Method for manufacturing a two- or three-dimensional part having a composite architecture with at least two different micro-lattices connected to each other

Abstract

TITLE: Method for manufacturing a two- or three-dimensional part having a composite architecture with at least two different micro-lattices connected to each other.The invention relates to a method for manufacturing a two- or three-dimensional part having a composite architecture with at least two different micro-lattices connected to each other, comprising the following steps: performing (100) a computer-implemented design step comprising the following steps: A) defining (100A) a domain representing said part to be manufactured, then defining a first sub-domain for a first micro-lattice and a second sub-domain, complementary to the first sub-domain, to delimit a second micro-lattice different from the first micro-lattice; B) defining (100B), over the entire domain, the coordinates of generating centers for the two micro-lattices, C) defining (100C) the first micro-lattice D) defining (100D) the second micro-lattice E) connecting (100E) the second micro-lattice to the first micro-lattice.the design stage also includes defining a shape and associated transverse dimensions for each micro-beam, then: manufacturing (200) the architecture thus designed. Figure for the abstract: Fig. 1.

Description

Title of the invention: Method for manufacturing a two- or three-dimensional part having a composite architecture with at least two different micro-lattices connected to each other Technical field of the invention

[0001] The invention relates to the field of materials having a composite architecture. Technical background

[0002] A composite material is generally obtained by assembling two (or more) individual materials with different mechanical properties.

[0003] Existing solutions are generally based on the use of different individual materials. A composite material can then bring about more advantageous mechanical behaviors that the individual constituent materials do not possess alone. Generally speaking, the mechanical behavior of a material is defined by its Young's modulus (E) and its Poisson's modulus (v) to characterize the rigidity, its elastic limit (oY) to characterize the hardness, and its toughness (Kc) to characterize the resistance to fracture. It is necessary, for these quantities to be material constants, that the microstructure of each of the constituent materials be isotropic.

[0004] Among the composite materials, we can for example cite reinforced concrete (composite with concrete to ensure compressive strength, and a steel reinforcement to ensure tensile strength), glass fibers embedded in a resin (assembly of glass fibers to ensure rigidity and resin, for example a thermoplastic resin such as polyester to ensure fracture resistance) or, taking into account this time an example from the natural environment, mother-of-pearl whose brick and mortar structure, composed of a hard mineral phase (brick) and a soft organic phase (mortar) confers an unequaled combination of hardness and toughness properties. We can more generally refer to what is proposed by Clyne, D. Hull, An introduction to composite materials, 3rd edition, Cambridge University Press (2019).

[0005] In addition to the choice of the individual constituent materials of the composite material, the spatial organization of the different individual constituent materials is a key element for optimizing the mechanical properties. Thus, for example, in the case of mother-of-pearl, the fact that the mineral phase (hard) is geometrically in the form of bricks and the organic phase (soft) is geometrically in the form of mortar between the bricks gives it a toughness three orders of magnitude higher than that of the individual constituent materials. Reference may be made to Song F, Soh AK, Bai YL, Structural and mechanical properties of the organic matrix layers of nacre, Biomaterials (2003), Sept. 24 (20): 3623-31; doi:10.1016 / s0142-9612(03)00215-l. PMID:12809793.

[0006] However, constraints, whether environmental, cost, access to raw materials or recycling, can limit the use of certain materials and consequently also limit the possibilities for producing certain composite materials.

[0007] These same constraints encourage the most sparing use possible of raw materials in the manufacture of structural materials. Finally, a widely explored way to reduce the energy and carbon impact, particularly of vehicles, is to reduce as much as possible the volumetric mass q (or density) of the materials used without harming their mechanical behavior.

[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 carried out randomly. This is for example the case of solid foams or aerogels.

[0010] Alternatively, the introduction of pores into the material can be carried out in a controlled manner.

[0011] This control can in particular be obtained by means of additive manufacturing. Additive manufacturing makes it possible to modulate the architecture of the material in extenso, and therefore to arrange the pores in space in a controlled manner and, in fact, to control their impact on mechanical performance.

[0012] For example, we can refer to the article by TX Zheng & al.: Ultrastiff Mechanical Metamaterials, Science, 3434(6105890), 9621373-965 1377 (20112014) which proposes a micro-lattice type architecture composed of periodically arranged micro-beams. As can be seen in this article (figure 3A of this article), a so-called "octet-truss" arrangement leads to a very high ratio between rigidity and density, while a so-called "Kelvin foam" arrangement results in a much lower ratio.

[0013] The rules to follow to control this stiffness-density ratio in a micro-lattice made of periodically arranged micro-beams are known.

[0014] Indeed, for this, it is necessary to control the so-called Z connectivity, namely the number of micro-beams per node.

[0015] Thus, in two dimensions (2D), if the connectivity Z is strictly less than 4, the rigidity varies with the cube of the density and if the connectivity Z is greater than or equal to 6, the rigidity is substantially proportional to the density.

[0016] Similarly, in three-dimensional (3D), if the connectivity Z is strictly less than 6, the rigidity varies with the square of the density and if the connectivity Z is greater than or equal to 12, the rigidity is substantially proportional to the density. Thus, for a three-dimensional 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 the Anglo-Saxon terminology), the rigidity of the architecture of relative density 1% (with reference to the solid material) is reduced by a factor varying between 300 and 1000 compared to that of the material which constitutes it. And for a three-dimensional micro-truss with a connectivity of Z = 4 (the best-known example is the micro-truss called "Kelvin-foam" in the literature and according to the Anglo-Saxon terminology), the rigidity of the architecture of relative density 1% the rigidity is reduced by a factor 300000. 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. .

[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. Because of this ani-sotropy, 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] An objective of the invention is to propose a two- or three-dimensional part having an ultra-light composite architecture with adjustable mechanical properties.

[0019] In particular, an objective of the invention is to propose such a part with mechanical properties that can be modulated locally over a wide range of values ​​so as to be able, at a minimum, to reproduce the reinforcement mechanisms, the association of functional properties and / or the gradients of properties sought in known composite materials.

[0020] Another objective of the invention is to provide such a part without using different individual constituent materials.

[0021] To this end, the invention proposes a method for manufacturing a two- or three-dimensional part having a composite architecture with at least two different microlattices connected to each other, comprising the following steps: - carry out a computer-implemented design step comprising the following steps: A) define a domain representing the two- or three-dimensional part to be manufactured, then define a first sub-domain intended to delimit a first micro-lattice as well as at least one second sub-domain, complementary to the first sub-domain, intended to delimit a second micro-lattice different from the first micro-lattice; B) define, over the entire domain, the coordinates of generating centers for the first microlattice and the second microlattice, as follows: Bl) from a random two- or three-dimensional arrangement of non-deformable balls of given diameters in the whole of said domain, producing a random compact stack of said balls within said domain, B2) for each ball of the two- or three-dimensional random compact stack of said domain, determine the coordinates of the center of the ball, then B3) for each ball of the two- or three-dimensional random compact stack of said domain, associate the coordinates of the center of the ball with those of a generating center for any one of the first or second microlattices, C) define the first micro-lattice delimited by the first sub-domain as follows: Cl) carry out a Delaunay triangulation with the generating centers then associate two nodes connected by a side of the triangle to a micro-beam, C2) delete each micro-beam of which neither of the two nodes belongs to the first sub-domain, C3) identify and delete each micro-beam of which only one of the two nodes belongs to the first sub-domain, the node belonging to the first sub-domain then being identified as the border node of the first sub-domain, D) from the coordinates of the generating centers obtained at the end of step B3), define the second micro-lattice different from the first micro-lattice and delimited by the second sub-domain, as follows: Dl) generate a Voronoi diagram using the generating centers as seeds of said diagram then, associate two nodes connected by the Voronoi diagram to a micro-beam, D2) delete each micro-beam of which neither of the two nodes belongs to the second sub-domain, D3) identify and delete each micro-beam of which only one of the two nodes belongs to the second sub-domain, the node belonging to the second sub-domain being identified as the border node of the second sub-domain; E) connect the second micro-lattice to the first micro-lattice. the design stage also includes defining a shape and associated transverse dimensions for each micro-beam, then: - manufacture the architecture thus designed.

[0022] The method according to the invention may comprise at least one of the following additional steps, taken alone or in combination:

[0023] - step B1) is implemented from a random arrangement of beads of identical diameters;

[0024] - step B1) is implemented by a Lubachevsky-Stillinger algorithm, an al so-called force bias algorithm, an algorithm derived from these or any succession of these different algorithms;

[0025] - step E) comprises the following steps: El) for each identified micro-beam then deleted obtained in step C3), redefine the boundary node of the first sub-domain at the intersection point of the micro-beam identified then deleted with the boundary of the first sub-domain, then define a new micro-beam between the old boundary node and the boundary node thus redefined; E2) for each boundary node of the second sub-domain, search for the boundary node of the first sub-domain which is closest to it and connect these two nodes by a micro-beam; E3) for each boundary node of the first sub-domain which has not been connected at the end of step E2), search for the boundary node of the second sub-domain which is closest to it and connect these two nodes by a micro-beam;

[0026] - after step El), an additional step consisting of connecting each border node from the first subdomain with the border node closest to the first subdomain;

[0027] - step E) comprises the following steps: E' 1) for each micro-beam obtained identified then deleted in step D3), redefine the boundary node of the second sub-domain at the intersection point of the micro-beam identified then deleted with the boundary of the second sub-domain, then define a new micro-beam between the old boundary node and the thus redefined boundary node; E'2) for each boundary node of the first sub-domain, search for the boundary node of the second sub-domain which is closest to it and connect these two nodes by a micro-beam; E'3) for each boundary node of the second sub-domain which has not been connected at the end of step E'2), search for the boundary node of the first sub-domain which is closest to it and connect these two nodes by a micro-beam;

[0028] - the method comprises a step, implemented at the end of the design step and consisting of creating a mesh of each micro-lattice before implementing the manufacturing step;

[0029] - the manufacturing step is carried out by additive manufacturing.

[0030] The invention also relates to a two- or three-dimensional part having a composite architecture with at least two different micro-lattices connected to each other, the first micro-lattice, isotropic, having an architecture made with micro-beams connected to each other by forming Delaunay triangles and the second micro-lattice, also isotropic, having an architecture made with micro-beams connected to each other by forming Voronoi cells, each boundary node of the second sub-domain being connected to a boundary node of the first sub-domain and vice versa. Brief description of the figures

[0031] Other objects and characteristics of the invention will appear more clearly in the following description, made with reference to the appended figures, in which:

[0032] [Fig.l] is a schematic representation of the main steps of a method according to the invention for the manufacture of a two- or three-dimensional part having a composite architecture with at least two different micro-lattices connected to each other;

[0033] [Fig.2] represents a domain separated into two sub-domains obtained after the implementation implementing a first step of the method according to the invention;

[0034] [Fig.3] represents a compact random stack of non-deformable balls of almost identical diameters, obtained after having implemented by computer a subsequent step of the method according to the invention;

[0035] [Fig.4] 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.3];

[0036] [Fig.5] represents the micro-lattice obtained in the entire domain after having implemented by computer another step of the method according to the invention carried out from the cloud of nodes of [Fig.4];

[0037] [Fig.6] represents the micro-lattice obtained after computer implementation another step of the method according to the invention carried out from the micro-lattice of [Fig.5];

[0038] [Fig.7] represents the micro-lattice obtained after computer implementation another step of the method according to the invention, within the second sub-domain;

[0039] [Fig.8] is an enlarged view of [Fig.7] at a boundary area between the two subdomains visible in [Fig.2];

[0040] [Fig.9] represents the micro-lattice obtained for the first sub-domain after having implemented by computer another step of the method according to the invention which can be carried out from the micro-lattice of [Fig.6];

[0041] [Fig. 10] represents the micro-lattice finally obtained within the whole of the domain shown in [Fig.2] after having implemented by computer an additional step of the method according to the invention carried out from the micro-lattice of [Fig.8];

[0042] [Fig. 11] is an enlarged view of [Fig. 10] at a boundary area between the two subdomains visible in [Fig.2];

[0043] [Fig. 12] shows in two dimensions the Young's modulus (E) of the architecture composite as a whole as a function (on the abscissa) of the density of the material, for several values ​​of relative proportion of “soft zones” (Voronoi) compared to the “hard zones” (Delaunay).

[0044] [Fig. 13] shows in two dimensions the modularity of the ratio (G / K) between the shear modulus (G) and the compression modulus (K) of the composite architecture as a whole as a function (on the abscissa) of the density of the material, for several values ​​of relative proportion of “soft zones” (Voronoi) compared to “hard zones” (Delaunay). Detailed description of the invention

[0045] [Fig.l] is a schematic representation of the different main stages of the method according to the invention.

[0046] The invention relates to a method for manufacturing a two- or three-dimensional part having a composite architecture with at least two different micro-lattices, connected to each other, comprising the following steps: • perform 100 a computer-implemented design step; then • manufacture 200 of the architecture thus designed.

[0047] The computer-implemented design step comprises the following steps A) to E).

[0048] Step A) consists of defining 100A a domain representing the two- or three-dimensional part to be manufactured, then defining a first sub-domain intended to delimit a first micro-lattice as well as at least one second sub-domain, complementary to the first sub-domain, for its part intended to delimit a second micro-lattice different from the first micro-lattice.

[0049] B) define (100B), over the entire domain, the coordinates of generating centers for the first micro-lattice and the second micro-lattice, as follows:

[0050] Step B) consists of defining, over the entire domain, the coordinates of the generating centers for the first micro-lattice and the second micro-lattice as follows:

[0051] B1) from a random two- or three-dimensional 100BINIT arrangement of non-deformable balls of given diameters in the whole of said domain, producing 100B1 a random compact stack of said balls within said domain,

[0052] B2) for each ball of the random two- or three-dimensional compact stack of said domain, determine 100B2 the coordinates of the center of the ball, then

[0053] B3) for each ball of the random two- or three-dimensional compact stack of said domain, associate 100B3 the coordinates of the center of the ball with those of a generating center for any of the first or second micro-lattices,

[0054] Step C) consists of defining the first micro-lattice delimited by the first sub-domain as follows:

[0055] Cl) carry out 100C1 a Delaunay triangulation with the generating centers (in this case nodes) then, associate two nodes connected by a side of a triangle to a micro-beam,

[0056] C2) delete 100C2 each micro-beam of which neither of the two nodes belongs to the first subdomain,

[0057] C3) identify and delete 100C3 each micro-beam of which one of the two nodes only belongs to the first subdomain, the node belonging to the first subdomain being then identified as the boundary node of the first subdomain.

[0058] Then, step D) consists, from the coordinates of the generating centers obtained at the end of step B3), of defining 100D a second micro-lattice different from the first micro-lattice and delimited by the second sub-domain, as follows:

[0059] Dl) ​​generate 100D1 a Voronoi diagram using said generating centers as seeds of said diagram then, associate two nodes connected by the Voronoi diagram to a micro-beam,

[0060] D2) delete 100D2 each micro-beam of which neither of the two nodes belongs to the second subdomain,

[0061] D3) identify and delete 100D3 each micro-beam of which one of the two nodes only belongs to the second subdomain, the node belonging to the second subdomain being identified as the boundary node of the second subdomain.

[0062] Step E) consists of connecting 100E the second micro-lattice to the first micro-lattice. From a practical point of view, there are different ways of connecting the second micro-lattice to the first micro-lattice, which will be detailed later.

[0063] The design step also provides for defining a shape and associated transverse dimensions for each micro-beam.

[0064] We will explain this process with the help of an example of implementation. For the sake of clarity of representation, we have chosen to do it in 2 dimensions, but the extrapolation into 3 dimensions is direct. Step A)

[0065] Step 100A consists of defining a domain representing the two- or three-dimensional part to be manufactured, then defining a first sub-domain intended to delimit a first micro-lattice as well as a second sub-domain, complementary to the first sub-domain, for its part intended to delimit a second micro-lattice different from the first micro-lattice.

[0066] An example of a domain separated into a first subdomain (in white) and a second subdomain (in gray) is provided in [Fig.2]. Step B)

[0067] We start 100BINIT from a three-dimensional random arrangement of non-deformable balls. The term balls covers indifferently a ball (solid) or a sphere (hollow) in the mathematical sense of the term.

[0068] 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 micro-beams.

[0069] The diameter of the different balls is not necessarily identical.

[0070] 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 defining an isotropic architecture.

[0071] From this initial state, the step aims to obtain 100B1 a random compact stack of said balls within the entire domain.

[0072] There are different types of algorithms in the literature for obtaining this type of stacking. Thus, it is possible to use a Lu-bachevsky-Stillinger algorithm, a so-called "force-biased" algorithm according to English terminology which can be translated as "force bias" in French, an algorithm derived from these or even any succession of these different algorithms.

[0073] 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): Geometry properties of random disk packings, Journal of Statistical Physics, 60 (5-6): 561-583.

[0074] 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.

[0075] In the present case, here is the procedure used in the example considered to generate the random arrangement of balls within said domain and therefore implement step 100B1.

[0076] We used the algorithm developed by Vasili Baranau, accessible at https: / / github.com / VasiliBaranov / packing-generation (distributed under the MIT License).

[0077] 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.

[0078] The container, circular (we are in 2D), was chosen with a radius of size 100 (arbitrary dimension). This is the size of the container before compaction of the balls.

[0079] The balls were chosen with almost identical diameters, with a distribution log normal with mean value fixed at 1 (arbitrary dimension) and a standard deviation of 0.2. 8800 marbles were considered.

[0080] 100 iterations were performed.

[0081] The contraction rate was chosen to be 0.1 (arbitrary unit). The lower the contraction rate, the greater the compactness of the stack of balls.

[0082] 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 balls in the container.

[0083] The execution of the algorithm (called PackingGeneration.exe) is then carried out in "fba" mode (this is a "Forced-Biased" algorithm). The pre-stacking obtained after implementing this algorithm is given in a packing.xyzd file containing the X, Y 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).

[0084] We then use these last two files as inputs to the same algorithm (PackingGeneration.exe) but executed in “1s” mode (indicates a Lu-bachevsky-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.

[0085] These new packing.xyzd and packing.nfo files are used as inputs to the same algorithm (PackingGeneration.exe) but now in "Isgd" mode (algorithm derived from that of Lubachevsky-Stillinger, 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 on the stack and in particular, its compactness. The compactness obtained in this example implementation is 0.88.

[0086] Finally, the X, Y 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: [Maths 1] \ 1 / 3 UpJ where the parameters pfin and pth are both given in packing.info. 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.

[0087] [Fig.3] represents the compact random stacking of non-deformable balls of almost identical diameters (the variability of the diameters does not exceed 20% compared to at an average diameter), obtained after having implemented by computer step 100B1 of the method according to the invention. The 2D geometry of the stack in fact imposes a statistical distribution of the diameters to avoid crystallization. Here this distribution is log normal with an average value fixed at 1 and a standard deviation of 0.2.

[0088] Then, step 100B2 consists, for each ball of the two- or three-dimensional random compact stack of said domain, in determining 100B2 the coordinates of the center of each ball.

[0089] In this case, the coordinates of the center of each ball are in this case available in the packing.xyzd file obtained at the end of step 100B1.

[0090] Then, step 100B3 consists, for each ball of the two- or three-dimensional random compact stack of the domain, in associating the coordinates of the center of the ball with those of a generating center for any one of the first or second microlattices.

[0091] [Fig.4] represents the cloud of generating centers obtained after having implemented step 100B3 by computer. Step C)

[0092] The objective of step 100C is to define a first micro-lattice delimited by the first sub-domain.

[0093] During a step 100C1, a Delaunay triangulation is carried out with the generating centers obtained at the end of step B3).

[0094] This triangulation defines the triangles with the closest nodes, which 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 rest 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 to obtain good mechanical properties, in particular with regard to rigidity (E / q ratio). A Delaunay triangulation was implemented in the example implementation followed. More precisely, we can refer to the following document giving the algorithm: https: / / docs.scipy.org / doc / scipy / reference / generated / scipy.spatial.Delaunay.html (Python). This is what was used in the context of the example implementation described here.

[0095] Then, to define the micro-lattice, it is sufficient to associate in a dedicated file two nodes connected by a triangle side to a micro-beam.

[0096] 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 100B1 of carrying out the random compact stacking within said domain.

[0097] The shape of the micro-beams and the associated transverse dimensions are data provided independently.

[0098] The definition of the shape and transverse dimensions of the micro-beams can be carried out at various times during the design step 100. This data only becomes useful for carrying out the actual manufacturing.

[0099] In particular, once the shape is fixed, determining the transverse dimensions makes it possible to adjust the final relative density of the micro-lattice. 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 possible to easily control the relative density of the architecture that one seeks to manufacture. Thus, for example in two-dimensional (2D), if these transverse dimensions are significantly smaller than the length of the micro-beams (a situation making it possible to obtain a low relative density), the relative density of the architecture that will be manufactured evolves as the ratio between this transverse dimension and the average length of the micro-beams.

[0100] In practice, in 2D, a micro-beam in the form of a plate can be provided. In 3D, for example, a cylindrical shape can be provided.

[0101] [Fig.5] represents the micro-lattice obtained at the end of step 100C1.

[0102] Next, a step 100C2 is implemented consisting of deleting each microbeam of which neither of the two nodes belongs to the first sub-domain.

[0103] Then, a step 100C3 is implemented consisting of identifying and deleting each micro-beam of which only one of the two nodes belongs to the first sub-domain. The node belonging to the first sub-domain is then identified as the border node of the first sub-domain.

[0104] [Fig.6] represents the micro-lattice obtained at the end of step 100C3.

[0105] Step C) thus makes it possible to generate within the first sub-domain a micro-lattice with a globally amorphous, isotropic architecture and a maximum E / p ratio. The construction of this micro-lattice is based on a Delaunay triangulation, applied to a random compact stack of beads, advantageously monodisperse. This triangulation guarantees, for a given domain of size consistent with those of a triangle (namely a domain of size much larger than those of triangles), that the connectivity at any node is at least equal to 6 in two dimensions (2D), or at least equal to 12 in three dimensions (3D) and the global isotropy is then inherited from the globally amorphous construction of the stack of beads. This micro-lattice therefore has a substantially well-defined Young's modulus and a Poisson's modulus, and a high rigidity. The rigidity then varies substantially linearly with the density in 2D as in 3D. Step D)

[0106] The objective of step 100D is to define the second micro-lattice, different from the first micro-lattice, and delimited by the second sub-domain. The second sub-domain is complementary to the first sub-domain within the domain.

[0107] Here, from the coordinates of the generating centers obtained at the end of step B3), step 100D1 consists of generating a Voronoi diagram using the generating centers as seeds of said diagram and then, said diagram to connect two nodes of the Voronoi diagram by a micro-beam. In other words, each of the edges of the polygons (in two dimensions) or polyhedra (in three dimensions) defined by the Voronoi diagram is associated with a micro-beam, and each of the vertices of these polygons or polyhedra with a node.

[0108] Then, it is appropriate to delete during step 100D2 each micro-beam of which neither of the two nodes belongs to the second sub-domain.

[0109] Then, finally, it is appropriate to identify and delete 100D3 each micro-beam of which only one of the two nodes belongs to the second sub-domain, the node belonging to the sub-domain then being identified as the border node of the second sub-domain.

[0110] The result of the Voronoi tessellation performed in the second subdomain is visible in Figures 7 and 8. [Fig.8] is an enlarged view of [Fig.7], at a boundary area between the two subdomains. The boundary nodes are identified by circles.

[0111] Step D) thus makes it possible to generate a micro-lattice for the second sub-domain with a globally amorphous, isotropic architecture and minimal E / p ratio. The construction of this micro-lattice is based on a Voronoi tessellation applied to a random compact stack of beads, advantageously monodisperse. The Voronoi tessellation guarantees that the connectivity at any node is equal to 3 in two dimensions (2D), or equal to 4 in three dimensions (3D) and the global isotropy is then inherited from the globally amorphous construction of the stack of beads. This micro-lattice therefore has a substantially well-defined Young's modulus and Poisson's modulus, and low rigidity. The Young's modulus varies substantially as the cube of the density in 2D, or as the square of the density in 3D. Step E)

[0112] Step 100E consists of connecting the second micro-lattice (obtained at the end of step D) to the first micro-lattice (obtained at the end of step C).

[0113] [Fig.9] allows us to better visualize what is done on the first sub-domain since the configuration of [Fig.7] to match the Delaunay triangulation with the limits of the first sub-domain.

[0114] Figures 10 and 11 show more precisely the connection between the two sub-domains.

[0115] In step C3), each micro-beam of which only one of the two nodes belonged to the first sub-domain was identified before being deleted.

[0116] Thus, initially, for each micro-beam thus identified then deleted at the end of step C3), we can redefine 100E1 the boundary node of the first sub-domain at the point of intersection of the micro-beam identified then deleted with the limit of the first sub-domain, then define a new micro-beam between the old boundary node and the boundary node thus redefined.

[0117] In this case, a step 100E1B (optional) is also provided after step 100E1 during which each border node of the first sub-domain is connected to the closest border node of the first sub-domain. This makes it possible to increase the connectivity of the border nodes of the first sub-domain. This step 100E1B can be carried out immediately after step 100E1, but can also be carried out later during step 100E.

[0118] [Fig.9] represents the micro-lattice obtained at the end of step 100E1B.

[0119] For each border node of the second sub-domain identified in step 100D3, it is appropriate to search during step 100E2 for the border node of the first sub-domain which is closest to it and to connect these two nodes by a micro-beam.

[0120] Then, for each border node of the first sub-domain which has not been connected at the end of step 100E2, it is then necessary to search during step 100E3, the border node of the second sub-domain which is closest to it and to connect these two nodes by a micro-beam.

[0121] This ensures that each border node of one subdomain is connected to a border node of the other subdomain.

[0122] [Fig. 10] shows what is obtained at the end of step E) as described above. [Fig. 11] is an enlarged view of [Fig. 10] at a boundary zone between the two subdomains.

[0123] The design is at this stage complete.

[0124] It is then sufficient to implement manufacturing step 200.

[0125] However, depending on the manufacturing method used, it may be necessary to implement an additional step 100AE during the design step 100 consisting of producing a mesh representative of the micro-lattice obtained at the end of step 100E. This mesh is typically produced using computer-aided design (CAD) software. This is the case, for example, if the manufacturing step 200 is carried out by additive manufacturing. Step 100AE can also be used to define a shape and associated transverse dimensions for each micro-beam, for example a plate shape for a bidi micro-lattice dimensional (2D), or a cylinder shape with the definition of its diameter for a three-dimensional (3D) micro-lattice.

[0126] Furthermore, it should be noted that other connection strategies between the two subdomains are possible.

[0127] For example, we can proceed as follows.

[0128] In step D3), each micro-beam of which only one of the two nodes belonged to the second sub-domain was identified before being deleted.

[0129] Thus, initially, for each micro-beam thus identified then deleted at the end of step D3), we can redefine IOOE'1 the boundary node of the second sub-domain at the point of intersection of the micro-beam identified then deleted with the limit of the second sub-domain, then define a new micro-beam between the old boundary node and the boundary node thus redefined.

[0130] For each border node of the first sub-domain identified in step 100C3, it is appropriate to search during step 100E'2 for the border node of the second sub-domain which is closest to it and to connect these two nodes by a micro-beam.

[0131] Then, for each border node of the second sub-domain which has not been connected at the end of step 100E'2, it is appropriate to search during step 100E'3 for the border node of the first sub-domain which is closest to it and to connect these two nodes by a micro-beam.

[0132] It is possible to envisage an additional (optional) step, for example after step 100E' 1, aimed at increasing the connectivity of the nodes at the border of the two sub-domains, with the aim of being able to achieve a smoother transition with the other sub-domain.

[0133] Furthermore, it should also be noted that the order of the steps, going from step A) to step E) following the alphabetical order in the exemplary embodiment provided previously, can be adapted. Thus, steps C) and D) can be interchanged.

[0134] Finally, it is understood that if in the example embodiment provided previously, the first sub-domain in which the Delaunay triangulation is carried out is the larger of the two sub-domains (see figures), this is only a choice for the purposes of the illustration. Thus, depending on the desired result, the first sub-domain in which the Delaunay triangulation is carried out could very well be the smaller of the two sub-domains.

[0135] In the context of the invention, it is possible to manufacture a composite architecture composed of hard zones (Delaunay triangulation) and soft zones (Voronoi tessellation) on a domain capable of presenting any geometry, whether in two dimensions or in three dimensions. The density of each of these microlattices is modular over a wide range, their elastic modulus also, as well as the ratio of shear response to compression response. The accessible ranges cover several orders of magnitude.

[0136] By judiciously assembling the hard and soft areas, it is also possible, without using different constituent materials for these areas, to reproduce the different mechanisms manipulated in classic composites: reinforcement mechanisms, gradients of functional properties, combination of a priori exclusive properties (brick and mortar structure of mother-of-pearl giving it hardness and toughness for example).

[0137] Furthermore, in the context of the present invention, for each microlattice of the composite architecture, an amorphous architecture is generated without starting from a periodic network, and which therefore presents an absence of medium and long-range order. Within each microlattice, the mechanical behavior is therefore globally isotropic. Furthermore, the mechanical performances obtained are optimal (for example, maximum E / p ratio in the hard zones and minimum E / p ratio in the soft zones).

[0138] Finally, depending on the prescribed distribution of hard and soft zones, the local mechanical behavior in the total micro-lattice is modular.

[0139] [Fig. 12] shows for example the modularity of the Young's modulus (E) of the composite architecture as a whole as a function (on the abscissa) of the density (d) of the material, for several values ​​of relative proportion of "soft zones" (Voronoi) compared to "hard zones" (Delaunay). In particular, the figure shows a straight line representing the evolution of the Young's modulus as a function of the density in pure Voronoi, as well as, conversely, another straight line representing this same evolution but in pure Delaunay. Between these two straight lines, we observe that by varying the density of the material as well as the proportion of the different soft or hard zones, it is possible to tile a wide range of Young's modulus values.

[0140] [Fig. 13] shows the modularity of the ratio (G / K) between the shear modulus (G) and the compression modulus (K) of the composite architecture as a whole as a function (on the abscissa) of the density (d) of the materials, for several values ​​of the relative proportion of "soft zones" compared to the "hard zones". In particular, the figure shows a straight line representing the evolution of the G / K ratio as a function of the density in pure Voronoi, as well as, conversely, another straight line representing this same evolution but in pure Delaunay. Between these two straight lines, we observe that by varying the density of the material as well as the proportion of the different zones, it is possible to modularly obtain a material that preferentially resists compression deformations or shear deformations.

[0141] It is also possible to subdivide during step A) the domain into more than two sub-domains to delimit as many micro-lattices as are different from each other. Thus, for example, the domain can be subdivided into N sub-domains, with N a natural integer greater than or equal to 3, in which the different subdomains are complementary to each other within the domain.

[0142] It is then sufficient to adapt the method with additional steps. For example, if we consider N = 3 sub-domains during step A), we continue with steps B) and C) then we add a step C') on another sub-domain similar to step C) before continuing with step D) for the last sub-domain. The connection between two sub-domains then follows the same rules as those set out for step E).

[0143] The invention also relates to a two- or three-dimensional part having a composite architecture with at least two different micro-lattices connected to each other, the first micro-lattice, isotropic, having an architecture made with micro-beams connected to each other by forming Delaunay triangles and the second micro-lattice, also isotropic, having an architecture made with micro-beams connected to each other by forming Voronoi cells, each boundary node of the second sub-domain being connected to a boundary node of the first sub-domain and vice versa.

[0144] This part is the one which is directly obtained by implementing steps A) to E) described previously.

Claims

Claims

1. Method for manufacturing a two- or three-dimensional part having a composite architecture with at least two different micro-lattices connected to each other, comprising the following steps: • carry out (100) a computer-implemented design step comprising the following steps: A) defining (100A) a domain representing the two- or three-dimensional part to be manufactured, then defining a first sub-domain intended to delimit a first micro-lattice as well as at least one second sub-domain, complementary to the first sub-domain, for its part intended to delimit a second micro-lattice different from the first micro-lattice; B) define (100B), over the entire domain, the coordinates of generating centers for the first microlattice and the second microlattice, as follows: Bl) from a random two- or three-dimensional arrangement (100BINIT) of non-deformable balls of given diameters in the whole of said domain, producing (100B1) a random compact stack of said balls within said domain, B2) for each ball of the two- or three-dimensional random compact stack of said domain, determine (100B2) the coordinates of the center of the ball, then B3) for each ball of the two- or three-dimensional random compact stack of said domain, associating (100B3) the coordinates of the center of the ball with those of a generating center for any one of the first or second micro-lattices, C) define (100C) the first micro-lattice delimited by the first sub-domain as follows: Cl) carry out (100C1) a Delaunay triangulation with the generating centers then associate two nodes connected by a side of the triangle to a micro-beam, C2) delete (100C2) each micro-beam of which neither of the two nodes belongs to the first sub-domain, C3) identify and delete (100C3) each micro-beam of which only one of the two nodes belongs to the first sub-domain, the ap- belonging to the first sub-domain then being identified as a boundary node of the first sub-domain, D) from the coordinates of the generating centers obtained at the end of step B3), define (100D) the second micro-lattice different from the first micro-lattice and delimited by the second sub-domain, as follows: Dl) generate (100D1) a Voronoi diagram using the generating centers as seeds of said diagram then, associate two nodes connected by the Voronoi diagram with a micro-beam, D2) delete (100D2) each micro-beam of which neither of the two nodes belongs to the second sub-domain, D3) identify and delete (100D3) each micro-beam of which only one of the two nodes belongs to the second sub-domain, the node belonging to the second sub-domain being identified as a boundary node of the second sub-domain;E) connecting (100E) the second micro-truss to the first micro-truss, the design step also providing for defining a shape and associated transverse dimensions for each micro-beam, then: • manufacturing (200) the architecture thus designed.;

2. Method according to claim 1, characterized in that step B1) is implemented from a random arrangement of balls of identical diameters.

3. Method according to one of the preceding claims, characterized in that step B1) is implemented by a Lu-bachevsky-Stillinger algorithm, a so-called force bias algorithm, an algorithm derived from these or any succession of these different algorithms.

4. Method according to one of the preceding claims, characterized in that step E) comprises the following steps: E1) for each identified then deleted micro-beam obtained in step C3), redefine (100E1) the boundary node of the first sub-domain at the point of intersection of the identified then deleted micro-beam with the boundary of the first sub-domain, then define a new micro-beam between the old boundary node and the boundary node thus redefined, E2) for each boundary node of the second sub-domain, search (100E2) the border node of the first sub-domain which is closest to it and connect these two nodes by a micro-beam, E3) for each border node of the first sub-domain which has not been connected at the end of step E2), search (100E3) the border node of the second sub-domain which is closest to it and connect these two nodes by a micro-beam.

5. Manufacturing method according to the preceding claim, characterized in that step E) comprises, after step El), an additional step (100E1B) consisting of connecting each border node of the first sub-domain with the border node closest to the first sub-domain.

6. Method according to one of claims 1 to 3, characterized in that step E) comprises the following steps: E' 1) for each micro-beam obtained identified then deleted in step D3), redefine (100E' 1) the boundary node of the second sub-domain at the intersection point of the micro-beam identified then deleted with the limit of the second sub-domain, then define a new micro-beam between the old boundary node and the thus redefined boundary node, E'2) for each boundary node of the first sub-domain, search (100E'2) for the boundary node of the second sub-domain which is closest to it and connect these two nodes by a micro-beam, E'3) for each boundary node of the second sub-domain which has not been connected at the end of step E'2), search (100E'3) for the boundary node of the first sub-domain which is closest to it and connect these two nodes by a micro-beam.

7. Method according to one of the preceding claims, characterized in that it comprises a step (100AE), implemented at the end of the design step (100) and consisting of producing a mesh of each micro-lattice before implementing the manufacturing step.

8. Method according to the preceding claim, characterized in that the manufacturing step is carried out by additive manufacturing.

9. Two or three-dimensional part having a composite architecture with at least two different micro-lattices connected to each other, the first micro-lattice, isotropic, having an architecture made with micro-beams connected to each other to form Delaunay triangles and the second micro-lattice, also isotropic, having an architecture made with micro-beams connected to each other to form forming Voronoi cells, each boundary node of the second subdomain being connected to a boundary node of the first subdomain and vice versa.

Images