which are represented in Fig. 3 as examples, even if it is obvious that the invention is not limited to these examples but rather also extends to other types of hinges which will neither be shown nor described in the present document.

In the example of figure 3a, the hinge is constituted by two separate parts. This articulation is obtainable by means of the technique of additive manufacturing (AM) and possesses only one degree of freedom. Since one part of the articulation 4 is associated with the joint 1 and the other part is associated with the strut (or rigid connecting element) 2, in figure 3a these parts of the hinge 4 are indicated with the reference numbers 4.1 and 4.2. The part 4.1 of the hinge 4 comprises two parallel projections 4.1.1 and 4.1.2, while the part 4.2 of the same hinge 4 comprises only one projection 4.2.1. On the sides of the parallel projections 4.1.1 and 4.1.2 that face each other, two respective opposite conical holes are made (mirrored symmetry) in which respective conical projections of (nearly) complementary shape are inserted, integrally made on opposite sides of the single projection 4.2.1 of the part 4.2. Specifically, "the insertion" of the conical projections in the conical holes, where the projection 4.2.1 is simultaneously "inserted" between the two parallel projections 4.1.1 and 4.1.2, occurs during the production with the additive manufacturing technique: at the end of the process, the assembled condition of the hinge 4 is thus directly obtained, shown in figure 3a at the top. With other techniques this of course would not be possible.

The invention does not only incorporate this hinge type with only one degree of freedom. For example, a similar articulation with two degrees of freedom, also preferably obtained by the same production process, would be possible with a spherical head that rotates in a spherical cavity, even if such solution could encounter problems due to the friction and possible seizure, in particular for smaller-size structures.

Instead, in the example of figure 3b, a hinge 4' formed by a single body is represented. Since the present invention aims to cancel or at least reduce to a minimum the bending ("bending stresses") in the material (indeed in the first embodiment there is no bending in the material), the first hinge (4) variant just described is preferred over the hinge 4' described below. In any case, it is essential for the invention that (see the case of figure 3b) the bending deformations be local, i.e. circumscribed only in the zone of the hinge; this point will be discussed further hereinbelow.

The hinge 4' of figure 3b is distinguished from the hinge 4 of figure 3a due to the fact that it is formed by a single body that comprises two sections (1, 2) integral with a thin corrugated strip of the material. Such embodiment allows absorbing considerable axial loads in each section 1, 2 (without deforming them) while the entire deformation stress (in any case small) is limited to the thin corrugated strip, being well-distributed therein, also due to the radii of curvature that are made at every corner 6. This hinge type is less subjected to the risk of blocking due to friction problems, with respect to the preceding type.

A basic concept of the present invention consists of the fact that that within the metamaterial of the invention, several elements are suitably designed in order to introduce elastic forces (the elastic connecting elements 3). In other words, all the other elements are exclusively required to absorb/oppose axial loads (rigid elements 2), and to be arranged according to specific positions and orientations under the action of said elastic forces and external loads, without incurring any deformation such to produce considerable internal stresses. However, the elements suitably designed for generating elastic forces (elements 3) perform their function by means of simple extensions (or even compressions; see the second embodiment described hereinbelow).

With reference to Fig. 4, this shows an example of connection (termed "topological connection") between two rigid supports 11, 11; the latter could be the diagonally opposite two rigid joints 1, 1 of fig. 1, connected together by an elastic connecting element 3, which in Fig. 4 is indicated with reference number 13. The elastic element 13 can be made of an elastomer while the two (more) rigid supports 11 can be obtained from a much more rigid plastic.

It is observed that, due to the possibility offered by multi-jet additive manufacturing (AM), these two materials can be connected together during a single manufacturing process. In such a manner, notwithstanding the absence of welding between the two materials, these cannot be separated when the two supports 11 are pulled in opposite directions. The object of the present invention regards these and other configurations of similar topological connections between different materials.

Specifically, it is the same "topology" of the connection in figure 4 that prevents the mutual separation of the elements. Indeed, the elastomer element 13 is incorporated/fit at its two ends in the more rigid elements 11 since the wall of the hole 12 is continuous and traverses the elastomer material 13, which at that point has a larger hole (not visible). Such connection can be made by means of a AM process and it would be impossible to obtain by means of conventional mechanical tools.

A second possible embodiment of the present invention will now be briefly illustrated.

In this second embodiment, unlike the example of fig. 1, the elastic elements instead of being tensile-stressed while the metamaterial lattice is compressed, are compression-stressed. Hence, the present invention extends its inventive concept also to other structures in which the elastic connections can be subjected to a compression load, as in the diagram of fig. 5. In this diagram, the elastic elements 3 ' form helical springs 3' with equal elasticity constant, k _n , hinged at their ends to rigid joints 1 that are not completely represented (see Fig. 5, on the left).

In figure 5, on the right, there is instead a representation of the "negative stiffness" principle according to a mechanical-mathematical model that is not the object of the present invention. Returning to Fig. 5, left side, it is seen that in the single "cell" of metamaterial, the position which in Fig. 1 (first embodiment of the invention) was occupied by the rigid struts 2 is now occupied by the compression springs 3', while the hinges 4 and the joints 1 are only schematized.

Once again, it is observed that while in the state of the art the crushable structures and the relative metamaterials based on the concept of the "clamped-clamped beam" (beam constrained at the ends) [ref. 3 and 13] can generally sustain various modes of "buckling", the rotating articulated elements of the metamaterial of the present invention, independent of whether they comprise elastic connecting elements that work in extension/elongation or in compression, only have one essential mode of deformation by rotation. Such characteristic simplifies the design of the overall material properties.

The bending and compression stresses are simultaneously present in the base elements of a metamaterial based on the concept of a beam constrained at the ends ("clamped-clamped beam"), so that the entire structure must be carefully designed in order to maintain said deformation during inflection or deflection under the yield limits of the material. Indeed, the risk of fracture becomes increasingly critical with the increase of the alternated stress cycles (load-unload), and it is necessary to consider the fact that a smaller scale/size design requires a greater fracture resistance.

The structural energy within the curved or bent beam comprises both the bending energy and the compression energy. Qualitatively, from the energy standpoint, the bending energy in the beam increases in a monotonous manner each time that the beam is moved downward; instead, the compression energy increases up to a maximum approximately at the central line, in order to then be reduced after traversing this line. If the beam is designed in a manner such that the reduction in the compression energy after traversing the central line occurs more quickly with the increase of the bending energy, then a negative force thereof results, an indication of bistability. Such behavior leads to a characteristic load-movement curve that is strongly asymmetric in the multistable metamaterials based on "snapping" between two forms (configurations) of the beams constrained at the ends.

This is represented in figure 7, which shows a qualitative schematic representation [taken from ref. 13] of the dependence of the force (f) on the deflection (or infection) (d) in the case of a bent beam obliged to be bent according to a first mode, since the second mode is prevented ("second-mode constrained") by the particular structure of the beam of the example.

A symmetrical form of such characteristic curve would be desirable for a variety of applications, since generally the two states would be stable in the same manner. In addition, by starting from a symmetrical curve f-d, and incorporating several mechanical constraints in the structure by means of design, it would be possible to obtain a total control over the depth of the potential well of each stable state. In the case of the present invention, as is inferred from Fig. 8, the curve f-d is perfectly symmetrical since it reflects the intrinsic symmetry of the structure. Such symmetry is made possible by the hinges which connect the structural elements of the lattice. Indeed, these allow the snap in position ("snapping") between two stable states with the accumulation - i.e. the onset - of a negligible or irrelevant amount of bending energy, or with the total absence of said bending energy.

However, even in the most recent metamaterials belonging to the state of the art, the entire structure must be made with a first stable state lacking stresses in the constituent elements, while when the metamaterial passes (i.e. "switches") towards the other stable state, it is observed that a non-negligible stress value is accumulated at its interior.

For example, in the article of ref. 3, a multistable metamaterial is described that is obtained from only one material, based on a stratified assembly of cells, in which each cell is based on the "clamped-clamped beam" model, where every single cell comprises a substantially U- shaped rigid element and a thin layer or membrane extended between the vertical walls of the "U". Each single "U" of every single cell then has a rigid central projection directed downward, which is integral with the membrane of the underlying cell and acts on such membrane during the stress of the metamaterial by a load/external force. It is obvious that in this case the bending energy is distributed over the entire membrane or thin layer of the cell, while it is not localized at the points of the hinges of membrane, different from the present invention, in which such bending energy is either entirely absent (hinges as in Fig. 3a) or it is negligible and localized precisely at the corrugated hinges (for the corrugated hinges of the type of fig. 3b).

It is also observed that the symmetry of Fig. 8 would in reality correspond to a greater vertical length of the joints 1 of fig. 1, length such to allow a completely symmetrical travel of the struts 2 downward, while such downward travel is reduced in Fig. lc due to the reduced vertical length of the joints 1. In this sense, the joints carry out the function of constraints, since their length constrains the width of the negative angle formed by the struts with the horizontal plane for the purpose of the compression. In reality, the symmetry of Fig. 8 that would be found in the case of a greater vertical length of the joints 1, in the metamaterial of the present invention, allows incorporating said mechanical constraints in the structure (see above) by means of design, in order to obtain a total control over the depth of the potential well of each stable state (Fig. 2). In other words, by introducing (exactly as in Fig. 1) smaller vertical lengths for the joints 1, stable states are obtained with potential wells that are not very deep (Fig. 2), which allow easily recovering the initial shape of the metamaterial. The depth of the potential wells of fig. 2 can be adapted for the various applications.

For example, this characteristic is usable in many different applications.

The general idea consists of providing for, for example, a film of strong material on the outer side of the metamaterial of the invention. In this case, by injecting gas within the (airtight) space occupied by the metamaterial, by means of a suitable valve provided on the film of strong material, the metamaterial can be "inflated", exceeding the energy of the single potential wells and restoring the initial state of the metamaterial energy absorber. The same criterion, or other criteria can be used for restoring said initial state in a telescopic structure, for example "by pulling" the surface of the metamaterial from the outside or pushing it from the inside by means of suitable means.

The applications of the metamaterial of the invention could therefore be (non-limiting list):

1) Energy absorbers for protecting the payload in the landing phase of spacecraft. In the launch and cruise phases, the energy absorber could be reversibly "compacted" in the payload bay of the spacecraft, in order to then be extended up to the final form just before the landing phase or in any case after said spacecraft has separated from the launcher. This would allow saving space in the housing of the launcher of said spacecraft.

2) Telescopic structures, in substitution of the other abovementioned devices of the prior art, whose problems have already been indicated.

3) Vehicle bumper. The lattice of the metamaterial of the invention is suitably designed and preloaded in order to absorb (in a more efficient manner than the bumpers of the state of the art) the energy of a vehicle impacting at moderate speed. The original shape can be recovered in a few seconds by virtue of the strong and flexible film fixed on the outermost layers of the metamaterial. It will be sufficient to pull, from the outside, said (external) strong and flexible film with a moderate force in order to restore the original shape of the bumper. The same result could also be obtained in a more facilitated manner by inserting gas or simply air within the bumper provided (as stated above) with a strong and flexible film, but which is airtight.

4) A reusable mold for molding objects of various type. In this case, in addition to the flexible external film, the metamaterial could be formed by a lattice structure in turn composed of substructures, i.e. such that after the application of the external stimulus such material is situated in a state in which the amount of potential energy trapped in each substructure (or "cluster") of the metamaterial differs from one substructure to another. The variable stress, from one point to another of the surface of the external film (which winds the metamaterial of the invention), applied by an object in order to form a (negative) impression of any shape, is absorbed in different ways due in fact to the presence of metamaterial clusters, always based on the same inventive concept of fig. 1 or the like, but with different elastic pliability properties. With regard to the preceding applications 1) and 3), as energy absorber, the metamaterial of the present invention allows having rather more convenient compression ratios with respect to the materials of the state of the art, with the relative advantages indicated in the introduction of this document regarding the prior art and the drawbacks thereof.

With regard to the application as energy absorber, the "working point" of the absorber would usually be selected - for each cell - on the positive ascending section of the curve of fig. 8. In this manner, the metamaterial would preserve the capacity of elastically responding up to certain deformations, without necessarily passing to a state of stable (even if reversible) deformation.

Returning to figure 8, enclosed with the present patent application, it is observed that this comprises a maximum and a minimum in such representation of the curve f-d relative to a single cell of the metamaterial, object of the present invention. Between said maximum said minimum of the force, there is a nearly linear deflection range, where every single cell shows a nearly linear characteristic f-d with "negative stiffness": this signifies that in such deflection range or region the system behaves in a manner opposite that of a conventional compression spring. A simple mechanical model of negative stiffness is shown in Fig. 9a taken from ref. 6; a simple mechanical model of quasi-zero stiffness is obtained as in Fig. 9b (also taken from ref. 6) by means of a compensator spring with positive stiffness k _v . In the latter case, it is noted that the force necessary for compressing the material has a nearly constant value plateau in a wide normalized deflection range.

From that just stated above, a further application of the metamaterial of the present invention follows, that is as vibration isolator. In other words, by coupling the metamaterial of the present invention, suitably preloaded by working in the aforesaid negative stiffness range, to any one material of suitable positive stiffness, it is possible to obtain a vibration isolator (HSLDS: High Static Low Dynamic Stiffness) with quasi-zero stiffness.

In addition, the system can be suitably preloaded and/or constrained to work only in a predetermined range of its characteristic f-d. This signifies, for example, that in the case of the vehicle bumper it is possible to modulate the elastic reaction force of the metamaterial that forms the bumper, according to the amount of impact energy that it is desired to elastically absorb.

In addition, a constraint that is introduced by design in the metamaterial of the present invention is represented (as already stated) by the height of the joints 1, which determines the angle between the struts (rigid connecting elements) 2 and the horizontal plane in the compressed condition: the lower the height of the joints, the smaller the angle formed by the struts in the stable compressed state and hence the potential energy well will be less deep. The total symmetry according to Fig. 8 ensured by the present invention allows playing with such angle in order to obtain the best response of the metamaterial, i.e. in order to obtain the desired depth of the potential wells.

The potential usefulness of the hinges in obtaining the symmetric curve f-d has already been recognized in the past (ref. 13). Nevertheless, up to now the advantages deriving from a total control over the depth of the potential energy wells in the stable states had not been fully identified. In any case, it appears that an actual hinge structure has not yet been proposed for a multistable metamaterial, probably also - but not only - due to the fact that the previously- available manufacturing techniques, for example the DRIE (Deep-Reactive Ion Etching) technique, laser cutting, or the like, did not allow making small-size hinges in a suitable and convenient manner. On the other hand, the new potentials of the 3D printing machines ("3D- printing"), presently available, are the expression of a key technology that allows the attainment of the metamaterial, object of the present invention, in all parts thereof. Such potentials comprise the relatively simple manufacturing of the hinges according to repeated patterns on reduced scales, as well as the attainment of metamaterials composed of materials different from each other, during a single manufacturing process, each of these materials being optimized for a (well-defined) type of element of the metamaterial, and for obtaining the specific function performed by this precise element.

Consequently, the overall properties of the metamaterial of the invention are not only determined by the geometric arrangement of its constituent elements (as in the case of most of the existing metamaterial s) but also by the synergistic action of the different types of elements (preferably) made of different materials, where each type of element is "specialized" in carrying out a specific function.

Hence, the present invention contributes to completely exploiting the potential offered by multistable metamaterials of mechanical type, by optimizing the performances thereof and extending their range of applications.

The size range of the cells for the prefigured applications (as a non-limiting example) is variable, for example from several millimeters up to several centimeters, and clearly depends on the application. Of course, the reduction of the size of the cells of the metamaterial depends not only on the type of application but also on the possibility to provide new manufacturing techniques, not only used for the attainment of metamaterials; therefore, the size is not fundamental for the present inventive concept and for the protective scope of the present invention. The preceding range is therefore only given as a non-limiting and non- binding example.