Pentamode metamaterial with high bulk modulus

Abstract

The present invention relates to a pentamode metamaterial (1) having a plurality of unit cells (2), each unit cell (2) comprising: − a plurality of groups (3) of elongated elements (4), − at least a central core (5) from which elongated elements (4) branch off in a plurality of directions, − a plurality of core portions (5'), each core portion (5') being spaced from said central core (5) and from the other core portions (5'). For each unit cell (2): − each elongated element (4) develops between the central core (5) and one of said core portions (5'), − the elongated elements (4) of each group (3) of elongated elements branch off from the same side and / or surface of the central core (5), are spaced from each other and run parallel to each other, − the elongated elements (4) of each group (3) of elongated elements extend in a direction or in a sheaf of directions transverse to a direction or to a bundle of directions of the elongated elements (4) of one or more close or adjacent groups (3) of elongated elements, − optionally, the mass is concentrated at the central core (5). The repetition of unit cells (2) in space defines a two- or three-dimensional pentamode metamaterial structure (1).

Description

[0001] “Pentamode metamaterial with high bulk modulus”

[0002] D E S C R I P T I O N

[0003] Technical field of the invention

[0004] The present invention refers to a pentamode metamaterial provided with determined acoustic properties.

[0005] The invention regards also a product made at least partially of the pentamode metamaterial.

[0006] The invention refers also to a use of the pentamode metamaterial, or of the product made at least partially of the pentamode metamaterial, for an acoustic application, for example in water.

[0007] Moreover, the invention refers to a process of realising the pentamode metamaterial or the product made at least partially of the pentamode metamaterial.

[0008] Prior art

[0009] “Pentamode” materials (aka pentamodes) are known. The so called pentamodes (PM) are solid metamaterials which behave analogously to fluids, this means that they are only capable of bearing a pressure stress). In 1995, Milton and Cherkaev proposed pentamode materials.

[0010] With reference to the prior art regarding pentamode materials, it is typically made reliance on double cone geometries which enable to obtain very flexible joints, unfortunately at the same time they restrict the general rigidity of the metaliquid. A material of this kind having a periodic lattice formed by Face-Centred Cubic (FCC) cells and by the presence of the double cone geometry is known. In this way, the bulk modulus B of the unit cell is substantially greater than its shear modulus G; therefore, the shear waves and the compression waves are always uncoupled, in this way a material having a behavior completely similar to one of a liquid is obtained.

[0011] A more extensive research on such double cone geometries has shown the existence of a theoretical upper limit with reference to the effective bulk modulus of a cell when it is desired a G / B ratio less than a determined value, which is an index of good pentamode behavior.

[0012] Therefore, it is clear that the already existent geometries are not suitable to obtain a pentamode material sufficiently rigid and dense to approximate a liquid.

[0013] The Applicant, by studying the structures of the pentamode materials and by devising a way to improve them, has developed a new pentamode metamaterial, the purposes, characteristics and applications thereof will be described in the following.

[0014] Objects of the invention

[0015] Therefore, the main object consists of overcoming the inconveniences beforehand described with reference to the prior art.

[0016] Therefore, an object of the present invention consists of providing a pentamode metamaterial exhibiting elastic properties, particularly optimized acoustic properties.

[0017] The invention has the object to realise a pentamode metamaterial, and products made of such metamaterial, having acoustic properties which are the same as the ones of water.

[0018] These and other objects are met by a pentamode metamaterial, by a product at least partially made of such pentamode material, by a use of the pentamode metamaterial and / or by a product and process of realising the pentamode metamaterial and / or the product according to the following description, to the attached claims, and the following aspects. Summary of the invention

[0019] Aspects being an integral part of the technical contents of the present patent text are herein described. One or more of said aspects can be used for limiting the invention and / or for defining further claims during the life of the patent document.

[0020] The invention regards a material, particularly a metamaterial, whose acoustic properties are the same as the ones of a liquid, particularly water, and for this reason it can be also called “ metalwater' unlike the known pentamodes (PM), the density and the bulk modulus obtained by the invention are at least 100 higher.

[0021] Preferably, the pentamode material is a pentamode metamaterial.

[0022] The elastic properties of the pentamode metamaterial according to the invention are the same as the ones of water at low frequencies. Using such metafluid enables to obtain a material which from the acoustic point of view is the same as water except for the fact that the shape thereof is distinctly defined, the properties thereof being obtained by adjusting geometric parameters of the unit cell. The unit cell of the material according to the invention exploits a Face-Centred Cubic (FCC) geometry or a hexagonal geometry (HCP, Hexagonal Close- Packed).

[0023] Preferably, the pentamode metamaterial is three-dimensional and periodic; it can be isotropic (as water) or anisotropic.

[0024] 1 . Pentamode metamaterial provided with a plurality of unit cells, each unit cell comprising:

[0025] - a plurality of groups of elongated elements, each group of elongated elements comprising a plurality of elongated elements.

[0026] - one or more central cores from which the elongated elements branch off in a plurality of directions,

[0027] - a plurality of core portions, each core portion being spaced from said central core and from the other core portions, wherein, in or for each unit cell:

[0028] - each elongated element develops between the central core and one of said core portions,

[0029] - the elongated elements of each group of elongated elements branch off from the same side and / or surface of the central core, are spaced from each other and develop parallel to each other,

[0030] - the elongated elements of each group of elongated elements extend in a direction or in a sheaf of directions transverse to the direction or to a sheaf of directions of the elongated elements of one or more close or adjacent groups of elongated elements.

[0031] 2. Aspect according to aspect 1 , wherein the mass of the unit cell is concentrated at the central core and / or a mass center of gravity of the unit cell is displaced at the central core or in proximity to the central core.

[0032] 3. Aspect according to aspect 1 or 2, wherein the core portions spaced from the central core are peripheral core portions for a determined unit cell.

[0033] 4. Aspect according to the aspect 1 or 2 or 3, wherein the mass of the unit cell is concentrated at the central core and a part of which is distributed at the (peripheral) core portions.

[0034] 5. Aspect according to anyone of the preceding aspects, wherein the repetition of the unit cells in the space defines a two-dimensional or three-dimensional structure of the pentamode metamaterial.

[0035] 6. Aspect according to anyone of the preceding aspects, wherein core portions of close or adjacent unit cells in turn forming a central core for a close or adjacent unit cell.

[0036] 7. Aspect according to anyone of the preceding aspects, wherein the pentamode metamaterial exhibits a lattice structure, the central core and the core portions forming the nodes of the lattice.

[0037] 8. Aspect according to aspect 7, wherein the lattice has a Face-Centred Cubic (FCC) structure or a hexagonal structure (HCP) or a structure provided with a Kelvin cell.

[0038] 9. Aspect according to anyone of the preceding aspects, wherein the unit cell exhibits a density and / or mass which is / are greater at the central core than a density and / or mass defined at one or more spaced portions of the central core.

[0039] 10. Aspect according to anyone of the preceding aspects, wherein the unit cell exhibits a density and / or mass which is / are greater at the central core than a density and / or mass defined at an intermediate portion of the unit cell defined between the central core and one or core portions, elongated elements being defined in said intermediate portion.

[0040] 1 1 . Aspect according to anyone of the preceding aspects, wherein each elongated element exhibits a first end and a second end opposite to the first end, the first end being engaged to and / or constrained by the central core and the second end being engaged to and / or constrained by said core portion.

[0041] 12. Aspect according to anyone of the preceding aspects, wherein the elongated elements are rods or fibres.

[0042] 13. Aspect according to anyone of the preceding aspects, wherein the unit cell exhibits a ratio between the shear modulus and bulk modulus of about, or less than 3% and / or a bulk modulus of about, or in the order of magnitude of 3*10A9 Pascal (3 gigaPascal). As a reference, it is noted that the bulk modulus of water is 2.2*10A9 Pascal (2.2 gigaPascal).

[0043] 14. Aspect according to anyone of the preceding aspects, wherein the arrangement of the elongated elements in the space forms a determined pattern, optionally, wherein said pattern being the same for a plurality of unit cells or for all the unit cells of the material.

[0044] 15. Aspect according to anyone of the preceding aspects, wherein the pentamode metamaterial has a modular and / or periodic and / or quasi-periodic structures.

[0045] 16. Aspect according to anyone of the preceding aspects, wherein the plurality of groups of elongated elements comprises at least three or at least four groups of elongated elements.

[0046] 17. Aspect according to anyone of the preceding aspects, wherein the material exhibits a rigidity comparable with or equal to the rigidity of water or of another liquid.

[0047] 18. Aspect according to anyone of the preceding aspects, wherein the arrangement of the elongated elements of each group of elongated elements form, on a plane transverse to the main development direction of the elongated elements, a determined pattern.

[0048] 19. Aspect according to anyone of the preceding aspects, wherein a plurality of groups of elongated elements of the same unit cell, particularly all the groups of elongated elements of the same unit cell, exhibit the same determined pattern.

[0049] 20. Aspect according to anyone of the preceding aspects, wherein the determined pattern is a geometrically shaped pattern, preferably, the geometrically shaped pattern being polygonal, for example hexagonal.

[0050] 21 . Aspect according to anyone of the preceding aspects, wherein the pentamode metamaterial is two-dimensional or three-dimensional.

[0051] 22. Aspect according to anyone of the preceding aspects, wherein the pentamode metamaterial is periodic or quasi-periodic.

[0052] 23. Aspect according to anyone of the preceding aspects, wherein the unit cell exhibits a Face- Centred Cubic (FCC) geometry or a hexagonal geometry (HCP) or a Kelvin cell geometry.

[0053] 24. Aspect according to anyone of the preceding aspects, wherein each elongated element does not exhibit a double cone structure.

[0054] 25. Aspect according to anyone of the preceding aspects, wherein each elongated element exhibits a constant cross-section along its extension.

[0055] 26. Aspect according to anyone of the preceding aspects, wherein each elongated element exhibits a circular cross-section.

[0056] 27. Aspect according to anyone of the preceding aspects, wherein the metamaterial is at least partially made, particularly completely made of metal material.

[0057] 28. Aspect according to anyone of the preceding aspects, wherein the metamaterial is at least partially made, particularly completely made, of at least one among: titanium, bronze, brass, aluminum, a copper-beryllium alloy.

[0058] 29. Aspect according to anyone of the preceding aspects, wherein the metamaterial is at least partially, particularly completely of a plastic type.

[0059] 30. Aspect according to anyone of the preceding aspects, wherein the metamaterial is made by the additive manufacturing.

[0060] 31 . Product comprising at least one portion made of pentamode metamaterial according to anyone of the preceding aspects and / or attached claims.

[0061] 32. Aspect according to aspect 31 , wherein the determined portion being substantially transparent to sound.

[0062] 33. Aspect according to the aspect 31 or 32, wherein the product is modular and comprises a plurality of modules of pentamode metamaterial.

[0063] 34. Aspect according to the aspect 33, wherein the plurality of core portions of pentamode metamaterial provides male core portions and female core portions, the female core portions being configured to house corresponding male core portions for assembling said modules.

[0064] 35. Aspect according to the aspect 33 or 34, wherein the plurality of modules comprises at least one module equipped with a male connector and at least one module equipped with a female connector configured to receive the male connector.

[0065] 36. Aspect according to the aspect 35, wherein the module equipped with at least one male connector and the module equipped with at least one female connector are assembled or can be assembled together.

[0066] 37. Use for an acoustic application, of a pentamode material according to anyone of the preceding aspects or of the attached claims and / or of a product according to anyone of the preceding aspects of product or of the claims of product.

[0067] 38. Use, optionally according to the preceding aspect, of a pentamode material according to anyone of the preceding aspects or claims and / or of a product according to anyone of the preceding aspects of product or of the claims of product, wherein the acoustic application involves lensing or cloaking. 39. Use according to one of the preceding aspects of use and / or of the attached claims of use, wherein the pentamode metamaterial and / or the product is at least partially, particularly completely placed or immersed in a liquid, for example in water, said liquid being not present in the defined cavities of the metamaterial, particularly in the cavities defined by the unit cells.

[0068] 40. Use according to anyone of the aspects of use and / or the attached claims of use, which provides to immerse the pentamode metamaterial and / or the product at least partially, particularly completely, in a liquid, for example in water, said liquid being not present in the defined cavities of the metamaterial, particularly in the cavities defined by the unit cells.

[0069] 41 . Use according to one of the preceding aspects of use and / or of the attached claims of use, the use being made in a marine environment.

[0070] 42. Process of realising a pentamode metamaterial according to anyone of the preceding aspects and / or of anyone of the attached claims comprising the step of realising a plurality of said unit cells, said step comprising:

[0071] - realising the elongated elements of each group of elongated elements spaced and parallel to each other,

[0072] - optionally, concentrating the mass of the unit cell at the central core.

[0073] 43. Aspect according to aspect 42, wherein the step of realising a plurality of said unit cells is performed by additive manufacturing.

[0074] 44. Aspect according to the aspect 42 or 43, wherein the step of realising a plurality of unit cells comprises also the step of distributing, for each unit cell, the mass (or a part of which) at the core portions spaced from the central core.

[0075] 45. Aspect according to the aspect 42 or 43 or 44, wherein the process is a process of realising a product or a portion of product made of a pentamode material and provides to realise the product or portion of product of the pentamode material according to anyone of the claims of product and / or of the preceding aspects of product.

[0076] 46. Aspect according to anyone of the aspects from 42 to 45, wherein the process provides to realise a plurality of modules provided with at least one male connector and a plurality of modules with at least one female connector, each module being at least partially made of, particularly completely made of pentamode metamaterial, the modules provided with at least one male connector and the modules provided with at least one female connector being assembled and / or can be assembled together.

[0077] 47. Aspect according to anyone of the aspects from 42 to 46, wherein the plurality of core portions of pentamode metamaterial provides male core portions and female core portions.

[0078] 48. Aspect according to the preceding aspect, wherein the female core portions are configured to house corresponding male core portions in order to assemble the modules for forming the product.

[0079] 49. Process of assembling a modular product comprising the steps of:

[0080] - predisposing at least one module provided with a male connector and at least one female module of a female connector configured to house the male connector, each module being made of pentamode metamaterial according to anyone of the preceding aspects and / or of claims of pentamode metamaterial, the modules provided with at least one male and female connectors being assembleable together,

[0081] - assembling the modules provided with at least one male connector and the modules provided with at least one female connector for forming a product.

[0082] 50. Aspect according to the aspect 49, wherein the step of predisposing at least one module provided with a male connector and at least one female module of a female connector provides to predisposing at least a plurality of modules provided with at least one male connector and a plurality of modules provided with at least one female connector.

[0083] 51 . Aspect according to anyone of the preceding aspects, wherein each elongated element exhibits a characteristic dimension of the transverse cross-section (for example: a diameter or a width) which is less than a characteristic dimension of the core or core portion which is engaged with.

[0084] 52. Aspect according to the preceding aspect, wherein the characteristic dimension of each elongated element is less than at least 5 or 10 times the characteristic dimension of the core or core portion which is engaged with.

[0085] 53. Aspect according to anyone of the preceding aspects, wherein “central core” can be interchanged with “core”.

[0086] 54. Aspect according to anyone of the preceding aspects, wherein the distance between elongated elements of a same group is comparable with, and / or has the same order of magnitude of a characteristic dimension, such as a diameter, of the elongated elements.

[0087] Conventions and definitions

[0088] It is observed that in the following detailed description, corresponding parts / components / ele- ments are indicated by the same numeral references. The Figures could illustrate the object of the invention by not-to-scale representations; therefore, parts / components / elements illustrated in the attached Figures and regarding the object of the invention, could only refer to schematic representations. Using 7” in the present text means “and / or”, if it is not expressly indicated otherwise.

[0089] In the context of the present disclosure, the use of terms such as “on”, “top”, “upper”, “under”, “bottom”, “below”, “alongside”, “lateral”, “laterally”, “internal”, “internally”, “external”, “externally”, “horizontal”, “horizontally”, “vertical”, “vertically”, “frontal”, “frontally”, “posterior”, “posteriorly”, “right”, “left”, similar terms and corresponding variants refer, except for specific different indications, to at least one spatial orientation that the object of the invention can take under conditions of use; the terms refer to what the drawings show, illustrating the orientation associated to a normal use of the invention. Such terms are used only for helping the reader and are not limiting.

[0090] Except for specific different indications, the terms “condition” or “configuration” can be interchangeably used in the context of the present disclosure. The expression “said at least one” is interchangeable with “each”. The expression “each” and similar do not necessarily imply that it is made reference to a plurality of elements; for example, “each element” can refer to just one element or to a plurality of elements, based on the context where it is used and / or based on the embodiment which it refers to.

[0091] When required, in the context of the present disclosure, one or more of the following defini- tions / conventions are applicable, unless otherwise indicated and / or except for where the context excluded them:

[0092] - “metamaterial” means a material that is artificially made and provided with peculiar properties which distinguish it from other materials. Its macroscopic characteristics do not depend only on its molecular structure, but also on its constructive geometry. In other words, the properties of a metamaterial depend on its structure rather than directly from its chemical composition. In the present disclosure, the properties of interest of the metamaterial according to the invention are the elastic properties, particularly the acoustic and mechanical ones. Except where it is otherwise indicated and / or when it is excluded by the context, in the following the metamaterial can be also simply called “material”;

[0093] - the “elastic properties” which can be static or quasi-static or dynamic, can refer to mechanical, acoustic, seismic, or anti-seismic properties, etc. With reference to the dynamic properties, it is noted that at low frequencies, but not at very low frequencies, the so called band gap pentamode appears, i.e. there is only the propagation of the pressure waves but not of the shear waves. At high frequencies, the so called complete band gaps appear, i.e. frequency intervals wherein no type of waves propagates in the metamaterial.

[0094] - the metamaterial according to the invention exhibits a repeated pattern (scheme), on smaller scales of the wavelength of the acoustic phenomenon which it influences. The properties of the metamaterial do not derive from the properties of the base materials forming it (for example: titanium), but from their newly designed structures;

[0095] - “pentamode”, in particular pentamode material, means an artificial structure - particularly a three-dimensional artificial structure - which, despite being a solid, it ideally behaves as a fluid. The properties of the pentamode material which are of interest from the point of view of the present disclosure are the acoustic properties;

[0096] - in essence, the acoustic properties of a pentamode material according to the invention can be comparable with the ones of a liquid, for example water. The use of these materials enables to have a material which is acoustically equivalent to a liquid except for its shape which is distinctly defined. The object of the invention is a material whose acoustic properties are substantially identical to the ones of water (metalwater). Unlike the known pentamode materials, the density and the bulk modulus obtained by the invention are at least 100 times greater.

[0097] - the pentamode metamaterial can be anisotropic or isotropic, depending on the application which it is destined to;

[0098] - “elongated element” means an element such as a rod o fibre extending along a main development direction along which its length is defined. For an elongated element, one or more dimensions (width and / or diameter) of its cross-section preferably is / are less than one order of magnitude of its length. In some embodiments, the ratio between one or more dimensions of its cross-section and its length can be also only equal to at least 3 or at least 5;

[0099] - “product” means any physical unit or an artifact;

[0100] - “elastic application” means any application (of the pentamode material, of a product, or artifact, etc.) aimed at exploiting the elastic properties of the metamaterial according to the invention;

[0101] - “acoustic application” means any application (of the pentamode material, of a product or artifact, etc.) aimed at redirecting or deflecting or transmitting or focusing or concentrating or determining a determined path of the acoustic waves (sound);

[0102] - “acoustic lensing” or “acoustic focusing” means concentrating the sound in a point or small region. This enables to focus and amplify the sound without requiring energy; in this way, acoustic energy can be concentrated in a small region, for example by intensifying the signal coming from a distant sound source;

[0103] - “acoustic cloaking” means that the acoustic waves are caused to follow a determined path, for example, by causing them to curve or deviate or deflect, so that a sound can pass around an object;

[0104] Said conventions and definitions can be used, when required, for interpreting the claims. When appropriate, one or more of said conventions and definitions can be included in one or more of the following claims and / or in one or more of the preceding aspects, particularly when these claims and / or aspects use one or more expressions object of one or more conventions or definitions.

[0105] Brief description of the drawings

[0106] In order to better comprehend the invention and appreciate the advantages, some embodiments thereof will be described in the following with reference to the attached Figures:

[0107] A brief description of the attached Figures follows:

[0108] Figure 1 a illustrates a composition of a group of fibres. More particularly, the left top part shows a group of tight intertwined fibres, the left lower part shows a group of tight straight fibres, the right top part shows a group of loose intertwined fibres, the right lower part shows a group of loose straight fibres;

[0109] Figure 1 b schematically illustrates a deformation of a group of fibres of Figure 1 a, wherein the relative motion of the two ends is indicated by a rotation 0 and by a displacement e;

[0110] Figure 2a illustrates a representation of the cross-section of a single group of fibres of the metamaterial according to an embodiment of the invention, illustrating the arrangement of reciprocally parallel and spaced fibres, in order to form a hexagonal shape or pattern;

[0111] Figure 2b illustrates a representation of the three-dimensional geometry of a group of thin fibres of a single group of fibres of the metamaterial according to an embodiment of the invention;

[0112] Figure 3a illustrates a possible unit cell of the metamaterial according to an embodiment of the invention;

[0113] Figure 3b illustrates a variant, according to the invention, of the unit cell of Figure 3a, wherein each group of fibres exhibits a greater number of fibres with a diameter less than the fibres of the group of fibres of Figure 3a;

[0114] Figure 4 shows another possible configuration (hexagonal geometry, HCP) of the unit cell of the metamaterial according to an embodiment of the invention;

[0115] Figure 5 illustrates a module made of metamaterial according to an embodiment of the invention. The module constitutes a portion of a product and is formed by a plurality of unit cells connected to each other, the product being assembleable from at least two modules;

[0116] Figure 6 illustrates a plurality of modules of the type illustrated in Figure 5, reciprocally assembled in order to form a product.

[0117] Detailed description of embodiments of the invention

[0118] Pentamode metamaterial

[0119] The invention refers to a pentamode metamaterial. The properties of such material, which are relevant to the present disclosure, are the elastic properties, particularly (but not exclusively) the acoustic ones. The characteristics of the pentamode metamaterial are described in the following, then it is described how this innovative result was obtained

[0120] The pentamode metamaterial according to the invention exhibits a plurality of unit cells; the unit cell constitutes the “base unit” of the pentamode material. The unit cell “repeats” in the space in order to form a determined structure, for example, a periodic one. It is noted that the structure of the metamaterial can be non-periodic or quasi-periodic, as a function of the application. Therefore, the properties of the material can gradually change because the geometry of the material varies in the space (for example this is the case when the material is applied to the cloaking), based on the application.

[0121] A pentamode metamaterial according to the invention is generally indicated by the numeral reference 1 in the Figures (Figures 5 and 6), while its unit cell is indicated by the numeral reference 2; examples of a unit cell are illustrated in Figures 3a, 3b, and 4.

[0122] The unit cell, herein described, can exhibit a Face-Centred Cubic (FCC) geometry as illustrated in Figures 3a, 3b, 5, and 6 or a hexagonal geometry (HCP) as illustrated in Figure 4; it is noted that further geometries of the cell can be provided which are not illustrated in the attached Figures, such as the Kelvin cell.

[0123] The unit cell 2 comprises a plurality of groups 3 of elongated elements 4, each of them comprises a plurality of elongated elements 4. The elongated elements 4 of a same group 3 can exhibit the same length L. All the elongated elements 4 of a same unit cell 2 can exhibit the same length L (isotropic embodiment). In case of anisotropy, the lengths of the elongated elements 4 can vary between one group and another; briefly stated, different groups 3 can exhibit elongated elements 4 having different lengths L. Preferably, also in the anisotropic embodiment, the elongated elements 4 of a same group 3 can exhibit the same length L.

[0124] Preferably, each elongated element is a rod or a fibre 4 developing between a first end 4a and a second end 4b which are reciprocally opposite. The rod or fibre 4 has a length L defined between the ends 4a, 4b. The length L is substantially greater, for example of at least one order of magnitude than a characteristic dimension such as a diameter d, of the cross-section of the rod or fibre 4 (see Figures 2a and 2b); therefore, the rods or fibres 4 can be rightly called thin. However, embodiments whose length L is at least 2, or 3, or 5 times greater (anyway no more than 10 times) than a characteristic dimension, such as a diameter d of the cross-section of the rod or fibre 4, are not excluded. Preferably, each rod or fibre 4 exhibits a constant cross-section along its extension. As illustrated in the attached Figures, the cross-section can be circular and provided with a determined diameter d.

[0125] The unit cell 2 comprises at least one central core 5 (or simply “core”) from which elongated elements 4 branch off in a plurality of directions. Briefly stated, the groups 3 of elongated elements 4 branch off from the central core. The term “central” core does not necessarily refer to the position of the core in the unit cell 2; the central core (or core) is a core from which the elongated elements 4 branch off.

[0126] Further, the unit cell 2 comprises a plurality of core portions 5’, each of them is spaced from the central core 5 (is “peripheral” in other words spaced from the central core) and from the other core portions 5’.

[0127] The unit cell exhibits cavities among the elongated elements 4, the at least one central core 5 and the core portions 5’; for a correct operation of the metamaterial; air or foam or material which does not alter the elastic properties of the metamaterial can be present in such cavities.

[0128] In the embodiments illustrated in the attached Figures, the mass of the unit cell 2 is concentrated at the central core 5; however, in other embodiments, the mass distribution can be different. In other words, if it is considered a “mass centre of gravity” of the unit cell 2, it is preferably displaced near the core. With reference to a single or each unit cell 2, it must be noted that the mass of the central core 5 is greater than the mass of each single elongated element 4; particularly, the mass of the central core 5 can be greater than or equal to the sum of the mass of the group 3 of elongated elements 4 of the same unit cell 2. In some embodiments, the mass of the central core 5 can be greater than or equal to the sum of the masses of two groups 3 of elongated elements 4, still more particularly greater than or equal to the one of two groups 3 of elongated elements 4 of the same unit cell 2. Moreover, part of the mass of the unit cell 2 is distributed at the core portions 5’ spaced from the central core 5. The distance of the core portions 5’ spaced from the central core 5 is given by the length L (isotropic embodiment) or by the lengths L (anisotropic embodiment) of the elongated elements 4 interposed between them.

[0129] The repetition of the unit cells 2 in the space defines a structure of the two-dimensional or three- dimensional pentamode metamaterial 1 . In order to obtain the two-dimensional pentamode metamaterial 1 , three groups 3 of elongated elements 4 can be sufficient for the unit cell, whereas four groups 3 of elongated elements 4 can be sufficient for the unit cell for obtaining the three-dimensional pentamode metamaterial 1 . The core portions 5’ of close or adjacent unit cells 2 cooperate to form in turn a central core 5 for a close or adjacent unit cell 2.

[0130] The pentamode metamaterial 1 exhibits a lattice structure and the central core 5 and the core portions 5’ are the nodes of the lattice.

[0131] As illustrated in Figure 3a and 3b and 4, each unit cell 2 provides that:

[0132] - each elongated element 4 develops between the central core 5 and a core portion 5’ and it is engaged to or constrained by these latter, at the respective opposite ends,

[0133] - the elongated elements 4 of each group 3 of elongated elements branch off from a same part and / or surface of the central core, are spaced from each other by a distance d’ and develop parallel to each other.

[0134] As illustrated in Figure 2a, the distance d’ between the elongated elements 4 of a same group 3 is comparable (for example has the same order of magnitude) with a characteristic dimension, such as the diameter d, of the elongated elements 4.

[0135] The parallelism and the distance among the elongated elements are important; they enable to approximate the elongated elements 4 to tight ropes separated from each other.

[0136] Furthermore, as illustrated in Figures 3a and 3b and 4, each unit cell 3 provides that the elongated elements 4 of each group 3 of elongated elements develop in a direction or in a sheaf of directions transverse to a direction or to a sheaf of directions of the elongated elements of one or more groups of close or adjacent elongated elements.

[0137] The acoustic properties of such pentamode metamaterial 1 are substantially identical to the ones of water; unlike the known pentamode metamaterials, the density and the bulk modulus of the metamaterial 1 according to the invention are at least 100 times greater.

[0138] Conception of the invention and respective two-dimensional model

[0139] From the point of view of the conception of the invention, it should be stressed that the Applicant has understood that, by drawing inspiration from the different technical field of the ropes, a pentamode material 1 can be realised which can be approximated, in terms of its behavior, to water; see what follows.

[0140] Therefore, by drawing inspiration from the kinematics of ropes, the Applicant has chosen to redesign the geometry of the unit cell 2 of a periodic metamaterial 1 in an innovative way by using, as elongated elements, bundle of thin beams 4 (fibres or rods, in the following simply called “fibres”) in other words the characteristic dimension (diameter d) of their cross-section is much smaller than the respective length L.

[0141] In essence, it is proposed for the unit cell 2 a family of connections consisting of different fibres 4; the result is a mechanical element 4 whose rigidity depends on the entire length L of the connection, both when shear actions and elongation actions are applied. As illustrated in Figure 2a, such fibres 4 can be arranged so that they form a hexagonal cross-section. It is understood that the hexagonal shape of the cross-section is not limiting; it is an exemplifying shape for realising the material according to the invention.

[0142] In particular, the groups or bundles 3 are characterized by a axial rigidity substantially higher and by a shear rigidity lower than the ones of the double cone rods of the prior art, therefore enabling to overcome the beforehand cited limitations, obtaining a pentamode material having the same rigidity as the one of water.

[0143] As said before, the metamaterial according to the invention, has, as base element, a unit cell 2. The unit cell 2 comprises groups 3, each of them comprises bundles of thin fibres 4 which, once they are suitably designed and dimensioned, enable to obtain the same rigidity as the one of water. The repetition of the unit cell 2 in the space realises the metamaterial 1 (periodic structure). It is noted that the material according to invention is transparent to sound in water in a range of frequencies which have an upper limit and its acoustic signature is almost irrelevant, independent from its dimensions, since it is completely equivalent to the one of water.

[0144] In the technical field from which the Applicant has found inspiration, the cables and ropes are based on intertwined twisted sheaves of small fibres (see the top left part of Figure 1 a) which are tightened together when the cable is tight and slide on each other when it is folded. This mechanism exhibits a high axial rigidity and a substantially low shear rigidity; however, it is a challenge to produce it in small numbers.

[0145] Firstly, the structure of a cable requires to produce separately each fibres and then to gather them, so that the sheaf is tight; this step becomes very challenging when it is desired a significant number of connections, as in a lattice. This problem is solved thanks to the additive manufacturing processes, with the expedient to providing a certain space between two fibres 4 for preventing them from adhering to each other during the manufacturing process.

[0146] Secondly, the high shear compliance of a cable exploits the torsion of the fibres; when a cable is subjected to bending, each fibre is simultaneously subjected to an elongation and compression, which consequently cancel each other, since the same fibre extends both inside and outside the curve applied to the cable. However, when an intertwined bundle is loosened (see the top right part of Figure 1 a), the axial rigidity of the cable drastically decreases because the intertwined shape of each fibre easily extends or compresses itself.

[0147] In order to develop the present invention, the elastic response of a connection consisting of many thin beams parallel to each other was studied. This assembly of beams 4 will be analogously called sheaf / bundle 3 (the one that was beforehand defined as group 3 of elongated elements 4) of beams / fibres 4 (elongated elements). The following will simply analyze the two-dimensional (2D) deformation shown in Figure 1 b, which is sufficient to comprehend the concept of such mechanism.

[0148] If N is the number of fibres of a sheaf / bundle or group 3, each of them is a cylinder having a height / length L and a diameter d of the cross-section, d being much smaller than L (d«L), so that it can be considered and approximated to a thin beam. The area of the cross-section of each ith fibre is:

[0149] A = TT * d2 / 4 therefore, the axial rigidity K'Sh for the ith bundle 3 is given by the following formula:

[0150] K'ax = E*A / L and the shear rigidity K'Sh for the ith bundle 3 is given by the formula:

[0151] K'sh= 3E*A2 / L3 It is considered a cartesian reference 2D system placed on the plane of the cross-section and centred on the neutral axis of the sheaf (group of fibres), where y: is the vertical coordinate of the centre of the ith bundle. By assuming that all the fibres 4 are rigidly connected to their two ends; this approximates two rigid terminations of the sheaf. The constraint of the fibres 4 at the two ends 4a, 4b is given by the connection to the central core 5 at an end 4a and to the core portion 5’ at the opposite ends of the fibres 4. It is obtained the kinematic model by applying the displacement method of the so that it is easily established the compatibility of the beams blocked on the two planes.

[0152] Without loss of generality, the deformation of the sheaf 3 was studied in a plane containing its neutral axis. With reference to Figure 1 b, the left end of the sheaf is left on the ground, at the same the transverse displacement £ and the rotation 0 of the right end are controlled. The transverse force S and the torque T required to impose a deformation are measured at this end. The displacement method, which is applied to linear systems, enables to apply the principle of the overlapping effects, so that £ and 0 vary independently and the forces and torques required to deform the ith fibre are measured.

[0153] If (e, 0) = (1 , 0), the shear of the fibre subjected to it, is:

[0154] Si£= (12 * E / L3) * I and the torque is:

[0155] Ti£= (6 ‘ E / L2) ‘ I wherein I is the second moment of the area of the fibre cross-section.

[0156] On the contrary, when (e, 0) = (0, 1 ), the shear is:

[0157] Si6= (12 * E / L2) * I and torque:

[0158] Ti6= (E / L) * (4 * I + Ayi2)

[0159] Hence, the rigidity matrix of the sheaf is obtained by summing the forces of each fibre in case of a general deformation (e, 0): wherein it is used the equivalence:

[0160] I = ( 1 / 4 TT ) * A2which is valid for a circle. Consequently, given the distribution of the beams { y: }Ni , it is calculated the rigidity matrix.

[0161] The axial rigidity Kaxof the sheaf is very important for the effective bulk module of the lattice and therefore it can be easily calculated by:

[0162] Kax = E*AtotI L wherein Atot = n * A is the total area of the cross-section.

[0163] K is calculated when a specific axial rigidity Kaxis the right one and the number N of fibres is arbitrarily high.

[0164] Given L and E, the total area is: and the area of each fibre 4 is calculated by: A = Atot / N

[0165] By substitution, the rigidity matrix becomes: because three terms out of fourth are proportional to N1, independently from the distribution of the fibres; viceversa, the fourth term tends to the lower limit: is the only term depending on the spatial distribution of fibres.

[0166] Further, if N is high, the hypotheses about the slenderness of each fibre 4 are completely confirmed. Obviously, there are some practical constraints: for example a fibre 4 similar to a hat can not bear any relevant axial compression, since the buckling phenomenon (instability at the peak load) is critical for thin beams. This tradeoff is also more stringent if we consider manufacturing constraints. In this regard, the freedom about the distribution of the fibres 4 play a very important role.

[0167] Since, for N high, the only term different from zero is T , a torque which is applied to an end of the sheaf is balanced only by the torque which is applied at the other end of the sheaf and no shear force is generated. Therefore, the pentamode behavior is mantained, since the quasi-static effective stress of the lattice is affected only by the forces transmitted from one node to another and not by the torques. It is noted that a three-dimensional sheaf or group of fibres exploits a torsional rigidity which disappears proportionally to fV-1. The same is true for the three-dimensional (3D) lattice. The presence of the torque transmission does not affect the regime at high frequency.

[0168] Thanks to this novel connection formed by the above described fibres 4, the upper theoretical limit of the ratio between bulk B and shear moduli G of a pentamode material (see the prior art section of the present text) is eliminated; the constrain is now given by geometrical and manufacturing obstacles. According to the invention, it is possibile to simultaneouly obtain both a ratio between the shear modulus and the bulk modulus of about or less than 3% and a bulk modulus of about or of an order of magnitude of 3*10A9 Pascal (3 gigaPascal). As a reference, it is noted that the bulk modulus of water is 2,2*10A9 Pascal (2,2 gigaPascal).

[0169] In the following section, these aspects are dealt with, and further provisions for designing the unit cell 2 of the pentamode metamaterial 1 according to the invention, are given.

[0170] Realising the unit cell of the pentamode metamaterial

[0171] The complexity of the construction is mainly due to the modelling of each group 3 of fibres 4 and to the conceptualization of an efficient method of connecting them. It is required a precise axial rigidity Kaxfor each group 3 in order to obtain a pentamode material 1 , the bulk modulus thereof approaching the one of water. This depends on the area of the cross-section Atotof the sheaf or group 3 which, in turn, defines the number N of its fibres 4, once their minimum dimension is selected. In the embodiments illustrated in the attached Figures, the fibres 4 of each bundle or group 3 are arranged according to a hexagonal scheme or pattern (particularly see Figure 2a), for increasing the compactness thereof. It is clear that the scheme or pattern of the fibres 4 of a same group 3 of fibres can exhibit a shape alternative to the hexagonal one.

[0172] In the embodiments of the attached Figures, it is noted that the four groups 3 of fibres 4 (four connections) are identical to each other, therefore the same construction mechanism is repeated four times; in this regard, see Figures 3a and 3b, which show a central core 5 from which four group 3 of fibres 4 branch off, each being connected to a respective core portion 5’. Such core portions 5’ are destined to connect the unit cell 2 to adjacent unit cell 2.

[0173] The reciprocal intersections between the sheaves 3 are arranged by placing a sphere of diameter DSPHat each node of the lattice; in Figures 3a and 3b it is noted that the central core 5 can be approximated to a sphere (because it is realised by it by providing a tetrahedral shape as described in the following). Substantially, the central core 5 can be considered as a sphere cut by 4 planes or the result obtained by intersecting a tetrahedron with a sphere.

[0174] As illustrated in Figures 3a and 3b, the unit or elementary cell 2 is therefore formed by four groups 3 of fibres 4 and by two spheres 5, 5’, with a face-centred cubic lattice formed by their spatial repetition. The illustration of Figures 3a and 3b shows a sphere 5 complete at the intersection point of the four sheaves 3 and a sphere divided by four quarters (four core portions 5’) positioned at the ends of the cell 2, for ensuring a suitable connection with the adjacent cells 2.

[0175] The above description is applicable, once the necessary changes have been made, to the embodiment of Figure 4, wherein the structure has a hexagonal geometry (HCP) provided with four cores 5, where each central core 5 can be considered as a sphere cut by 4 planes.

[0176] The spheres 5, 5’ have a double purpose: must be sufficiently large to house the groups or bundles 3 of fibres 4 and to provide means for adjusting the density of the unit cells 2. It is noted that the distance of the cutting planes from the centre of the cores 5 affects the length L of each bundle, consequently affecting the ratio between shear rigidity and axial rigidity of each fibre (KaxI KSh o L2), consequently the behavior of the pentamode metamaterial 1 is potentially worsened. Increasing the diameter DSPHincreases the effective mass of cell 2. Therefore, by adjusting the spheres according to a determined thickness by using a plane orthogonal to the bundles, it is possible to recover space, by substituting them with shapes similar to tetrahedrons (see Figures 3a and 3b).

[0177] It is clear that the central core 5 can exhibit further shapes alternative to the spheric or tetrahedral ones, as long as such shapes accomplish the task of adjusting the density of the unit cells 2 and of housing the groups 3 of fibres 4.

[0178] With respect to the known pentamode metamaterials, in the pentamode metamaterial 1 according to the invention, the mass is substantially placed at the nodes of the lattice (in other words of the cores) and not at the centre of each connection, as opposed to the double cone structure described in the prior art section. On the contrary, the flexibility of the pentamode metamaterial according to the invention, is ensured by the groups 3 of fibres 4 and not by the small hinges at the nodes. This affects the dynamics of the cell.

[0179] Moreover, the “quasi-static” analysis of the unit cell 2 of the metamaterial 1 according to the invention, shows that its effective elasticity tensor substantially approximates the one which is the characteristic elasticity tensor of water. The better this approximation is the thinner the fibres 4 composing the bundles 3 will be. Instead. The frequency analysis of the same cell shows that this material 1 exhibits a wide frequency range where the pentamode behavior (the so called “PM band gap”) appears, in other words wherein only the pressure waves propagates while there is an attenuation of the shear ones.

[0180] In essence, the polarization causes only the propagation of the longitudinal waves inside the shear band gap, while the transverse modes are subjected to the Bragg scattering.

[0181] At higher frequencies, a complete band gap appears, due to the local resonance of the spheres analogously to the known mass-spring type phenomenon. Lastly, different horizontal branches overlap the upper part of the calculated dispersion diagram, caused by the resonances localized in the thin fibres constituting each sheaf.

[0182] The Applicant has realised suitable prototypes according to the above and has verified the operation of the herein described pentamode material 1 . The Applicant has produced cells made of meltable resin, having a side of about 1 cm and a minimum diameter of fibres of about 0.35 - 0.40 mm. The attached figures 5 and 6 were drawn starting from such prototypes. It is clear that the dimensions are only illustrative and not restrictive in any way; in the realised prototypes, the meltable resin is used for making a model by micro-fusion and then metal was poured in a second step.

[0183] Scalability of the invention

[0184] It is noted that the characteristic dimension of the unit cell is inversely proportional to the frequencies that are allowed to pass through the pentamode metamaterial 1 according to the invention.

[0185] Consequently, the dimensions of the herein described pentamode metamaterial are scalable, for realising products of different dimensions, as a function of the desired application.

[0186] The metamaterial 1 can be at least partially, particularly completely, made of titanium or of another material apt to the purpose of being substantially transparent from the acoustic point of view. Other materials apt to this purpose can be bronze, brass, aluminum, a copper-beryllium alloy; a suitable opitmization of the geometry of the unit cell 2 can be required as a function of the material. The material of the unit cell 2 can be selected according to the application; for example, for acoustic applications in water it is advisable the use of a metal material or of a comparable one. Moreover, the selection of the metal (or other material) depends on the rigidity and density which are desired to obtain as a function of the application. In some applications, the material of the unit cell 2 can be plastic.

[0187] Product realisable from the pentamode metamaterial

[0188] Further, the invention refers to a product 21 which is made at least partially of the pentamode material 1 .

[0189] Particularly, at least one determined portion of product 21 , which should have the determined acoustic characteristics such as the herein described ones, is made of the pentamode material 1 according to the invention.

[0190] Preferably, the portion of the product 21 made of the pentamode material 1 according to the invention is substantially transparent to sound.

[0191] Optionally, the entire product 21 can be completely made of pentamode material 1 according to the invention.

[0192] The product 21 can be of a modular type and can comprise a plurality of modules 22 of pentamode metamaterial assembleable together in order to form the same product.

[0193] The plurality of core portions 5’ of the pentamode metamaterial comprises male core portions and female core portions. The female core portions 5’ are configured to house corresponding male core portions in order to assemble the modules for obtaining the product. In essence, the product 21 can be provided with one or more modules provided with at least one male connector 23 and with one or more modules provided with at least one female connector 24 configured to house a respective male connector 23.

[0194] As illustrated in Figures 5 and 6, the female connector 24 can exhibit a seat 24a and the male connector can exhibit an engagement end 23a configured to be engaged into the seat. In order to enable to easily engage together modules provided with at least one male connector 23 and modules provided with at least one female connector 24, the seat 24a and the engagement end 23a can be countershaped to each other. In the attached Figures, both the seat 24a and the engagement end 23a exhibit a hexagonal shape; it is understood that any other shape (for example: circular or square) adapted to the purpose of the reciprocal engagement can be used. As an alternative to the described connectors 23, 24, it is possible to provide other modes to connect together the modules 22, configured to provide a material continuity (preferably without any play) and without substantial variations of impedance (for example: interlocking joints, welding, etc.)

[0195] Therefore, product 21 or a portion thereof (see Figure 6) can be realised from a plurality of components, or pieces, or portions (modules 22) such as the one illustrated in Figure 5; such product 21 can be defined as modular. In other embodiments, product 21 can be monolithic.

[0196] Use

[0197] Further, the invention refers to the use of the beforehand described pentamode metamaterial 1 or product 21 .

[0198] Preferably, the use provides an elastic application, particularly acoustic or seismic or mechanical, of the metamaterial or product according to the invention.

[0199] Possible acoustic applications can be found in the field regarding the control of the sound propagation: if the geometry of the metamaterial 1 is suitably organized as hereinbefore described, it is possible to realise an anisotropic metamaterial (fluid) and to design devices configured to be applied in the acoustic lensing, such as superlenses, waveguides, and acoustic cloaking (invisibility cloaks).

[0200] Acoustics is essential to the communication and localization in marine environments, therefore the metamaterial 1 according to the invention, which is capable of simulating the acoustic behavior of water, represents an important result and is suited to be used in many applications generally in marine environments and in water. It is understood that the metamaterial can be used with a liquid different from water, as a function of the application which is destined to.

[0201] Therefore, the metamaterial 1 or product 21 according to the invention , when used, can be placed in water, particularly it can be immersed in water. When the metamaterial according to the invention is in water, it is fundamental that water does not enter the cavities of the metamaterial 1 , particularly the cavities of the unit cell 2; substantially, the metamaterial 1 , in order to operate, must contain air (or foam or a lightweight analogous substance which does not alter the elastic performances) in the cavities defined by the unit cell 2. Examples of such analogous materials which can be present in the cavities of the unit cell in order to not distort the operation of the metamaterial and which are not allowed to be rigid, distort the elastic properties, and be excessively dissipative (they are not allowed to excessively absorb waves), are gases, determined liquids, foams, lightweight and / or soft materials. Therefore, in order to use the metamaterial in water or in another liquid by preventing this latter from entering the cavities, the metamaterial must be coated, or the cavities must be filled with the above mentioned materials. Consequently, the metamaterial 1 , when used in water, must be waterproof. In an illustrative and non-limiting way, it is noted that possible uses of the metamaterial or product according to invention can realise:

[0202] - an acoustic window underwater,

[0203] - the control of the sound propagation.

[0204] For possible mechanical applications, it is noted the following mechanical application wherein the metamaterial 1 acts as a “mechanical filter”: the metamaterial according to the invention prevents the wave from passing through it, particularly shear or transverse waves (allowing at the same time the longitudinal or pressure waves to pass through), at determined frequencies (partial pentamode stop band / band gap), or frequency ranges. With reference to possible seismic applications, it is noted that if a structure is placed in abutment with a base of the metamaterial according to the invention, such structure is completely isolated from determined oscillations of the ground; therefore, the metamaterial 1 is suited for possible anti-seismic applications.

[0205] It is understood that further applications in addition to the herein described ones can be devised and realised, particularly using the isotropic (or anisotropic) configurations in addition to the ones illustrated in the Figures.

[0206] Process of realising a pentamode material

[0207] Moreover, the present invention refers to a process of realising a pentamode material 1 of the beforehand described type.

[0208] The process comprises the step of realising a plurality of unit cells 2 as follows:

[0209] - realising the elongated elements 4 of each group 3 of elongated elements 4 spaced and parallel to each other,

[0210] - optionally, concentrating the mass of the unit cell 2 at the central core 5.

[0211] The step of realising a plurality of unit cells 2 provides to distribute, for each unit cell, 2 part of the mass of the unit cell 2 at the core portions 5’ spaced from the central core 5.

[0212] The realisation of a plurality of unit cells 2 can be performed by additive manufacturing and / or microfusion, these two techniques being particularly suitable for realising small-sized components, enabling in any case to space the elongated elements 4 of the same group 3. Alternatively, the realisation of a plurality of unit cells 2 can be performed by any other manufacturing technique enabling to realise the above described structure of the unit cell and the resultant lattice. The manufacturing technique of the pentamode metamaterial can be selected also as a function of the dimensions of the product to be realised.

[0213] Preferably, the process enables to realise a product or a portion of product made of pentamode material of the beforehand described type.

[0214] The process can comprise the realisation of a plurality of modules 22 provided with at least one male connector 23 and a plurality of modules provided with at least one female connector 24 of the beforehand described type, can be assembled together. Each module 22 is, at least partially, particularly completely, made of pentamode metamaterial 1 .

[0215] Process of assembling a modular product

[0216] Further, the invention refers to a process of assembling a modular product 21 comprising the steps of:

[0217] - predisposing at least one module 22 provided with at least one male connector 23 and with at least one module 22 provided with at least one female connector 24 configured to house the male connector 23, such modules being assembleable together and each module 22 being made of the beforehand described pentamode metamaterial 1 ,

[0218] - assembling the modules 22 provided with at least one male connector 23 and the modules provided with at least one female connector 24 in order to form a modular product 21 .

[0219] Preferably, the step of predisposing at least one module provided with at least one male connector 23 and at least one module 22 provided with at least one female connector 24 provides to predispose at least one plurality of modules provided with at least one male connector 23 and a plurality of modules provided with at least one female connector 24.

[0220] Further advantages of the invention

[0221] The shape of groups 3 of fibres 4 distributes the conformity to shear along the bonds and the mass at the nodes of the lattice: this fact distinguishing the invention from the prior art.

[0222] It is noted that according to claim 1 , each group 3 of elongated elements 4 develops from a same portion and / or surface of the central core 5, which is the same for the elongated elements 4 of the same group 3; each group 3 of elongated elements 4 consequently connects such portion / surface of the core 5 to a respective core portion 5’. In this regard, see the following Figures 3a and 3b. Such configuration is given because it enables, differently from the prior art, to decrease / modulate as desired the transverse force transmitted from each group 3 of elongated elements 4, maintaining at the same time the capability of transmitting the desired longitudinal force. Therefore, this enables, by the new submitted design, to obtain a pentamode behavior having characteristics which are better than the ones of the prior art.

[0223] Therefore, the invention enables to realise a pentamode metamaterial 1 exhibiting a mass module and a density module similar to the ones of water.

[0224] By acting on the geometric configuration of the artificial unit cell 2, the pentamode metamaterial 1 according to the invention can be improved with anisotropic properties, in order to widen its applicability to many fields requiring properties analogous to the ones of liquids, such as the acoustics field for purposes such as the acoustic lensing and acoustic cloaking.

[0225] As beforehand described, the pentamode metamaterial 1 according to the invention has, among its noteworthy advantages:

[0226] - acoustic properties (in other words density and bulk modulus or, analogously, speed of sound propagation and acoustic impedance) identical to the ones of water,

[0227] - a bulk modulus comparable with or equal to the rigidity of water,

[0228] - density and bulk modulus substantially greater (about 2 order of magnitude) than the ones of the known pentamode materials.

[0229] Final notes

[0230] The persons skilled in the art will recognize, unless where otherwise indicated in the present disclosure, that the particular sequence of described steps of the processes is only illustrative and can be changed while falling into the scope of what is herein disclosed and protected by the attached claims. Consequently, unless where otherwise indicated and except for references to specific elements / steps by the use of the same terms, the process steps can be performed with any advantageous or desirable sequence.

[0231] The protection given by the claims extends to each element, component, and / or step of the invention equivalent to the claimed one / s.

[0232] It is understood that each element, component, and / or step of the product / method in accordance with the invention, can be substituted with an equivalent element and / or step (in the following “equivalent”); such equivalent can be already existent at the filing or priority date of the present patent text or can be devised / developed in the future.

Claims

C L A I M S1 . Pentamode metamaterial (1 ) having a plurality of unit cells (2), each unit cell (2) comprising:- a plurality of groups (3) of elongated elements (4), each group (3) of elongated elements (4) comprising a plurality of elongated elements (4),- at least a central core (5) from which elongated elements (4) branch off in a plurality of directions,- a plurality of core portions (5'), each core portion (5') being spaced from said at least one central core (5) and from the other core portions (5'), wherein, for each unit cell (2):- each elongated element (4) develops between said at least one central core (5) and one of said core portions (5'),- the elongated elements (4) of each group (3) of elongated elements (4) branch off from the same side and / or surface of said at least one central core (5), are spaced from each other and run parallel to each other,- the elongated elements (4) of each group (3) of elongated elements (4) extend in a direction or in a sheaf of directions transverse to a direction or to a sheaf of directions of the elongated elements (4) of one or more close or adjacent groups (3) of elongated elements (4), and in which the repetition of unit cells (2) defines a two-dimensional or three-dimensional structure.

2. Pentamode metamaterial according to claim 1 , wherein the mass of the unit cell (2) is concentrated at said at least one central core (5) and / or a mass centre of gravity of the unit cell (2) is displaced at or near the central core (5), preferably in which the unit cell (2) has a density and / or mass which is greater at said at least one central core (5) than a density and / or mass defined at one or more portions spaced from said at least one central core (5).

3. Pentamode metamaterial according to claim 1 or 2, each elongated element (4) having a first end (4a) and a second end (4b) opposed to the first end (4a), the first end (4a) being engaged to and / or constrained by said at least one central core (5) and the second end (4b) being engaged to and / or constrained by said core portion (5').

4. Pentamode metamaterial according to claim 1 or 2 or 3, in which the elongated elements (4) are rods or fibres, preferably the rods or fibres having a constant cross-sectional area along their extension (L).

5. Pentamode metamaterial according to any of the preceding claims, in which each elongated element (4) has a circular cross-section.

6. Pentamode metamaterial according to any of the preceding claims, in which the unit cell presents: a ratio of shear modulus to bulk modulus around, or less than, 3%, and a bulk modulus about, or in the order of magnitude of, 3*10A9 Pascal (3 gigaPascal).

7. Pentamode metamaterial according to any of the preceding claims, having a modular and / or periodic or quasi-periodic structure.

8. Pentamode metamaterial according to any one of the preceding claims, wherein the plurality of groups (3) of elongated elements (4) comprises at least three or at least four groups (3) of elongated elements (4).

9. Pentamode metamaterial according to any one of the preceding claims, wherein the arrangement of the elongated elements (4) of each group (3) of elongated elements (4) forms, on a plane transverse to a main direction of development of the elongated elements (4), a determined pattern,optionally, in which a plurality of groups (3) of elongated elements (4) of the same unit cell (2), in particular all groups (3) of elongated elements (4) of the same unit cell (2), have the same determined pattern.

10. Pentamode metamaterial according to claim 9, where the given pattern is a geometrically shaped pattern, preferably the geometrically shaped pattern being polygonal, e.g. hexagonal.1 1 . Product (21 ) comprising at least one portion made of pentamode metamaterial (1 ) according to any one of the preceding claims, preferably said portion being substantially transparent to sound.

12. Product according to claim 1 1 , in which:- the product (21 ) is modular and comprises a plurality of modules (22) in pentamode metamaterial (1 ),- the plurality of modules (22) comprises at least one module equipped with a male connector (23) and at least one module equipped with a female connector (24) configured to receive the male connector (23),- the module equipped with at least one male connector (23) and the module equipped with at least one female connector (24) are assembled and / or can be assembled together.

13. Use, for an elastic or acoustic or mechanical or seismic application, of a pentamode metamaterial (1 ) according to any one of claims 1 to 10 and / or of a product (21 ) according to claim 1 1 or 12.

14. Use according to claim 13, wherein the acoustic application involves acoustic lensing or cloaking, preferably in which the pentamode metamaterial (1 ) and / or the product (21 ) is at least partially, in particular completely, placed or immersed in a liquid, in particular in water, said liquid not being present in the cavities defined by the unit cells (2).

15. Process of realising a pentamode metamaterial (1 ) according to any one of claims 1 to 10 and / or a product (21 ) according to claim 1 1 or 12, comprising the step of realising a plurality of said unit cells (2), said step comprising:- realising, spaced parallel to each other, the elongated elements (4) of each group (3),- optionally, concentrate the mass of the unit cell (2) at said at least one central core (5), optionally the step of realising a plurality of such unit cells (2) being carried out by additive manufacturing.

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