ES2907514A1 - Meta-metamaterial and metamaterial unit formed from that cell unit (Machine-translation by Google Translate, not legally binding) - Google Patents

Abstract

Cell unit of metamaterial and metamaterial formed from said unit cell. Cell unit (c) of metamaterial in the form of straight hexagonal prism, provided with oblique beams joined together forming: a first group of nodes (B1, B2, B3, B4, B5, B6) arranged on a central horizontal plane (P) and that define the interior vertices of a star; a second group of nodes (S1, S2, S3, S4, S5, S6) that define the outer vertices of the star, and are located vertically alternately above and below the horizontal plane (P); and a third group of nodes (M1, M2) auxiliaries arranged vertically above and below the horizontal plane (p) (Machine-translation by Google Translate, not legally binding)

Description

DESCRIPTION

UNIT CELL OF METAMATERIAL AND METAMATERIAL FORMED FROM

OF SAID UNIT CELL

TECHNICAL SECTOR

The present invention belongs to the sector of the design and manufacture of materials, specifically to the field of metamaterials.

More particularly, the main object of the invention is a unit cell of metamaterial whose geometry and final macroscopic properties depend on variable geometric parameters. This allows generating metamaterial unit cells that maintain a given external shape and connectivity, but whose final macroscopic mechanical and/or electromagnetic properties can be varied widely, at will. In this way, it is possible to create, for example, a metamaterial with gradients in its Poisson's modulus mechanical property.

BACKGROUND OF THE INVENTION

In recent years, metamaterials have gained importance in different fields of research. However, the first studies of these materials date from the late nineteenth and early twentieth centuries. And already in the 21st century they have been enhanced with the emergence of 3D printing methodologies, which has generalized their use in the industry.

Metamaterials are a class of artificial materials whose mechanical and/or electromagnetic properties depend mainly on the geometry of their microstructure, rather than on their chemical composition. In this way, starting from the same base material, the geometry of its microstructure can be designed in such a way that the resulting metamaterial is specifically endowed with certain final properties and concrete functionalities.

For this reason, metamaterials currently have great potential in numerous different industries and applications, since they can be designed with a specific geometry that gives them certain characteristics, even characteristics that are not found in conventional materials, which opens a door to multitude of applications: engineering, medical, etc. Not only do they allow you to work on new concepts and ideas, but they will also make it possible to improve existing technologies.

The appearance of additive manufacturing (or 3D printing) has also played an important role in the rise of metamaterials, since this technology has become the main way of manufacturing this type of material, since it allows geometrically complicated structures to be achieved. accurately enough.

Considerable improvements have appeared in the technical field of additive manufacturing in recent years. In fact, both the manufacturing techniques themselves and the software used in this technology have been substantially improved.

Metamaterials usually have an ordered microstructure that results from the repetition in space of a basic unit, called a “unit cell”. Said unit cell of metamaterial usually comprises a plurality of bars (or beams) that are joined together forming nodes and give rise to a structure with a predetermined geometry.

In most cases, to manufacture the metamaterial, different unit cells are successively joined together, giving rise to a horizontal layer. Also, several of these horizontal layers are grouped -in turn- vertically with each other, to give rise to a portion of metamaterial.

Currently there are different metamaterial unit cell configurations with good properties. The problem with these cells is that their design is fixed, so their properties can only be changed by using another material at the time of manufacture.

In the field of metamaterials, there is therefore a need to develop new metamaterial unit cells that overcome these limitations of the state of the art.

DESCRIPTION OF THE INVENTION

The present invention aims to overcome the problems and disadvantages of the prior art, mentioned above.

To this end, a first object of the present invention refers to a unit cell of metamaterial in the shape of a right hexagonal prism, provided inside with oblique beams, characterized in that said beams are joined together forming:

- a first group of nodes arranged on a central horizontal plane, each of said nodes being located so as to define an interior vertex of a star,

- a second group of nodes, each of said nodes being arranged in such a way as to define an outer vertex (or point) of the star, each of said nodes also being located vertically, alternately, above and below the plane central horizontal; Y

- a third group of auxiliary nodes arranged vertically above and below the central horizontal plane.

This metamaterial unit cell according to the present invention is orthotropic. That is, it has mutually orthogonal axes, with double rotational symmetry, so that its mechanical properties are different in the directions of each of these axes.

Preferably, the metamaterial unit cell according to the present invention comprises two auxiliary nodes, the first of said auxiliary nodes being arranged vertically at a first predetermined distance (hereinafter called Djoint) below the central horizontal plane and the second of said nodes being auxiliaries arranged vertically at said first predetermined distance (Djoint) above the central horizontal plane.

More preferably, the first predetermined distance (Djoint) is determined by:

hlayers

Djoint = v i ^{* --------- -----------}

Where

vi is a parameter between 0.8 and 0.8; Y

Hlayers is the height between layers of the metamaterial.

Also preferably, the second group of nodes comprises six different nodes, each of said nodes being located alternately vertically, above and below a second predetermined distance (hereinafter called Heightstar) from the central horizontal plane.

More preferably, the second predetermined distance (Heightstar) is determined by:

Heightstar = v 2 * Djoint

Where v2 is a parameter between 0 and 0.5.

Therefore, in the embodiments of the metamaterial unit cell according to the present invention described above, its macroscopic mechanical behavior is determined by the following geometric parameters:

- The shape of the star in plan that defines the central beams of the unit cell forming the first group of nodes, controlled by the variable Dstar, - the height at which the nodes of the second group are found (which form the general hexagonal section ), controlled by the Heightstar variable, and

- the height of the auxiliary nodes of the third group (which join all the beams that start from the interior of the star), controlled by the Djoint variable.

The metamaterial unit cells according to the present invention change size, deforming slightly, when subjected to a load. The direction The preferred loading of said unit cells of the invention is the z (or vertical) direction. Depending on the values chosen for each geometric parameter, the positions of the nodes will change and with it their behavior against a load. However, the way loads are transmitted is generic regardless of the parameters. In this way, maintaining the same unit cell structure and only varying said characteristic geometric parameters, metamaterial unit cells with very different mechanical properties can be obtained, such as, for example: Young's modulus and Poisson's ratio.

In this way, the present invention allows the design of metamaterials that have predetermined final macroscopic mechanical and/or electromagnetic properties, without it being necessary to vary the structure of the unit cells that make up said metamaterial.

Likewise, thanks to the present invention it is also possible to obtain portions of metamaterial, whose structural properties are not constant, but rather vary in a predetermined manner along one or more zones thereof (for example, defining a gradient). To do this, it suffices to gradually vary the characteristic geometric parameters of the unit cells belonging to these zones.

The fact that all the bars (or beams) of the unit cells according to the invention are oblique facilitates their manufacture by 3D printing, since the appearance of errors is minimised, as they do not have horizontal or low-inclination elements.

BRIEF DESCRIPTION OF THE DRAWINGS

To complement the description that is being made and in order to help a better understanding of the characteristics of the invention, a set of drawings is attached as an integral part of said description, where for illustrative and non-limiting purposes, the following has been represented: Next:

Figure 1.- Shows a 3D view of a first embodiment of a metamaterial unit cell according to the present invention and with a sign Poisson's ratio positive.

Figure 2.- Shows a 3D view of a second embodiment of a metamaterial unit cell according to the present invention, with a negative Poisson's ratio (auxetic behavior).

Figure 3.- Shows a front view of the cell represented in Figure 1.

Figure 4.- Shows a plan view of the unit cell represented in Figure 1.

Figure 5.- Is a schematic plan view that represents a sample of metamaterial according to the second aspect of the invention, formed from the group of unit cells according to the first aspect of the invention.

Figure 6.- shows an image belonging to an stl type file, which is used to introduce the metamaterial model in an additive manufacturing machine or 3D printer for its manufacture.

PREFERRED EMBODIMENT OF THE INVENTION

Throughout this description, as well as in the figures, the elements with the same or similar functions will be designated with the same numerical references.

A first embodiment of unit cell (C) of metamaterial according to the present invention is illustrated in Figures 1, 3 and 4, and gives rise to a material with a positive Poisson's ratio.

The nodes corresponding to the first group are designated with the references B1, B2, B3, B4, B5, B6 and are arranged on the central horizontal plane P. Each of said nodes of the second group B1, B2, B3, B4, B5 and B6 defines one of the inner vertices of a star (plan view and shown in Fig. 3).

Likewise, the nodes corresponding to the second group are designated with the references S1, S2, S3, S4, S5, and S6. Said nodes S1 to S6 define the outer vertices of the star, and are located vertically, alternately, above and below the central horizontal plane (P) at a Heightstar height.

Finally, the auxiliary nodes, corresponding to the third group, are designated with the references M1 and M2, one of them (M1) being arranged above the central horizontal plane P and the other (M2), below it at a height Djoint .

Figure 2 shows a second embodiment of a unit cell C of metamaterial according to the present invention, which gives rise to a material with a Poisson's ratio of negative sign (that is, it exhibits auxetic behaviour).

The dimensions of the unit cells C shown in Figures 1 to 4 along the three space directions are defined by the x, y, z axes.

As can be seen in Figures 1 to 4, the different beams that form the unit cells C of the invention can be separated into various groups, depending on the function they perform and their position. Each group of beams has been indicated with a different color, and its function is as described below:

• Red (Type 0). It corresponds to the beams that form the central star of cell C. This area is the one that will differentially increase or decrease in size when the cell is loaded.

• Green and orange (Type 1). They are the beams in charge of transmitting the loads to the central part of cell C through the nodes (M1 and M2) and auxiliary beams.

• Gray (Type 2). They are the auxiliary beams that connect the interior nodes of the star with the auxiliary nodes.

The metamaterial unit cell (C) according to the invention receives external vertical loads through the upper (indicated in green in the figures) and lower (orange) Type 1 beams. Specifically, it is the nodes at the ends of these beams that move, so they move the auxiliary central nodes. As these are displaced, and through the Type 2 beams (grey), the interior vertices of the star are displaced. Depending on the conditions of the load case and the characteristics of the cell, the star section will increase or its surface will decrease, that is, the dimensions of the cell that are perpendicular to the vertical load will be altered, increasing or decreasing.

As explained above, it is possible to dimension the unit cells C of the invention, in such a way that the Poisson's Ratio of the resulting metamaterial has the sign that we want. More particularly:

• Coef. positive poisson. This case corresponds to Figure 1. When unit cell C is compressed, it expands in directions perpendicular to the vertical direction (Z). Given the particular position in which the central auxiliary nodes M1 and M2 are arranged (visible in said Fig. 1), the section of the star increases. Therefore, in case of subjecting the cell to traction, the section would decrease; Y

• Coef. Negative Poisson. This case corresponds to Figure 2. In it, by compressing the cell and, due to the auxetic nature of the unit cell, the dimensions perpendicular to the vertical direction will also be reduced. By placing the auxiliary nodes in opposite positions ( the upper node is in the lower half of the cell, and the lower node in the upper half), they generate an effect contrary to the geometry of Figure 1. If instead of compressing, a tensile stress is applied, the response it would be the opposite of compression and an expansion and an increase in the section are produced.

To design the metamaterial, the macroscopic geometric values do not vary despite the change in the mechanical properties of the unit cell. These control the macroscopic geometry of the piece that you want to design with the metamaterial. Its values for a cubic sample are the dimensions of the sample in the 3 directions of space and the dimensions in x, y, z of the unit cell that will define the macroscopic density and stiffness. One of these dimensions is called Hlayers.

In the unit cells C of metamaterial shown in figures 1 to 4, the following main geometric parameters are those that determine the final properties and those that are varied to see the evolution of these values:

Hlayers: is the height between layers of the metamaterial. This value directly influences the number of layers that the material sample will have, since it is calculated with this parameter and with the desired size of the sample in the z direction as follows:

s

c ^{= ----------------------} hlayers

- c is the number of layers of the metamaterial.

- s is the size of the sample in the z direction.

Djoint: controls the position of auxiliary nodes that are on the central axis of the unit cell. Its formula is as follows:

hlayers

Djoint = vi * -----------

The value of vi is arbitrarily between -0.8 and 0.8 and, as can be seen in the expression of its formula, it depends directly on the value of Hlayers, specifically half of it. This is so that the position of the auxiliary nodes does not go outside the cell itself. Despite this, if v1=1 the positions would coincide with the upper and lower limits of the cell. For this reason it is limited to 0.8 to leave a 20% safety margin.

Heightstar: is in charge of controlling the vertical “zigzag” that the vertices of the star present. It depends directly on Djoint as you can see from its expression:

Heightstar = v 2 * Djoint

Where v2 takes values from 0 to 0.5.

Dstar: is the percentage of the apothem of the hexagon that defines the input of the star.

The table below shows the possible values of the module

Young and Poisson's modulus characteristic of a metamaterial according to the present

invention, depending on the values that the Djoint geometric variables take,

Hlayers, Stepx, Stepy, Heightstar and Dstar that characterize its unit cell.

Poisson-Young

Djoint Hcapas Stepx Stepy Heightstar E

Xz yz (MPa) (mm) (mm) (mm) (mm) (mm)

Xzyz(MPa)

1.20 3.00 1.00 1.00 0.00 0.50 1.70 1.53 232.95 0.60 3.00 1.00 1.00 0.00 0.50 1.19 1.26 292.32 1, 00 2.50 1.00 1.00 0.00 0.50 0.88 0.88 121.94 0.00 3.00 1.00 1.00 0.00 0.70 0.81 0.73 716.23 0.00 3.00 1, 00 1.00 0.00 0.70 0.81 0.73 716.23 0.00 3.00 1.00 1.00 0.00 0.70 0.81 0.73 716.23 0.00 3.00 1.00 1.00 0.00 0.70 0.81 0.73 716.23 0.00 3.00 1.00 1.00 0.00 0.70 0.81 0.73 716.23 0.50 2.50 1.00 1.00 0.00 0 .50 0.50 0.62 170.81 0.80 2.00 1.00 1.00 0.00 0.50 0.51 0.57 83.02 0.40 2.00 1.00 1.00 0.00 0 .50 0.26 0.35 120.94 0.00 3.00 1.00 1.00 0.00 0.50 0.49 0.30 447.53 0.00 3.00 1.00 1.00 0.00 0.50 0, 49 0.30 447.53 0.00 3.00 1.00 1.00 0.00 0.50 0.49 0.30 447.53 0.00 3.00 1.00 1.00 0.00 0.50 0.49 0.30 447.53 0.00 3.00 1.00 1.00 0.00 0.50 0.49 0.30 447.53 0.80 2.00 1.00 1.00 0.00 0.20 0.44 0.25 111.69 0 .50 2.50 1.00 1.00 0.00 0.20 0.45 0.24 146.15 0.40 2.00 1.00 1.00 0.00 0.20 0.29 0.16 102.09 0 .00 2.50 1.00 1.00 0.00 0.70 0.08 0.13 152.41 0.00 2.50 1.00 1.00 0.00 0.70 0.08 0.13 152.41 0.00 2.50 1 .00 1.00 0.00 0.70 0.08 0.13 152.41 0.00 2.50 1.00 1.00 0.00 0.70 0.08 0.13 152.41 0.00 2.50 1.00 1.00 0 .00 0.70 0.08 0.13 152.41 0.80 2.00 1.00 1.00 0.00 0.10 0.28 0.12 133.09 -0.80 2.00 1.00 1.00 0.00 0.70 0.20 0.11 110.68 -0.50 2.50 1.00 1.00 0.00 0.70 0.21 0.10 183.81 0.50 2.50 1.00 1.00 0 .00 0.10 0.28 0.10 143.79 0.00 2.00 1.00 1.00 0.00 0.70 0.03 0.08 101.33 0.00 2.00 1.00 1, 00 0.00 0.70 0.03 0.08 101.33 0.00 2.00 1.00 1.00 0.00 0.70 0.03 0.08 101.33 0.00 2.00 1.00 1, 00 0.00 0.70 0.03 0.08 101.33 0.00 2.00 1.00 1.00 0.00 0.70 0.03 0.08 101.33 0.00 2.50 1.00 1.00 0.00 0.50 0.11 0.07 157.22 0.00 2.50 1.00 1.00 0.00 0.50 0.11 0.07 157.22 0.00 2.50 1.00 1.00 0.00 0.50 0.11 0.07 157.22 0.00 2.50 1.00 1.00 0.00 0.50 0.11 0.07 157.22 0.00 2.50 1.00 1.00 0.00 0.50 0.11 0.07 157.22 -0.40 2.00 1 .00 1.00 0.00 0.70 0.09 0.07 120.07 0.40 2.00 1.00 1.00 0.00 0.10 0.19 0.07 98.16 0.00 2, 00 1.00 1.00 0.00 0.50 0.05 0.04 111.15 0.00 2.00 1.00 1.00 0.00 0.50 0.05 0.04 111.15 0.00 2, 00 1.00 1.00 0.00 0.50 0.05 0.04 111.15 0.00 2.00 1.00 1.00 0.00 0.50 0.05 0.04 111.15 0.00 2, 00 1.00 1.00 0.00 0.50 0.05 0.04 111.15 0.00 3.00 1.00 1.00 0.00 0.20 0.08 0.02 145.12 0.00 3.00 1.00 1.00 0.00 0.20 0.08 0.02 145.12 0.00 3.00 1.00 1.00 0.00 0.20 0.08 0.02 145.12 0.00 3.00 1.00 1.00 0 .00 0.20 0.08 0.02 145.12 0.00 3.00 1.00 1.00 0.00 0.20 0.08 0.02 145.12 0.00 2.50 1.00 1.00 0.00 0, 20 0.04 0.01 99.89 0.00 2.50 1.00 1.00 0.00 0.20 0.04 0.01 99.89 0.00 2.50 1.00 1.00 0.00 0.20 0.04 0.01 99.89 0.00 2.50 1.00 1 .00 0.00 0.20 0.04 0.01 99.89 0.00 2.50 1.00 1.00 0.00 0.20 0.04 0.01 99.89 0.00 2.00 1.00 1.00 0, 00 0.20 0.03 0.01 82.26 0.00 2.00 1.00 1.00 0.00 0.20 0.03 0.01 82.26 0.00 2.00 1.00 1 .00 0.00 0.20 0.03 0.01 82.26 0.00 2.00 1.00 1.00 0.00 0.20 0.03 0.01 82.26 0.00 2.00 1.00 1.00 0.00 0.20 0.03 0.01 82.26 0.00 2.00 1.00 1.00 0.00 0.10 0.02 0.01 66.44 0.00 2 .00 1.00 1.00 0.00 0.10 0.02 0.01 66.44 0.00 2.00 1.00 1.00 0.00 0.10 0.02 0.01 66.44 0.00 2 .00 1.00 1.00 0.00 0.10 0.02 0.01 66.44 0.00 2.00 1.00 1.00 0.00 0.10 0.02 0.01 66.44 0.00 2.50 1.00 1.00 0.00 0.10 0.02 0.01 78.78 0.00 2.50 1.00 1.00 0.00 0.10 0.02 0.01 78.78 0.00 2.50 1.00 1 .00 0.00 0.10 0.02 0.01 78.78 0.00 2.50 1.00 1.00 0.00 0.10 0.02 0.01 78.78 0.00 2.50 1.00 1.00 0, 00 0.10 0.02 0.01 78.78 0.00 3.00 1.00 1.00 0.00 0.10 0.03 0.00 103.08 0.00 3.00 1.00 1.00 0.00 0.10 0.03 0.00 103.08 0.00 3.00 1.00 1.00 0.00 0.10 0.03 0.00 103.08 0.00 3.00 1.00 1.00 0.00 0.10 0.03 0 .00 103.08 0.00 3.00 1.00 1.00 0.00 0.10 0.03 0.00 103.08 -0.80 2.00 1.00 1.00 -0.08 0.70 0.08 - 0.01 118.61 -0.60 3.00 1.00 1.00 0.00 0.10 - 0, 21 -0.04 193.76 -0.40 2.00 1.00 1.00 0.00 0.10 -0.15 -0.05 113.32 -0.50 2.50 1.00 1.00 0.00 0.10 - 0.20 -0.06 158.71 -0.80 2.00 1.00 1.00 0.00 0.10 -0.23 -0.07 170.38 - 1.00 2.50 1.00 1.00 0 .00 0.10 -0.27 -0.08 254.35 -0.40 2.00 1.00 1.00 - 0.10 0.70 -0.07 -0.09 141.17 -0.50 2.50 1, 00 1.00 -0.13 0.70 0.03 - 0.11 224.10 -0.40 2.00 1.00 1.00 -0.04 0.10 -0.23 - 0.11 111.76 -0 .40 2.00 1.00 1.00 0.00 0.20 - 0.21 -0.13 130.93 -0.50 2.50 1.00 1.00 -0.05 0.10 -0.30 -0 .13 154.04 -0.40 2.00 1.00 1.00 0.00 0.50 0.00 -0.14 162.56 -0.60 3.00 1.00 1.00 0.00 0, 20 -0.35 -0.17 222.74 -0.50 2.50 1.00 1.00 0.00 0.20 -0.30 -0.18 179.79 -0.80 2.00 1.00 1.00 0 .00 0.50 -0.03 -0.19 163.92 -0.80 2.00 1.00 1.00 0.00 0.20 -0.34 -0.19 174.96 -0.40 2, 00 1.00 1.00 -0.16 0.70 -0.17 -0.19 161.39 -0.80 2.00 1.00 1.00 - 0.20 0.70 -0.08 - 0, 20 138.90 -0.40 2.00 1.00 1.00 -0.04 0.20 -0.30 - 0.20 132.59 -0.60 3.00 1.00 1.00 -0.06 0, 200 .38 - 0.20 223.92 -0.40 2.00 1.00 1.00 -0.10 0.10 -0.34 - 0.20 115.29 -0.40 2.00 1.00 1.00 - 0.04 0.50 - 0.11 - 0.22 170.36 - 1.00 2.50 1.00 1.00 0.00 0.20 -0.43 -0.24 254.21 -0.50 2.50 1, 00 1.00 -0.20 0.70 - 0.10 -0.24 264.33 -0.50 2.50 1.00 1.00 -0.13 0.10 -0.44 -0.25 154.18 -0, 50 2.50 1.00 1.00 -0.05 0.20 -0.40 -0.27 180.41 -0.40 2.00 1.00 1.00 -0.20 0.70 -0.25 -0.27 176.46 -0.40 2.00 1.00 1.00 -0.16 0.10 -0.43 -0.28 122.37 -0.40 2.00 1.00 1.00 - 0.10 0.20 -0.42 -0.30 139.26 -0.40 2.00 1.00 1.00 - 0.20 0.10 -0.49 -0.32 127.38 -0.40 2.00 1.00 1.00 - 0.10 0.50 -0.25 -0.33 187.23 -0.50 2.50 1.00 1.00 -0.25 0.70 -0.19 - 0.33 292.77 -0.50 2.50 1.00 1.00 - 0.20 0.10 -0.56 -0.35 158.94 -0.80 2.00 1.00 1.00 -0.08 0, 50 -0.26 -0.37 177.00 -0.40 2.00 1.00 1.00 -0.16 0.20 -0.52 -0.38 148.17 -0.50 2.50 1, 00 1.00 -0.13 0.20 -0.54 -0.38 185.43 -0.80 2.00 1.00 1.00 -0.32 0.70 -0.24 -0.40 166.32 -0.40 2.00 1.00 1.00 - 0.20 0.20 -0.58 -0.42 154.14 -0.40 2.00 1.00 1.00 -0, 16 0.50 -0.38 -0.45 208.80 -0.50 2.50 1.00 1.00 - 0.20 0.20 - 0.66 -0.47 192.11 -0.50 2.50 1.00 1.00 -0.13 0.50 -0.32 -0.51 277 .85 -0.50 2.50 1.00 1.00 -0.25 0.20 -0.72 -0.52 196.13 - 1.00 2.50 1.00 1.00 - 0.10 0.50 - 0.34 -0.52 256.91

The positions of the different nodes of a unit cell C according to any of figures 1 to 4, given in the form of coordinates, can be obtained from the coordinates of the center of the cell (xc, yc, zc) as described below :

• Group of nodes M:

or M1:

Xmi-Xc

yMi - yc

Z e - Zc ^Djoint

or M2:

XM2-xc

yM2 - yc

Z ^{m two} - Zc - Djoint •

• Group of nodes S:

or S1:

■ xS1 - xc stepx

■ ys1 - yc

■ zS1 - zc Heightstar

or S2:

■ xS2 - xc step x / 2

■ yS ^two -yc- stepy

■ zS2 - zc - Heightstar

or S3:

■ X ^s 3 - Xc - stepx / 2

■ yS ³ -yc-stepy

zS3 = zc Heightstar

or S4:

x ^S4 = Xc - stepx

ys4 = yc

zS4 = zc - Heightstar

or S5:

XS ⁵ =Xc-stepx/2

yS5 = yc stepy

zS5 = zc Heightstar

or S6:

xS6 = Xc step x / 2

yS6 = yc stepy

zS6 = zc - Heightstar

Node group B:

or B1:

xB1 = (2 - Dstar) * xc -(1- Dstar) * (xs6+ xs5) / 2 yBi = (2 - Dstar) * yc -(1- Dstar) * (yS6+ yS5) / 2 zB1 = (2 - Dstar ) * zc -(1- Dstar) * (zs6+ zs5) / 2 or B2:

xB2 = (2 - Dstar) * xc -(1- Dstar) * (xs6+ xs ¹ ) / 2 y ^B2 = (2 - Dstar) * yc -(1- Dstar) * (ys6+ ys ¹ ) / 2 zB2 = ( 2 - Dstar) * zc -(1- Dstar) * (zs6+ zs ¹ ) / 2 or B3:

xB3 = (2 - Dstar) * xc -(1- Dstar) * (xs ² + xs ¹ ) / 2 yB ³ = (2 - Dstar) * yc -(1- Dstar) * (ys ² + ys ¹ ) / 2 zB3 = (2 - Dstar) * zc -(1- Dstar) * (zs ² + zs ¹ ) / 2 or B4:

xB4 = (2 - Dstar) * xc -(1- Dstar) * (xs ² + xs3) / 2 y ^B4 = (2 - Dstar) * yc -(1- Dstar) * (ys ² + ys3) / 2 zB4 = (2 - Dstar) * zc -(1- Dstar) * (zs ² + zs3) / 2 or B5:

xB5 = (2 - Dstar) * xc -(1- Dstar) * (xs4+ xs3) / 2 yB ⁵ = (2 - Dstar) * yc -(1- Dstar) * (ys4+ ys3) / 2 ■z ^B5 = (2 - Dstar) * zc -(1- Dstar) * (zS4+ zS ³ ) / two

or B6:

■ Xb6 = (2 - Dstar) * Xc -(1- Dstar) * (xs ⁴ + X's ⁵ ) / two

■ Yb6 = (2 - Dstar) * yc -(1- Dstar) * (ys ⁴ + ys ⁵ ) / two

■ Z ^b 6 = (2 - Dstar) * Zc -(1- Dstar) * (zs4+ Zs5) / 2

Once you have the coordinates of the nodes, you can proceed to join them using the different types of beams:

■ Type 0. They join the nodes of groups B and S (the interior nodes of the star with its vertices), alternating nodes of the two groups, as follows: S1-B2, B2-S6, S6-B1 , B1-S5, S5-B6, B6-S4, S4-B5, B5-S3, S3-B4, B4-S2, S2-B3 and B3-S1.

■ Type 1. In this case, a separation is made in the classification of beams of this type:

or superiors. They link the cell with the cell above by joining the node M1 of the cell with certain nodes of the group S of the cell above in the form: M1-S2, M1-S4, M1-S6.

or lower. They link the cell with the lower cell by joining the node M2 of the cell with certain nodes of the group S of the lower cell in the form: M1-S1, M1-S3, M1-S5.

either

■ Type 2. They join the nodes of group M with those of group B, as follows: M1-B1, M1-B2, M1-B3, M1-B4, M1-B5, M1-B6, M2-B1, M2 -B2, M2-B3, M2-B4, M2-B5, M2-B6.

In Figure 3 two important distances of the unit cell C are bounded, which depend on two of the geometric parameters: the first predefined distance Djoint, and the second predefined Heightstar.

Likewise, in Figure 4. the distance 3 is bounded, which is equal to the apothem of the hexagon multiplied by ( 1-Dstar).

Figure 5 schematically shows a sample of metamaterial M according to the second aspect of the invention, formed from the grouping of cells unit C according to the first aspect of the invention. As can be seen in said figure, each node of the group S is shared by three different unit cells C.

Finally, Figure 6 shows a resulting 3D metamaterial sample. The metamaterial according to the present invention is preferably manufactured by 3D printing. In view of this, a possible digital design process for it is described below, which includes everything from conceptualization to the generation of an stl file, readable by most 3D printers.

According to this process, to manufacture the metamaterial, a mesh of nodes and elements is first created in a file that is later displayed in some software, for example Patran, Catia, or Paraview. This file contains the coordinates of each node and the connectivity of the elements in order to represent the structure.

The coordinates of the nodes are generated by means of a code, which can be programmed in practically any programming language and implements the equations expressed in this document.

A possible preferred implementation would be to use Python to create the coordinates of the nodes as well as the connectivity. After having all the data ready, the code creates a file of type vtk. VTK is a free software visualization toolkit. This type of file is widely used by viewing applications such as Paraview, which is the tool of choice in this case to view the structure in 3D.

Once you have the metamaterial sample in Paraview, you can create an stl file of the structure. This type of file contains a 3D model without color or texture that can be sent to a 3D printer or additive manufacturing machine for manufacturing.

A key aspect that can be exploited with this type of design is the creation of a library of combinations of geometric parameters to create a large number of structures and mechanically test them to obtain their final properties. In this way, a table would be obtained that relates each combination of parameters geometric parameters with their mechanical properties, and by means of some kind of reverse engineering, a function could be created that would have as input variables the desired final properties and would give as a result the geometric parameters necessary to obtain them.

The different applications of the metamaterial defined in this document come from the need to create any industrial element that needs a gradient of mechanical properties and must be done with the same material and manufacturing process. For this reason, this invention is very focused on 3D printing and topological optimization.

The present invention is in no way limited to the embodiments disclosed herein. In fact, in view of the present description, other possible embodiments of this invention will be evident to the person skilled in the art, whose scope of protection is defined exclusively by the set of claims that follows below.

Claims (1)

Unit cell (C) of metamaterial in the shape of a right hexagonal prism, provided inside with oblique beams, characterized in that said beams are joined together forming: - a first group of nodes (B1, B2, B3, B4, B5, B6) arranged on a central horizontal plane (P), each of said nodes (B1, B2, B3, B4, B5, B6) being located shape that defines an inner vertex of a star, - a second group of nodes (S1, S2, S3, S4, S5, S6), each of said nodes (S1, S2, S3, S4, S5, S6), being arranged so as to define an outer vertex of the star, each of said nodes being also located vertically, alternately, above and below the central horizontal plane (P); Y - a third group of auxiliary nodes (M1, M2) arranged vertically above and below the central horizontal plane (P). Unit cell (C) of metamaterial according to claim 1, characterized in that it comprises two auxiliary nodes (M1, M2), the first of said auxiliary nodes (M1) being arranged vertically at a first predetermined distance (Djoint) below the horizontal plane (P) and the second of said auxiliary nodes (M2) being arranged vertically at said first predetermined distance (Djoint) above the central horizontal plane (P). Unit cell (C) of metamaterial according to claim 2, characterized in that the first predetermined distance (Djoint) is determined by: hlayers Djoint = v i ^{* --------- -----------} where: v1 is a parameter between 0.8 and 0.8; Y Hlayers is the height between layers of the metamaterial. Four.

Unit cell (C) of metamaterial according to any of the preceding claims, characterized in that the second group of nodes comprises six different nodes (S1, S2, S3, S4, S5, S6), each of said nodes (S1, S2 , S3, S4, S5, S6) alternately located vertically above and below a second predetermined distance (Heightstar) from the central horizontal plane (P). 5. Metamaterial unit cell (C) according to claim 4, characterized in that the second predetermined distance (Heightstar) is determined by: Heightstar = v 2 * Djoint where v2 is a parameter between 0 and 0.5. 6. Metamaterial (M) formed from the iterative grouping of unit cells (C) of metamaterial, according to any of claims 1 to 5.