Method for producing an amorphous architecture of the micro-lattice type formed of micro-beams connected together by nodes

Abstract

The invention relates to a method for producing an amorphous three-dimensional architecture of the micro-lattice type formed of micro-beams connected together by nodes, which comprises: A) performing (100) a computer-implemented design step consisting, on the basis of a three-dimensional random arrangement (INIT) of non-deformable beads, in: a) producing (101) a three-dimensional random compact stack of said beads; b) for each bead, determining (102) the coordinates of the centre of the bead which correspond to those of a node; c) performing (103) a triangulation with said nodes, each triangle thus being defined with the nodes closest to one another, then associating two nodes connected by one side of a triangle to a micro-beam in order to define the micro-lattice; d) selecting (104) a sub-domain of the micro-lattice obtained in step c), not comprising the nodes located at the edge of the micro-lattice in order to define said amorphous three-dimensional architecture, the design step involving an average connectivity of the nodes greater than or equal to twelve, the design step providing for defining a shape and associated transverse dimensions for each micro-beam; and B) producing (200) the architecture designed in step A).

Description

[0001] DESCRIPTION

[0002] TITLE: Manufacturing process of an amorphous micro-lattice type architecture formed of micro-beams connected to each other by nodes

[0003] Technical field of the invention

[0004] The invention relates to the field of cellular materials, and more particularly to materials having a micro-lattice type architecture, which is formed of microbeams connected to each other by nodes.

[0005] Technical background

[0006] Constraints, whether environmental, cost, access to raw materials or recycling, encourage the most sparing use possible of raw materials in the manufacture of structural materials.

[0007] A widely explored approach is therefore to reduce the volumetric mass p (or density) of materials as much as possible without harming their mechanical behavior. The mechanical behavior of the material is defined in particular by its rigidity, its hardness and its resistance to fracturing.

[0008] The most natural way to lighten a material is to introduce pores into it.

[0009] The introduction of pores into the material can be done randomly.

[0010] This is the case, for example, with solid foams or aerogels. These are very porous solids and, therefore, very light. They therefore find numerous applications in industry, but their high porosity results in a drastic reduction in their mechanical strength. Typically, a solid foam with a relative density of 1% (in reference to the solid material) has a rigidity of 10 6times lower than that of the material from which it is made. The stiffness changes with the cube of the density. In other words, the ratio between stiffness and density therefore changes with the square of the density and is therefore divided by approximately 10,000 when going from solid material to a solid foam with a relative density of 1% made of this material.

[0011] The introduction of pores in a random manner, however, has the advantage of not presenting statistically privileged orientations and the mechanical behavior is globally isotropic. From then on, it is possible to use the usual constants (Young's modulus E and Poisson's coefficient v to define its rigidity, elastic limit o Y to define its hardness and toughness K cto define its resistance to fracturing) to mechanically characterize the material thus formed. These usual constants in fact make it possible to predict the mechanical behavior of structures, independently of the geometry of these structures and the stress exerted on these structures.

[0012] Alternatively, the introduction of pores into the material can be carried out in a controlled manner.

[0013] This control can be achieved, in particular, by means of additive manufacturing. Additive manufacturing makes it possible to modulate the architecture of the material in its entirety, and therefore to arrange the pores in space in a controlled manner and, in fact, to significantly improve mechanical performance.

[0014] For example, we can refer to the article by TA Schaedler & al.: Ultralight Metallic Microlattices, Science, 334(6058), 962-965 (2011) which proposes a microlattice-type architecture whose micro-beams are hollow tubes arranged periodically. As can be seen in this article (figure 4 of this article), this makes it possible to maintain the ratio between stiffness and density at relatively high values.

[0015] The rules to follow to control this stiffness-density ratio in a micro-lattice made of periodically arranged micro-beams are known.

[0016] Indeed, for this, it is necessary to control the so-called Z connectivity, namely the number of microbeams per node. If the Z connectivity is less than 6, the stiffness varies with the square of the density. If the Z connectivity is greater than or equal to 12, the stiffness is substantially proportional to the density. Thus, for a micro-truss with a connectivity of Z = 12 (the best-known example is the micro-truss called "octet-truss" in the literature and according to Anglo-Saxon terminology), the stiffness of the architecture of relative density 1% (with reference to the solid material) is only degraded by a factor varying between 300 and 1000 compared to that of the material which constitutes it. This information can be found in the article by VS Despandes & al. : Foam topology: bending versus stretching dominated architectures, Acta Materialia, 49(6), 1035-1040 (2001) and VS Despandes & al.: Effective properties of the octet-truss lattice material, Journal of the Mechanics and Physics of Solids, 49, 1747-1769. For a relative density of 1%, the performance on the evolution of the stiffness-density ratio is therefore 10 to 30 times better than that obtained with a random architecture with globally isotropic mechanical behavior (solid foam).

[0017] However, the periodicity induces a major defect since the mechanical behavior of the micro-lattice obtained is anisotropic. The material is less rigid or more brittle when stressed in certain orientations. It is this difference in mechanical behavior depending on the direction of stress that is reflected in the range of values ​​provided previously on the evolution of the stiffness-to-density factor between 300 and 1000. Because of this anisotropy, it is therefore no longer possible to define the material by the usual constants alone (Young's modulus, Poisson's modulus, elastic limit and toughness) used to size the structures.

[0018] Some authors have studied the impact of imperfections on the mechanical performance of micro-lattices whose micro-beams are arranged periodically.

[0019] To this end, it has been proposed to start with a micro-lattice whose microbeams are arranged periodically and to modify this structure to make it more random. This has been achieved by moving the nodes of a micro-lattice over a certain distance and in a randomly chosen direction, or by eliminating a certain proportion of microbeams from the micro-lattice chosen at random. It is known that the addition of disorder promotes isotropy. If micro-lattices with a periodic architecture thus disordered present more isotropic mechanical behaviors (the level of isotropy depending on the level of disorder introduced), the rigidity nevertheless deteriorates when the introduced disorder increases.

[0020] These approaches, which aim to more or less disorder the architecture of an initially periodic micro-lattice, therefore make it possible to partially improve the isotropy properties at the cost of a degradation of the rigidity. A compromise must therefore be found.

[0021] An objective of the invention is to define an architecture exhibiting both globally isotropic mechanical behavior and good mechanical performance.

[0022] To this end, the invention proposes a method for manufacturing an amorphous three-dimensional architecture of the micro-lattice type formed of micro-beams connected to each other by nodes, comprising the following steps:

[0023] A) performing a computer-implemented design step consisting, from a three-dimensional random arrangement of non-deformable balls of given diameters, of: a) producing a three-dimensional random compact stack of said balls, b) for each ball of the three-dimensional random compact stack, determining the coordinates of the center of the ball and then associating these coordinates with those of a node, c) performing a triangulation with the nodes thus defined so that each triangle is defined with the nodes closest to each other, then associating two nodes connected by a triangle side with a micro-beam to define the micro-lattice, d) selecting a sub-domain of the micro-lattice obtained in step c), this sub-domain not including the nodes located at the edge of this micro-lattice, in order to define the amorphous three-dimensional architecture of the micro-lattice type,the design stage involving an average connectivity of the micro-truss nodes greater than or equal to twelve, the design stage also providing for defining a shape and associated transverse dimensions for each micro-beam, then: B) manufacturing the architecture designed in stage A).,

[0024] This process produces an amorphous micro-lattice architecture whose behavior is then globally isotropic and for which the usual constants for defining a material can be defined (Young's modulus, Poisson's ratio, elastic limit and toughness). The amorphous nature of the micro-lattice architecture comes on the one hand from the fact that the process is implemented from a random arrangement of non-deformable balls whose random nature is consubstantial with the manufacturing process and on the other hand from the fact that the process provides steps aimed at homogenizing the lengths of the micro-beams within the micro-lattice architecture. In addition, the mechanical performances obtained with this architecture are much higher than those observed in microlattices with isotropic mechanical behavior known until now.

[0025] Thus, unlike the approach used in the state of the art where we seek to introduce imperfections into a micro-lattice of initially periodic architecture, there is no compromise to be found within the framework of the invention between isotropic behavior of the micro-lattice architecture and mechanical performance.

[0026] The method according to the invention may comprise at least one of the following additional steps, taken alone or in combination:

[0027] - step A) is carried out from a random arrangement of balls of identical diameters;

[0028] - step a) is implemented by a Lubachevsky-Stillinger algorithm, a so-called force bias algorithm, an algorithm derived from these or any succession of these different algorithms;

[0029] - the triangulation carried out in step c) is a Delaunay triangulation;

[0030] - the method comprises a step, implemented after step d) and consisting of producing a mesh of the micro-lattice obtained in step d) before implementing step B);

[0031] - step B) is carried out by additive manufacturing.

[0032] The invention also relates to an amorphous three-dimensional microlattice-type architecture, the microlattice being formed of microbeams connected to each other by nodes and in which each microbeam forms one side of a triangle connecting the nodes closest to each other with an average connectivity of the nodes greater than or equal to twelve.

[0033] This architecture is advantageously obtained by the method according to the invention. The architecture may also include at least one of the following characteristics, taken alone or in combination:

[0034] - the statistical distribution of the length of the micro-beams has a standard deviation to mean ratio less than or equal to 0.3;

[0035] - the statistical distribution of the length of the micro-beams has a standard deviation to mean ratio less than or equal to 0.2;

[0036] - each micro-beam is in the form of a cylinder of given diameter.

[0037] Brief description of the figures

[0038] Other objects and characteristics of the invention will appear more clearly in the following description, made with reference to the appended figures, in which:

[0039] [Fig. 1] is a schematic representation of the main steps of a method according to the invention for manufacturing a micro-lattice formed of micro-beams connected to each other by nodes;

[0040] [Fig. 2] represents a three-dimensional compact random stack of non-deformable balls of identical diameters, obtained after having implemented by computer a first step of the method according to the invention carried out from a compact random arrangement of said balls;

[0041] [Fig. 3] represents a cloud of nodes obtained after having implemented by computer a step of the method according to the invention carried out from the arrangement of [Fig. 2];

[0042] [Fig. 4] represents the micro-lattice obtained after having implemented by computer another step of the method according to the invention carried out from the cloud of nodes of [Fig. 3];

[0043] [Fig. 5] represents a statistical distribution of the number of micro-beams as a function of their length for the micro-lattice shown in [Fig. 4];

[0044] [Fig. 6] is a histogram representing the number of nodes associated with a given connectivity of this node, for different values ​​of this connectivity and for the micro-lattice represented in [Fig. 4],

[0045] [Fig. 7] represents the architecture finally obtained after having implemented by computer an additional step of the method according to the invention carried out from the micro-lattice of [Fig. 4]; [Fig. 8] represents a statistical distribution of the number of micro-beams according to their length for the architecture represented in [Fig. 7];

[0046] [Fig. 9] is a histogram representing the number of nodes with a given connectivity, as a function of the value of this connectivity and for the architecture represented in [Fig. 7];

[0047] [Fig. 10] represents the architecture obtained after a final, optional, computer-implemented step of the method according to the invention consisting of producing a mesh, for example using a computer-aided design (CAD) type tool, of the architecture of [Fig. 7];

[0048] [Fig. 11] represents the architecture obtained after a final step of the method according to the invention, consisting of the manufacture of the architecture of [Fig. 10];

[0049] [Fig. 12] provides numerical results, carried out on an architecture conforming to that of [Fig. 11] and aimed at determining its mechanical performances.

[0050] Detailed description of the invention

[0051] Figure 1 is a schematic representation of the different stages of the method according to the invention.

[0052] The invention relates to a method for manufacturing an amorphous three-dimensional architecture of the micro-lattice type, the micro-lattice being formed of micro-beams connected to each other by nodes, which comprises a step 100 of computer-aided design of the architecture and a step 200 of manufacturing the architecture thus designed.

[0053] For the design stage, we start IN IT with a three-dimensional random arrangement of non-deformable balls of given diameters, then we carry out the following steps:

[0054] - produce 101 a three-dimensional random compact stack of said balls,

[0055] - for each ball in the three-dimensional random compact stack, determine 102 the coordinates of the center of the ball and then associate these coordinates with those of a node,

[0056] - carry out 103 a triangulation with the nodes thus defined so that each triangle is defined with the nodes closest to each other, then, associate two nodes connected by a triangle side to a micro-beam to define the micro-lattice,

[0057] - select 104 a sub-domain of the micro-lattice obtained in step 103, this sub-domain not including the nodes located at the edge of this micro-lattice and this, so as to define the amorphous architecture of micro-lattice type, and, possibly:

[0058] - produce 105 a mesh representative of the architecture obtained in step 104; the design step also provides for defining a shape and associated transverse dimensions for each micro-beam.

[0059] We will explain this process using an example of how it is implemented.

[0060] Initially, we start with a random three-dimensional arrangement of non-deformable balls. The term balls covers indifferently a ball (solid) or a sphere (hollow) in the mathematical sense of the term.

[0061] These balls each have a given diameter. It is important to be able to fix these diameters since they determine, in the method according to the invention, the length of the microbeams.

[0062] The diameter of the different balls is not necessarily identical.

[0063] However, it is advantageous to start from an arrangement with balls having close diameters, typically with a variation not exceeding 30% compared to an average value, or identical to minimize the standard deviation from the average length of the micro-beams present in the micro-lattice that one seeks to manufacture. The homogeneity of the length of the micro-beams contributes in fact, with the random nature of the distribution of the balls within the three-dimensional compact stack of balls, to define an amorphous architecture.

[0064] From this initial state, step 101 aims to obtain a three-dimensional random compact stack of the balls.

[0065] There are different types of algorithms in the literature that can achieve this type of stacking. For example, it is possible to use a Lubachevsky-Stillinger algorithm, a so-called "force-biased" algorithm, an algorithm derived from these, or even a succession of these different algorithms.

[0066] The Lubachevsky-Stillinger algorithm is widely known and has been the subject of numerous publications. However, reference may be made to the article by Lubachevsky, Boris D.; Stillinger, Frank H. (1990): Geometric properties of random disk packings, Journal of Statistical Physics, 60 (5-6): 561-583.

[0067] The so-called "force-biased" algorithm is also widely known and has been the subject of numerous publications. However, reference may be made to J. Moscihski, M. Bargiel, ZA Rycerz & PWM Jacobs (1989) The Force-Biased Algorithm for the Irregular Close Packing of Equal Hard Spheres, Molecular Simulation, 3:4, 201-212. In the present case, here is the procedure used in the example considered to generate the initial three-dimensional random arrangement IN IT of beads and to implement step 101.

[0068] We used the algorithm developed by Vasili Baranau, available at https: / / aithub.com / VasiliBaranov / packinq-qeneration (distributed under the MIT License).

[0069] The user must specify as input: 1) the size of the container containing the stack, 2) the diameters of the balls, 3) the number of iterations of the algorithm, 4) the contraction rate, 5) an integer serving as a seed for the pseudo-random number generator.

[0070] The container, cubic, was chosen with a side of size 1 1 .7 (arbitrary dimension). This is the size of the container before compaction of the balls.

[0071] The balls were chosen with identical diameters, of value 1 (arbitrary dimension). 1075 balls were taken into consideration.

[0072] 100 iterations were performed.

[0073] The contraction rate was chosen to be 0.1 (arbitrary unit). The lower the contraction rate, the more compact the stack of balls will be.

[0074] The integer that serves as the seed for the pseudo-random number generator was chosen at random. The algorithm uses this seed to generate the initial positions of marbles in the container.

[0075] The execution of the algorithm (called PackingGeneration.exe) is then carried out in "fba" mode (it is a "Forced-Biased" algorithm). The pre-stacking obtained after implementing this algorithm is given in a packing.xyzd file containing the X, Y and Z positions and diameters D of each ball. This packing.xyzd file is supported by another packing.nfo file containing various characteristic parameters of the pre-stacking (eg compactness).

[0076] We then use these last two files as inputs to the same algorithm (PackingGeneration.exe) but executed in "Is" mode (indicates a Lubachevsky-Stillinger algorithm). We then obtain a new packing.xyzd file containing the X, Y, Z positions and the diameters D updated after compaction and also a new packing.nfo file containing information on the pre-stacking thus obtained.

[0077] These new packing.xyzd and packing.nfo files are used as inputs to the same algorithm (PackingGeneration.exe) but now in "Isgd" mode (an algorithm derived from Lubachevsky-Stillinger's algorithm, including a so-called gradual densification option). At this stage, the packing.xyzd file contains the positions and diameters of the balls in the three-dimensional random compact stack and the file contains various information about the stack and in particular, its compactness. The compactness obtained in this example implementation is 0.6345.

[0078] It is therefore understood that several different compaction algorithms are successively used here to obtain the three-dimensional random compact stack. The objective is to have the highest possible compactness, typically between 0.6 and 0.64 in three dimensions. Indeed, a high compactness is of interest to ensure good mechanical performance, for example concerning the rigidity (E / p ratio; in particular) of the micro-lattice to be manufactured.

[0079] Finally, the X, Y, Z coordinates of the center of each ball were modified in the packing.xyzd file, by dividing the mentioned values ​​by a rescaling factor F defined as follows:

[0080] [Maths 1] where the parameters p^ nand pth are both given in packing.nfo. In this case, the rescaling factor F is F = 1.0842. The implementation of this correction is linked to the implementation of the computer program chosen to illustrate the method according to the invention, but is not systematic for implementing step 101 of the method according to the invention.

[0081] Figure 2 represents the three-dimensional compact random stack of balls of identical diameters, obtained after having implemented by computer this first step 101 of the method according to the invention.

[0082] Then, step 102 consists, for each ball of the three-dimensional random compact stack, in determining the coordinates of the center of the ball and then associating them with a node. In this case, the coordinates of the center of each ball are available in the packing.xyzd file obtained at the end of step 101. It is sufficient to extract them from this file to put them in a dedicated file where they are associated with the nodes of the microlattice that we are trying to create.

[0083] Figure 3 represents the three-dimensional node cloud obtained after computer-implementing step 102.

[0084] Then, during a step 103, a triangulation is carried out with the nodes thus defined (three-dimensional point cloud in figure 3).

[0085] Triangulation allows to obtain a so-called Z connectivity of the nodes, namely the number of micro-beams per node, as high as possible. The triangle is in fact the non-degenerate polygon of smallest order. Any higher order polygon (quadrilateral, pentagon, etc.) will offer fewer possibilities on the connectivity of the nodes. We know in fact that it is important to have a high connectivity in the architecture, and advantageously at least 12 in three dimensions, to maintain good mechanical properties, in particular with regard to rigidity (E / p ratio).

[0086] In the context of the invention, the triangulation is also carried out with the nodes closest to each other, in the three-dimensional cloud of nodes obtained at the end of step 102. Defining the triangles with the closest nodes makes it possible to maintain a certain homogeneity in the length of the sides of each triangle. This homogeneity is important because it defines, as will be seen in the remainder of the description, the homogeneity in the length of the micro-beams. However, defining micro-beams with homogeneous lengths (low dispersion) within the micro-lattice to be manufactured is important for obtaining good mechanical properties, in particular with regard to rigidity (E / p ratio). This homogeneity contributes in fact, with the random nature of the distribution of the balls within the three-dimensional compact stack of balls, to defining an amorphous architecture.

[0087] Several types of triangulation are possible.

[0088] A widely used triangulation is the Delaunay triangulation.

[0089] A Delaunay triangulation was implemented in the example implementation followed. More precisely, we can refer to the following document giving the algorithm: htps: / / docs.scipy.org / doc / scipy / reference / gg .s atial.Delaunay.html (Python).

[0090] This is what was used in the implementation example described here.

[0091] Among the other possible triangulations, we can generalize to the different regular triangulations, of which the Delaunay triangulation is only a special case. We can also consider, if necessary, a Pitteway triangulation.

[0092] Then, to define the micro-lattice, it is sufficient to associate in a dedicated file two nodes connected by a side of a triangle to a micro-beam.

[0093] The length of a micro-beam is then entirely determined by the distance separating two nodes belonging to the same triangle. The distance separating two nodes belonging to the same triangle is itself defined by the chosen diameter of the balls before implementing the method according to the invention and step 101 of producing the three-dimensional random compact stack.

[0094] The shape of the micro-beam section and the associated transverse dimensions are data provided independently. In particular, once the shape of the section is fixed (e.g. circular to form cylindrical micro-beams), determining the transverse dimensions (this is reduced to the diameter for cylindrical micro-beams) allows the final relative density of the micro-lattice to be adjusted. These transverse dimensions can be different from one micro-beam to another. However, the choice of a section of identical shape with the same transverse dimensions on all the micro-beams makes it easy to control the relative density of the architecture that one seeks to manufacture.Thus, if these transverse dimensions are significantly smaller than the length of the micro-beams (a situation which allows a low relative density to be obtained), the relative density of the architecture which will be manufactured evolves as the square of the ratio between this transverse dimension and the average length of the micro-beams.

[0095] The definition of the shape and transverse dimensions of the micro-beams can be carried out at various times during the design stage 100. This data only becomes useful for carrying out the actual manufacturing.

[0096] Figure 4 represents the micro-lattice obtained at the end of step 103.

[0097] Figure 5 shows the statistical distribution of the number of NP micro-beams as a function of their LMP length for the micro-lattice shown in Figure 4. There is a significant dispersion of the diameter of the balls compared to the unit length (unit diameter = diameter of the balls initially chosen). Micro-beams of greater length exist, in significant quantity up to lengths of 2 and even, admittedly, in smaller quantity up to lengths of more than 6. More precisely, the results shown in Figure 5 are characterized by a statistical distribution of the length of the micro-beams presenting a standard deviation to mean ratio of 0.568.

[0098] Figure 6 is a histogram representing the number of NDS nodes associated with a given Z connectivity of this node, for different values ​​of this connectivity and for the micro-lattice represented in Figure 4. The nodes present on the edges of the micro-lattice have been taken into account. As can be seen in this Figure 6, the nodes have a high average connectivity, which is a consequence of the triangulation, between 13 and 14, therefore well above or equal to 12. However, there is a significant dispersion since we find nodes with a connectivity between 5 and 30, and mainly between 8 and 20.

[0099] Then, a step 104 is implemented consisting of selecting a sub-domain of the micro-lattice obtained in step 103, this sub-domain not including the nodes located at the edge of this micro-lattice and this, to finally define the amorphous three-dimensional architecture of micro-lattice type. Indeed, we can see in Figure 4 edge effects which imply that certain triangles, located at the edges of the micro-lattice, have sides whose length is very different from the average length of a triangle side.

[0100] The selection of this sub-domain therefore makes it possible to avoid including in the material elements of great length compared to the average length and therefore to increase the homogeneity of the length of the micro-beams. It should be remembered that this homogeneity contributes in fact, with the random nature of the distribution of the balls within the three-dimensional compact stack of balls, to define an amorphous architecture, with its consequences on the isotropic mechanical behavior and with high mechanical characteristics.

[0101] But it should also be noted that the implementation of this step 104 ultimately makes it possible to obtain a micro-lattice with rigidity maintained at the edge, which is obviously of great interest for a real structural part.

[0102] In the example embodiment that we describe, the chosen sub-domain is in this case a cubic sub-domain whose center merges with the center of the microlattice (also cubic) of figure 4, but of which each dimension X, Y and Z of the space is reduced by a quarter (in figure 7, the dimensions go from -3 to +3 while they go from -4 to +4 in figure 3).

[0103] The micro-lattice thus obtained is shown in Figure 7.

[0104] As can be seen in Figure 7, the side effects are therefore eliminated.

[0105] Figure 8 shows the statistical distribution of the number of micro-beams NP as a function of their length LMP for the micro-lattice shown in Figure 7. It can be seen that almost all of the micro-beams have a unit length (= the diameter of the balls initially chosen). Micro-beams of greater length exist, up to lengths of approximately 1.5, but in very small proportions. The length of the micro-beams is therefore homogeneous throughout the micro-lattice shown in Figure 7. More precisely, the results shown in Figure 8 are characterized by a statistical distribution of the length of the micro-beams with a standard deviation to mean ratio of 0.136.

[0106] Incidentally, we note that the selection of this subdomain also has an effect on the connectivity of the nodes.

[0107] Figure 9 is a histogram representing the number of NDS nodes associated with a given Z connectivity of this node, for different values ​​of this connectivity and for the micro-lattice represented in Figure 7. In this figure, the nodes present on the edges of the micro-lattice present a significantly lower connectivity than the others and have not been taken into account. As can be seen in this Figure 9, all the nodes thus preserved present a high connectivity. Indeed, the vast majority of nodes present a Z connectivity at least equal to 12, with a connectivity most often of Z = 13 or Z = 14. The average value of the connectivity is therefore always greater than or equal to 12. We also see that the connectivity is not too high either, which is a good thing since too high a connectivity, i.e. beyond Z = 12, has no real interest in terms of the mechanical behavior of the micro-lattice.

[0108] The design of the amorphous micro-lattice type architecture is at this stage complete.

[0109] It is then sufficient to implement a step 200 of manufacturing the architecture obtained in step 104.

[0110] Depending on the manufacturing method used, it may be necessary to implement an additional step during the design step 100 consisting of producing 105 a mesh representative of the micro-lattice obtained in step 104. This mesh is typically produced with computer-aided design (CAD) software. This is the case, for example, if the manufacturing step 200 is carried out by additive manufacturing. Step 105 can also be used to define a shape and associated transverse dimensions for each micro-beam, for example a cylinder shape with the definition of its diameter.

[0111] An amorphous micro-lattice type architecture obtained in accordance with the method according to the invention was manufactured by implementing steps 101 to 104 as described previously in support of the embodiment example presented previously, with the difference that the final shape of the architecture is here chosen to be parallelepiped and not cubic. This choice was made when defining the sub-domain of the micro-lattice in step 104. It was also necessary to choose a ball diameter, with a non-arbitrary value for manufacturing to determine the length of the micro-beams.

[0112] In this case, step 105 was also implemented. This step was used to choose the shape of the micro-beam section and the associated transverse dimensions before moving on to manufacturing.

[0113] The three-dimensional amorphous micro-lattice architecture obtained at the end of this step is shown in Figure 10.

[0114] It is a parallelepiped architecture with dimensions of 100 x 100 x 50mm 3 , composed of 17938 micro-beams of (roughly) identical diameters, and worth 500 pm. This type of sample (parallel) is particularly suitable for conducting compression tests. For this, step 105 relied on the Python library FreeCAD (CAD) in which cylindrical micro-beams were generated. The diameter of each micro-beam was chosen to be 1 mm. The software used to visualize this representation is FreeCAD. As can be seen in Figure 10, upper and lower plates were added to the micro-truss in FreeCAD for the purpose of manufacturing and performing compression tests on the architecture.

[0115] The manufacturing process was then carried out using additive manufacturing. The 3D printer used for this purpose was a FormLabs Form3 printer. The resin (material used to form the micro-lattice) used was Clear V4 resin.

[0116] Figure 11 shows the final architecture obtained.

[0117] The mechanical behavior of the architecture in Figure 11 could be simulated numerically, by numerical homogenization. This behavior is represented in Figure 12.

[0118] The figure on the left represents the evolution of the ratio of the Young's modulus E of the microlattice to the Young's modulus E sof the solid material as a function of the ratio of the density p of the micro-lattice to the density ps of the solid material. The abscissa and ordinate axes are logarithmic. The line thus represented has a slope of 1 / 6. This value corresponds to the maximum value theoretically predicted for an isotropic porous material. This predicted theoretical value can be found in the article by G. Gurner and M. Durand: Stiffest elastic networks, Proceedings of the Royal Society A, 470, 20130611. The stiffness is therefore maximum.

[0119] The figure on the right represents the Poisson's ratio v as a function of the ratio of the density p of the micro-lattice to the density ps of the solid material. The Poisson's ratio is relatively constant and is approximately 0.25. This is the expected value in an isotropic porous material of maximum rigidity. Reference may be made here to the article by G. Gurner and M. Durand: Stiffest elastic networks, Proceedings of the Royal Society A, 470, 2013061 1 .

[0120] The calculations carried out therefore provide proof that we obtain an architecture with optimal mechanical properties, in this case in terms of rigidity.

[0121] Furthermore, the applicant considers that the same will apply to the hardness (which can be characterized by the ratio of the elastic limit to the density) of the architecture thus obtained. Indeed, it has been shown that, in a micro-lattice where the micro-beams are arranged periodically, the shear bands play a role similar to that played by dislocations in a crystalline solid: their appearance promotes plastic deformation (plastic deformation is the deformation obtained beyond the elastic limit) and consequently reduces the performance in terms of hardness. This phenomenon can be transposed to the micro-lattice with amorphous architecture which is obtained with the method according to the invention. Indeed, such a micro-lattice prohibits the existence of dislocations and can therefore only improve the performance in terms of hardness. Reference may be made to the article by Pham, MS, Liu, C., Todd, I., & Lertthanasarn, J.(2019): Damage-tolerant architected materials inspired by crystal microstructure, Nature, 565(7739), 305 311; which concerns a micro-lattice architecture with periodic arrangement.

[0122] The present invention therefore proposes a new way of generating an amorphous three-dimensional micro-lattice type architecture without starting from a periodic network, and which therefore presents an absence of medium and long-range order. The mechanical behavior is therefore globally isotropic. Furthermore, the mechanical performances obtained are optimal. Contrary to what is proposed in the state of the art, there is therefore no longer a compromise to be found between isotropy and mechanical performances. The micro-lattice defined within the framework of the invention makes it possible to obtain both.

[0123] The invention also relates to an amorphous three-dimensional micro-lattice type architecture, the micro-lattice being formed of micro-beams connected to each other by nodes and in which each micro-beam forms one side of a triangle connecting the nodes closest to each other with an average connectivity of the nodes greater than or equal to twelve.

[0124] It should again be recalled that an amorphous micro-lattice type architecture is an architecture that is on the one hand random, i.e. without preferential directions, and on the other hand whose micro-beams have homogeneous lengths. Thus, the statistical distribution of the length of the micro-beams may have a standard deviation to mean ratio less than or equal to 0.3, advantageously less than or equal to 0.2 and even more advantageously less than or equal to 0.15 or even less than or equal to 0.1.

[0125] Each micro-beam could, for example, be in the form of a cylinder of a given diameter. The choice of the cylinder diameter allows the density of the architecture to be adjusted.

[0126] Advantageously, this architecture is obtained by implementing the method according to the invention. The method involves in particular the design step 100 involving the implementation of steps 101 to 104 followed by the manufacturing step 200.

Claims

DEMANDS 1. A method for manufacturing a three-dimensional amorphous microlattice architecture formed of micro-beams connected to each other by nodes, comprising the following steps: A) perform (100) a computer-implemented design step consisting, starting from a three-dimensional random arrangement (INIT) of rigid balls of given diameters, of: a) creating (101) a three-dimensional random close packing of said balls, b) for each ball in the three-dimensional random close packing, determining (102) the coordinates of the center of the ball and then associating these coordinates with those of a node, c) performing (103) a triangulation with the nodes thus defined so that each triangle is defined with the nodes closest to each other, then associating two nodes connected by a side of the triangle with a micro-beam to define the micro-lattice, d) selecting (104) a subdomain of the micro-lattice obtained in step c), this subdomain not including the nodes located on the edge of this micro-lattice, in order to define the amorphous three-dimensional micro-lattice architecture,the design stage involving an average connectivity of the micro-truss nodes greater than or equal to twelve, the design stage also providing for defining a shape and associated transverse dimensions for each micro-beam, then:, B) manufacture (200) the architecture designed in step A).

2. A method according to claim 1, characterized in that step A) is implemented from a random arrangement of balls of identical diameters.

3. A method according to any one of the preceding claims, characterized in that step a) is implemented by a Lubachevsky-Stillinger algorithm, a so-called force bias algorithm, an algorithm derived from these or any succession of these different algorithms.

4. A method according to any one of the preceding claims, characterized in that the triangulation carried out in step c) is a Delaunay triangulation.

5. A method according to any one of the preceding claims, characterized in that it comprises a step (105), implemented after step d) and consisting of creating a mesh of the micro-lattice obtained in step d) before implementing step B).

6. A method according to the preceding claim, characterized in that step B) is carried out by additive manufacturing.

7. A three-dimensional amorphous micro-lattice architecture, the micro-lattice being formed of micro-beams connected to each other by nodes, and wherein each micro-beam forms one side of a triangle connecting the nearest nodes, with an average node connectivity greater than or equal to twelve.

8. An architecture according to the preceding claim, wherein the statistical distribution of the micro-beam lengths has a standard deviation-to-mean ratio less than or equal to 0.

3.

9. Architecture according to any one of claims 7 or 8, wherein the statistical distribution of the length of the micro-beams has a standard deviation to mean ratio less than or equal to 0.

2.

10. Architecture according to any one of claims 7 to 9, wherein each micro-beam is in the form of a cylinder of a given diameter.

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