DESCRIPTION

The present invention relates to a multilayer metamaterial and a related device engineered to be advantageously used for the dissipation of energy by friction and can therefore be used to mitigate the propagation of vibrations and the effects of shocks in applications such as civil, industrial, naval and aerospace also having the peculiarity of being re-centering, i.e. returning to the initial configuration at the end of the dynamic process, allowing to be reused.

In the field of civil engineering it finds application in the seismic protection of buildings, while in the industrial field in the rapid attenuation of vibrations, in the naval and aerospace fields in the attenuation of vibrations and in the containment of the effects of shocks. Possible applications also in the defense field.

The design and construction of materials and devices for the attenuation of vibrations and shock absorption through the dissipation of energy have long been the subject of interest in the R&D and industrial fields for the numerous applications ranging from aerospace engineering, naval, automotive up to civil engineering for seismic protection. The dissipators proposed in the literature and which currently find technological application are mostly based either on the viscous properties of the material or on the elastic-plastic properties. The first case includes suitably reinforced polymeric matrix materials, such as seismic dampers in buildings or antivibration silent-blocks made of natural rubber used in the automotive, naval and aeronautical engineering industries. In the second case, we recall the materials having a random microstructure such as foams, wherein the dissipation of energy takes place by progressive crushing phenomena.

More recently, thanks also to the diffusion of 3D printing procedures exploiting high-precision additive manufacturing also on metals, materials with a periodic and/or hierarchical microstructure (architectured materials) have found applications, whose periodic cell is suitably designed to obtain desired and/or unconventional mechanic performances typical of mechanical metamaterials. Among the most interesting exotic properties are auxeticity, i.e. the characteristic of dilating transversely to the direction of a traction effort to which they are subjected and vice versa of transversely compacting when subjected to compression, negative reflection, non-reciprocity and acoustic invisibility of fundamental importance for the realization of functional mechanical meta-devices. More recently, studies and technological applications have been launched aimed at the design of microstructured metamaterials, whose periodic cells are equipped with suitable devices for attenuating vibrations and the effects of shocks. The optimal design of these devices should ensure the following requirements: i) hysteretic response with maximum dissipation of mechanical energy; ii) possibility of reusing the device without external interventions with restoration of the initial configuration at the end of the dynamic process; iii) multi-directionality of the dissipative response; iv) bilaterality of the response, i.e. equal behavior in traction and compression.

The phenomenon of elastic-brittle or better elastic-plastic collapse of the single components of the periodic cell in materials/latices with a hierarchical microstructure has been studied and proposed in various technological applications. As expected from the mechanical conception of such devices and confirmed by the experimental results, this design solution does not generally satisfy the requirements ii), iii) and iv) listed above.

More recently, meta-devices with a periodic microstructure have been conceived and proposed wherein snap-through phenomena of internal instability take place. In the loading process, suitably shaped micro-beams can assume different equilibrium configurations as the external action varies with a progressive succession of snaps. When unloading in displacement control, a hysteresis process can be performed with the possibility of returning to the initial configuration. This circumstance may not occur in force control, thus highlighting, especially in experimental tests, that the return to the initial configuration, necessary for the satisfaction of requirement ii), is only possible with the intervention of an external action. Furthermore, it can be seen from the state of the art that devices developed according to this approach very hardly satisfy requirements iii) and iv). A different approach, however based on multi-stable microstructures, involves the realization of the material as a two-layer medium with tetrachiral lattice microstructures with opposite chirality. This allows the activation of relative rotation mechanisms between components of the microstructure controlled by magnetic coupling forces that allow the multi-stability of the equilibrium configurations.

Numerical experimentation shows, however, that such devices do not generally satisfy requirement ii).

Finally, a further limitation of these devices based on the multi-stability of the balance configurations consists in the difficulty of controlling the overall response of the device which manifests itself with a succession of snaps between the various balance configurations.

A promising alternative proposal is based on two-dimensional cells constituting the microstructure of the meta-device wherein dissipation mechanisms of the Coulomb type are inserted, with a topology of the elementary cell of the microstructure which guarantees the fulfillment of requirements i) and ii), but not iii) and iv). An example of such an application is present in document US 10,808,794B1 .

This patent application too is based on the use of Coulomb dissipation mechanisms for vibration attenuation and shock absorption. However, these mechanisms differ from those described in the previous point and allow to satisfy all the requirements required as detailed below and moreover it aims to define a metamaterial which has low constructional and operational complexity.

The present invention solves these and other problems of the prior art through a multilayer metamaterial comprising at least two substantially flat and superimposed individual layers, each of said layers being composed of a plurality of elementary cells, each of a predetermined thickness, mutually interconnected according to a predetermined order to form a reticular structure, each of said elementary cells comprising a core, having a predetermined plan shape and a rotational axis which crosses said core in a rotation center, to the core of which are connected a plurality of elastic ligaments which branch off from at least two different points of the perimeter edge of the core itself for connection with adjacent cells belonging to the same layer, said core being provided with a fulcrum seat which is arranged coaxially with the rotational axis and is intended to house a through pin around which said cell is rotatively pivoted, wherein the second of said at least two layers, or a further adjacent layer, is provided with a symmetrically specular geometry with respect to the first of said layers in accordance with a plane of symmetry parallel to the plane subtended by said layers, at least said second layer, or an adjacent layer, adhering with one face thereof against a face of said first layer in such a position that each core of said second layer, or of the adjacent layer, is coaxial to a corresponding core of said first layer and pivoted on the same through pin on which the corresponding core of the first layer is pivoted.

In accordance with this main feature, the invention aims to obtain a layered material consisting of a repetition of two-dimensional lattices or grids made by the periodic assembly of mutually connected elementary cells, wherein each cell is provided with a rigid core provided with elastic ligaments which allow the connection with the adjacent cells to create a layer of the metamaterial.

The quantity of elastic ligaments provided on each core contributes, among other parameters, to obtaining the damping effect of the metamaterial and its behavior when subjected to the actions of external forces. As shown below, an embodiment provides for the configuration with six ligaments per core with the consequence of obtaining an isotropic behavior of the metamaterial. Other possible forms provide for the construction of four-ligament cells which is shown to result in an orthotropic behavior of the resulting material.

Specifically, the topology of the single cell is chosen in such a way that a traction of the cell itself applied to the ligaments leads to the rotation of the core around a rotational axis of the core pivoted around said axis and consequently a traction force applied in the subtended plane from the layer of cells leads to the rotation of the rigid cylinders due to the stress states contained in the plane.

Furthermore, contiguous lattices exhibit mirror-image geometry such that they cause opposite rotations of the contiguous cylinders with relative rotation between the cores. Preferably the single cell and the single layer have a chiral topology while the layers are arranged in alternating opposing chirality. The various layers which are superimposed may possibly differ in the thicknesses and/or in the materials used for their construction. The possibility of producing single layers and/or stratified materials wherein the mechanical characteristics can be chosen differently between groups of cells of the same layer or of different layers which make up the metamaterial should not be excluded.

Instead, in the case of layers that are similar and differ only in specular geometry, a further implementation advantage is obtained since each layer is made individually without the need to differentiate the geometry during production, while the structure with alternating layers is made simply by arranging each overturned layer (rotated by 180° with respect to an axis contained in the plane subtended by the layer itself) with respect to the adjacent one.

In a preferred embodiment, the metamaterial comprises a plurality of alternating superimposed layers and at least partially pivoted by through pins which connect the coaxial cores of at least two layers. The presence of through pins to comprise at least two cores of adjacent layers imposes the equality of the displacement between the cells. It is possible for a pin to cooperate with adjacent cores of all layers or only with a subset of them; it is preferable that all the cores of a layer are individually centered with the corresponding cores of adjacent layers but the person skilled in the art, in putting the teachings of the present invention into practice, will be able to choose the best configuration according to his experience and average knowledge of the scope of application.

Furthermore, the invention is not limited by the size of the single core or by the number of elastic ligaments connected to each core or by the number of layers or by the material used for its construction. The Applicant has carried out simulations with parameterized dimensions and implemented practical applications of cells having dimensions of the order of a few centimeters and a few tens of centimeters, obtaining the predetermined purposes and the results commented below.

Preferably, the core of each cell has a rotational symmetry with respect to the rotational axis, commonly in the shape of a disk (see the executive examples attached and discussed below) said disk having two main faces, parallel to each other and intended to cooperate with similar faces of cores superimposed on it, and a lateral perimeter edge from which the elastic bridges or ligaments branch off for connection to adjacent cells. In the more general case of a shaped core, however, it will be possible to have two faces parallel and orthogonal to a rotational axis with a number of lateral faces intended, at least partially, to be connected to said elastic bridges.

Preferably, the metamaterial comprises pretensioning means intended to exert a compressive force between two or more adjacent cores; it will be seen later how this force contributes to the dissipation of mechanical energy by friction at the interface between two cores following their reciprocal rotation. Furthermore, this force can also or alternatively oppose an axial expansion between two or more adjacent cores in the event that the latter are provided with shaped and complementary contact surfaces such as to exert a spacing force when subject to reciprocal rotation.

These compression means can be made according to the prior art and, among other things, according to the characteristics of the material and/or the dimensions of the cells. Among the possible configurations, flanges or radial crowns arranged on the lateral surface of the cylindrical pin can be conceived; alternatively, embodiments can be provided wherein the through pin is threaded in at least one end so as to guide, for one or both ends, a screwable element such as a nut with possibly a washer intended to exert a compressive force on an area of the core and consequently on the opposing cores. This configuration is advantageous in practical uses wherein it is convenient to be able to calibrate the forces during the installation, adjustment or maintenance of the device comprising the metamaterial presented here.

According to at least one variant, which can be made in combination or as an alternative to the previous ones, said mechanical compression means can comprise terminal layers arranged on the external surfaces of the external layers, such as for instance two plates of specially selected material, preferably interconnected with adjustable and lockable transverse bridges in position so as to be able to adjust and spatially balance the forces compressing the two or more layers making up the metamaterial.

With reference to the core of the single cell, it can be made in such a way that the contact surfaces of two adjacent cores of two adjacent layers have a mutually congruent plan shape and have at least one contact area and/or a contact band coaxial to the rotational axis with which said two cores are in contact. In a possible implementation of this feature, the single core has two substantially flat and opposite surfaces intended to enter at least partially into contact with the corresponding surfaces of adjacent cores or with a possible containment surface to protect and/or compress the cores stacked and pivoted on a common pin. In a variant of the previous embodiment, included in the graphic tables attached hereto, the surfaces have at least one ridge arranged on this flat surface which has a constant axial thickness along a path coaxial to the axis of the core; in the specific case wherein the core has a rotational geometry around the same axis, this ridge becomes a circular crown arranged on the flat surface of the cylinder defining the core itself.

In this way the contact between adjacent cores takes place on a flat contact surface and for only a portion of the upper and/or lower surfaces of the core. Obviously it is not strictly necessary that the two opposite surfaces of the same core have identical plane geometry, even if this is advantageous at least in terms of manufacturing the metamaterial.

Alternatively, the contact surfaces between two cores belonging to adjacent layers can be made at least partially of a non-flat shape and mutually complementary, presenting at least one ridge in a direction preferably parallel to the rotational axis. A specific shape is shown in the attached graphics and it can be seen how this configuration introduces a dilating effect into the interface between adjacent cores with an expansion force in the axial direction which is formed in response to the counter-rotation of the two cores due to traction or compression of the layered material in one of the directions coplanar to the layers themselves.

In a variant of the invention, at least one of the preceding claims wherein the contact surfaces of two adjacent cores of two adjacent layers are at least partially made or covered with material which has a predefined sliding friction value so as to generate a friction force when said two adjacent cores are subject to mutual rotation. The material choice and/or the friction coefficient must also be made taking into account the conformation of the device in general and of the dissipative characteristics to be obtained. The friction material can be a coating of the contact surfaces of the cores or, by way of non-limiting example, an additional layer which is intercalated to form the interface of the cores. Therefore, considering the different configurations previously exposed, i.e. flat faces as an alternative to shaped faces of the cores, the friction mechanism is controlled according to two different compression modes orthogonal to the layers, designed to recover the initial configuration. In the first case the compression is applied externally, while in the second case a specially shaped interface between the layers is exploited to induce dilatancy coupled to the relative rotation of the interlayer.

The invention also refers to a panel with high energy absorption comprising two or more layers made according to one or more of the characteristics of the metamaterial described herein. The multiple embodiments, also in the light of the different implementation dimensions, allow its application in the seismic protection of buildings, while in the industrial field in the rapid attenuation of vibrations, in the naval and aerospace fields in the attenuation of vibrations and in the containment the effects of shocks. Furthermore, preferably, the stratified material thus obtained is limited to containment plates suitable for receiving external forces and/or impacts. The layers of metamaterial are therefore contained or packed inside boundary surfaces which are in contact with the ends of said through pins and/or adjacent to the free surfaces of the cores of the outer layers and wherein, optionally, they are provided with peripheral edges in contact with one or more of the elastic ligaments of material which branch off from the cores flanking said edges.

According to a possible variant, the metamaterial layers have a chiral topology and are arranged alternately in such a way that two adjacent layers have opposite chirality.

Some examples representing possible, albeit non-limiting, embodiments of the invention are described with reference to the attached drawings, wherein:

- Figure 1 represents an elementary cell of the generic positive chirality layer with the relative geometrical parameters;

- Figure 2 represents a possible geometry of the single layer with positive chirality;

- Figure 3 represents a chiral and antichiral configuration of the unit cell of Figure 1 ; - Figure 4 represents an example of stacking of layers with alternating chirality and centered by pins;

- Figure 5 represents a schematization of the stratified material and displacements and rotation of the cells;

- Figure 6 represents the cell assembly along the pin and resulting configuration for a non-dilating type system;

- Figure 7 represents a representation of the layered system of Figure 4 homogenized and the plane stress state;

- Figure 8 represents the flat interface between the disks of two superimposed cells and the relative static and kinematic sizes;

- Figure 9 shows the elastic-dissipative response in the case of a non-dilating plane interface in a Cartesian plane of the tension/strain type;

- Figure 10 represents the uniaxial response of the non-dilating frictional model considered in the example of the previous figure;

- Figure 11 represents a three-dimensional view of a variant wherein, unlike Figure 8, there is a friction-dilating interface between the disks of two superimposed cells assembled along a common pin;

- Figure 12 represents a schematization of two adjacent cores of the previous figure and the relative static and kinematic sizes;

- Figure 13 represents the elastic-dissipative response in the case of a dilatant interface with return to the initial configuration with the absence of permanent deformations;

- Figure 14 represents the bilateral hysteretic response with return to the initial configuration with no permanent deformations;

- Figure 15a represents the uniaxial response of the dilating friction model considered in the example of figure 11 and following;

- Figure 15b represents the uniaxial response of the dilating friction model considered in the example of figure 11 and following.

The following examples refer to cells with a regular hexagonal structure, obtained with six ligaments each of equal length and uniformly arranged on the perimeter profile of a cylindrical-shaped core which is shown to result in an isotropic behavior of the metamaterial. As mentioned, the quantity of elastic ligaments provided on each core contributes, among other parameters, to obtaining the damping effect of the metamaterial and the behavior of the same when subjected to the actions of external forces and other possible forms contemplate the realization of four ligaments cells which is shown to result in an orthotropic behavior of the resulting material.

With reference to the enclosed figures, non-limiting variants of a metamaterial, a layered material are presented. Each layer 10, 20, 30 is a flat lattice/grid having a periodic microstructure whose cell 100 has the chiral topology illustrated in figure 1 (3D view at 100 and structural diagram at 100A) and consists of a central core 101 to which six elastic ligaments 102 are connected, whose geometrical parameters are indicated in figure 1 , 100B. By way of example, figure 2 illustrates the geometry of a portion of layer (further extensible) having a first chiral conformation, here indicated with a positive chirality conformation. It should be noted how the ligaments 102 of a first core are connected to the ligaments 102' of an adjacent core and this is repeated for all the cores of the layer, with the exception of the cores in an external perimeter position of the plane wherein the layer lies. The layers are stacked with opposing chirality thus obtaining a material which at the macroscopic level is isotropic in the plane of the layers and orthotropic in the direction orthogonal to them, see figure 4. The stacking is obtained by means of a pin 103 for cell passing through a pin seat or through the hole 104 located in the collar at the center of the disc. The pin has the function of exerting a uniform compression at the interface between contacting discs belonging to contiguous layers and of aligning, also due to the effect of the central collar in the disc, the displacements in the plane of stacked discs. The succession of layers with opposing ch iral-antich iral chirality is conceived to obtain differentiated response to traction/com pression states as indicated in fig- ure 3. For instance, in the configuration of figure 3, a traction TF on the positive chirality cell (β>0) causes an anti-clockwise rotation of the disk, while the same trac- tion TF' on the negative chirality cell causes a clockwise rotation. The microstructure of the resulting material is shown in figure 4, where 100 refers to a cell of a first layer while 200 refers to a second cell of a second layer and adjacent to cell 100. The elastic ligaments are such as not to create mechanical interference between adja- cent layers. The representation of figure 4 does not include any plates placed at the end of each pin having the function of tightening and therefore pre-traction of the pins with an axial force to be established according to the operation of the device, as described below.

The kinematics of the disks of stacked/overlapping layers 10, 20, 30 is illustrated in figure 5 wherein, due to the effect of the system described, the disks of the various layers connected by the same pin translate by the same amount II while the rotation differs between the layers with positive and negative chirality giving rise to a relative rotation. The layers in Figure 5 are shown as non-adherent to support the explanation of operation while they will definitely be in contact in implementations of the invention. Figure 6 shows details of the assembly of six periodic cells belonging to six contiguous layers and an exploded view of two adjacent periodic cells.

The mechanical response of the multilayer material can be described through homogenized synthetic models in the simplified but non-restrictive hypothesis of homogeneous strains and stresses. In particular, with reference to Figure 7, the plane stress state in the homogenized material is represented by the three stress components and , and the corresponding strain components ɛ ₁₁ , ɛ ₂₂ and ɛ12 ^ɛ 21 , .

In the event that the interfaces between the disks are designed in such a way as to prevent relative rotation between adjacent disks, remembering that the multilayer material is transversely isotropic, its constitutive bond in the hypothesis of hard disks is characterized by the average elastic modules being ^anc * ^E _s the elastic module of the ligaments and p the angle of chi rality. It is important to note that auxetic behavior occurs for chirality angles

The mean elastic modules can also be expressed in the following equivalent formula wherein the macro-parameters are introduced

In the opposite case wherein the relative rotations between adjacent disks are free, the stratified material retains the transversal isotropy and the average elastic modules are those of the single layer and assume the form:

The metamaterial object of the invention can dissipate mechanical energy by dissipation by frictional sliding between the disks of the adjacent layers with relative rotation Δ Φ . By exerting a controlled pre-traction N on each pin through rigid confining plates as illustrated in Figure 8, a state of normal n and tangential t stress is achieved on the flat interface 800, between the disk of the positive chirality layer 100 and the negative chirality layer 2 related by Coulomb friction with coefficient f.

The application of average stresses in the plane leads to the activation of interaction pairs between adjacent disks, the relative rotations being counteracted by the frictional forces which in turn depend on the controlled pre-traction N. As the level of stress increases, a limit condition of friction is reached, beyond which slips are activated with consequent relative rotation between the disks and dissipation of mechanical energy, partly contained by the elasticity of the microstructure of the individual layers. It is shown that the uniaxial stress determining the friction limit state and the corresponding strain are and are linearly linked by the mean elastic module E. Beyond this stress value, the relative rotations between the discs are activated with a response characterized by an increasing elastic module ET. The response to unloaded load states, valid for both traction and compression, is synthetically illustrated in Figure 9 which also shows the dissipative properties of the devised device. In this case the reversibility and therefore the reuse of the device after the impact is possible by releasing the pre-traction in the pins, thus canceling the permanent/final deformations .

Figure 9 shows the elastic-dissipative response in the case of a non-dilating plane interface.

It should be noted that the same behavior can be found for biaxial stress/strain states with adjustable mechanical energy dissipation through pre-trac- tion.

Descriptive example.

For instance, consider a device characterized by the following mechanical parameters:

Microstructure β = 30° , α = 40mm , R = 10mm , ℓ = 34.6mm , S = 1.73mm , b = 6mm , E = 2loooo\//>« ,

Interface and pin f = 0.75 , ct = 5MPa , d = 3mm which correspond to the following modules of mean elasticity E = 10931.91MPa , v = 0.2 and mean incremental elasticity E _T = 354.01 a , v _T = -0.96. The elastic-dissi- pative response of the device is summarized in figure 10.

Multilayer material: discs with dilating interfaces

In a different embodiment, the invention introduces cores/discs with dilating interfaces 1100 shown in the overall view in Figure 11. Compared to the previous diagram, the compression exerted on the discs 100, 200 through the rigid containment plates at the ends of the pins is exerted as an effect of the dilatancy induced by the relative rotation of the discs. In fact, the relative rotation A(|) induces a relative tangential displacement u which is coupled to a relative displacement v in the direction of the pin due to the sliding due to friction on the inclined plane of the angle 0.

Note the presence of ridges 104 arranged along a circular crown on the surfaces of the disc, ridges which protrude in a direction parallel to the rotational axis and in the current embodiment have a plane development of a triangular shape and in particular of an isosceles triangle with base angle 0. The isosceles triangle shape guarantees the complementarity of the surfaces of two cores in contact and the invariance of the compression or traction behavior of the layer, as well as bilaterality with return to the initial configuration.

The elastic-dissipative response with return to the initial configuration, i.e. in the absence of permanent/final deformations, is detailed in figure 13 in the case of mono-axial tension. This response is characterized by the mechanisms:

OA - unlimited load (compatibly with the resistance of the ligaments) with sliding by friction already from the initial configuration O;

AB - elastic unloading with relative rotations between the blocked discs;

BC - unloading with return scrolling until the stop of the relative accumulated rotations and the return to the initial configuration.

Specifically, this response is characterized by the average elastic modules at loading and unloading detailed in the following formula: wherein wherein the following macro-parameters are introduced being Et and At the elastic module and the transversal area of the pin, while A _cell is the area of the periodic cell.

The energy dissipated in a load-unload cycle up to the maximum load stress depends on the discharge stress in state B which results

The mechanical energy dissipated in the OABC cycle results

It is observed that if the system were hyperelastic with elastic module at the same maximum load stress it would store an energy density per unit volume equal to from which the ratio is derived which is representative of the hysteretic damping of the layered material.

It is important to highlight that since the dissipative mechanism is invariant from the direction of relative rotation, its hysteretic response is bilateral with return to the initial configuration and therefore with the absence of permanent/final deformations as detailed in figure 14 with reference to mono-axial stress states. It can also be observed that this behavior remains valid even in the case of biaxial stress states.

In the following, two detailed, non-limiting embodiments are presented, with numerical indications and positive results obtained in support of the advantages ob- tained from two of the many possible practical applications of the invention claimed herein.

Descriptive example 1.

For instance, consider a device characterized by the following mechanical parameters:

Microstructure β = 30° , α = 40mm , R = 10mm , ℓ = 34.6mm , 5 = 1.73mm , b = h = 15mm , E = 210000 Mpα

Dilatant interface and tubular aluminum pin 0.8 mm thick

0 = 15° , f = 0.75 , d = 5mm , A _t = 10.56mm ² , E = 70000. Mpa . which correspond to the following module of mean elasticity E = i093i.91 Mpα , v = 0.2 , mean elastic module at loading = 1196.2 Mpa and unloading E _V = 57.6MPα . The elastic-dissipative response of the device is summarized in figure 15a.

The volumetric density of energy dissipated in a uniaxial load-unload cycle up to the maximum load stress = 10 Mpα is d = 0.03562 N/mm ² = 35.6ikj/m ⁱ . The volumetric density of elastic energy stored in the reversible system with the module = 1196.2 Mpα with the same maximum load stress results = 0.04 is v/mm ² = 41.8/kj/m ³ . It can be deduced that the ratio between the dissipated energy density and the accumulated energy density in the elastic system is d _f /w _a = 85% .

Descriptive example 2.

For instance, consider a device characterized by the following mechanical parameters:

Microstructure β = 30° , α = 4Qmm , R = 10mm , ℓ = 34.6mm , s = 1.73mm , b = 8mm , h = 6m m = 210000 Mpα

Dilatant interface and pin in TECATRON GF40 black (Polyphenylene sul- phide) diameter 5mm

0 = 15° , f = 0.75 , d = 5mm , A _t = 19.63mm ² , E = 6500MPa . which correspond to the following module of mean elasticityE = 8198.93 Pα , v = 0.2 , mean elastic module at loading E* = 784.8 Fa and unloading E _V = 86.5MPa . The elastic-dissipative response of the device is summarized in figure 15b.

The volumetric density of dissipated energy in a uniaxial load-unload cycle up to the maximum load stress is d = 0.0518N/mm ² = 5i.8kj/m ³ . The volu- metric density of elastic energy stored in the reversible system with module = 784.8 Mpα for the same maximum load stress = 63.7kj/m ³ . It can be deduced that the ratio between the dissipated energy density and the accu- mulated energy density in the elastic system is d _f /w _a = 81% .

The results obtained demonstrate that the invention fully satisfies the require- ments: i) hysteretic response with maximum dissipation of mechanical energy; ii) possibility of reusing the device without external interventions with restoration of the initial configuration at the end of the dynamic process; iii) multi-directionality of the dissipative response; iv) bilaterality of the response, i.e. equal behavior in traction and compression.

The devised meta-device is capable of dissipating a significant energy den- sity per load-unload cycle. In the case of dilatant interface between the disks, the ability to return to the initial configuration at the end of the cycle without external interventions is demonstrated. Finally, the device is effective against states of biaxial tension indifferently for states of tension and compression.

However, it is evident that the invention must not be considered limited to the particular arrangements illustrated above, which constitute only exemplary embodiments thereof, but that different variants are possible, all within the reach of a person skilled in the art, without thereby exiting from the scope of protection of the invention itself, which is defined by the following claims.