A method for manufacturing a two- or three-dimensional part with a composite architecture featuring at least two different micro-meshes connected to each other.
A composite architecture method using Delaunay and Voronoi micro-lattices addresses anisotropy in periodic lattices, enabling ultra-lightweight parts with modular mechanical properties and isotropy without multiple materials, achieving optimal stiffness and property gradients.
Patent Information
- Authority / Receiving Office
- FR · FR
- Patent Type
- Patents
- Current Assignee / Owner
- COMMISSARIAT A LENERGIE ATOMIQUE ET AUX ENERGIES ALTERNATIVES
- Filing Date
- 2023-12-14
- Publication Date
- 2026-05-08
AI Technical Summary
Existing composite materials face limitations due to environmental, cost, and raw material constraints, and periodic micro-lattices exhibit anisotropic mechanical behavior, making it difficult to achieve ultra-lightweight parts with modular mechanical properties without using different constituent materials.
A method for manufacturing a two- or three-dimensional part with a composite architecture comprising two different micro-lattices connected through Delaunay triangulation and Voronoi tessellation, allowing for controlled pore arrangement and isotropic mechanical properties.
The method enables the creation of ultra-lightweight parts with locally modulated mechanical properties, replicating strengthening mechanisms and property gradients without using multiple materials, achieving optimal stiffness and isotropy.
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Abstract
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 provide more advantageous mechanical behavior than the individual constituent materials alone possess. Generally, the mechanical behavior of a material is defined by its Young's modulus (E) and Poisson's modulus (v) to characterize stiffness, its yield strength (oY) to characterize hardness, and its toughness (Kc) to characterize fracture resistance. For these quantities to be true material constants, the microstructure of each of the constituent materials must be isotropic.
[0004] Examples of composite materials include reinforced concrete (a composite with concrete to provide compressive strength and steel reinforcement to provide tensile strength), glass fibers embedded in resin (an assembly of glass fibers to provide rigidity and resin, for example, a thermoplastic resin such as polyester to provide fracture resistance), and, taking an example from nature, mother-of-pearl, whose brick-and-mortar structure, composed of a hard mineral phase (brick) and a soft organic phase (mortar), provides an unparalleled combination of hardness and toughness. More generally, see Clyne, D. Hull, An Introduction to Composite Materials, 3rd edition, Cambridge University Press (2019).
[0005] In addition to the choice of individual constituent materials of the composite material, the spatial arrangement of the various individual constituent materials is a key element for optimizing mechanical properties. Thus, for example, in the case of mother-of-pearl, the fact that the mineral (hard) phase is geometrically arranged in the form of bricks and that the organic (soft) phase is geometrically arranged in the form of mortar between the bricks gives it a toughness three orders of magnitude greater than that of nacre. higher than that of the individual constituent materials. See 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-related, related to access to raw materials or recycling, may 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 approach to reducing the energy and carbon impact, particularly of vehicles, is to minimize the density (or mass density) of the materials used without compromising 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 be achieved in particular by means of additive manufacturing. Additive manufacturing makes it possible to extensively modulate the architecture of the material, and therefore to arrange the pores in space in a controlled manner and, consequently, to control their impact on mechanical performance.
[0012] Reference may be made, for example, to the article by TX Zheng et al.: Ultrastiff Mechanical Metamaterials, Science, 3434(6105890), 9621373-9651377 (2011-2014), which proposes a micro-truss architecture composed of periodically arranged microbeams. As can be seen in this article (Figure 3A), an "octet-truss" arrangement results in a very high stiffness-to-density ratio, while a "Kelvin foam" arrangement results in a much lower ratio.
[0013] The rules to follow to control this stiffness-density ratio in a micro-truss 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 stiffness varies with the cube of the density and if the connectivity Z is greater than or equal to 6, the stiffness is substantially proportional to the density.
[0016] Similarly, in three dimensions (3D), if the connectivity Z is strictly less than 6, the stiffness varies with the square of the density, and if the connectivity Z is greater than or equal to 12, the stiffness is substantially proportional to the density. Thus, For a three-dimensional microtruss with a connectivity of Z = 12 (the best-known example being the microtruss referred to as "octet-truss" in the literature and according to Anglo-Saxon terminology), the stiffness of the architecture with a relative density of 1% (with reference to the solid material) is reduced by a factor ranging from 300 to 1000 compared to that of the constituent material. And for a three-dimensional microtruss with a connectivity of Z = 4 (the best-known example being the microtruss referred to as "Kelvin-foam" in the literature and according to Anglo-Saxon terminology), the stiffness of the architecture with a relative density of 1% is reduced by a factor of 300,000. This information can be found in the article by VS Despandes et 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 introduces a major drawback since the mechanical behavior of the resulting micro-lattice is anisotropic. The material is less rigid or more brittle when subjected to stresses along certain orientations. Due to this anisotropy, it is no longer possible to define the material solely by the usual constants (Young's modulus, Poisson's modulus, yield strength, and toughness) used for structural design.
[0018] An objective of the invention is to provide a two- or three-dimensional part with an ultra-lightweight composite architecture with modular 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 strengthening 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: - to carry out a computer-implemented design phase 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 a 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 the generating centers for the first micro-lattice and the second micro-lattice, as follows: (b) Starting from a random two- or three-dimensional arrangement of rigid balls of given diameters throughout said domain, achieve a random compact packing of said balls within said domain, B2) for each ball in the two- or three-dimensional random close packing of said domain, determine the coordinates of the center of the ball, then B3) for each ball in the two- or three-dimensional random close packing 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 micro-lattice, C) Define the first micro-lattice delimited by the first subdomain as follows: C1) Perform a Delaunay triangulation with the generating centers, then associate two nodes connected by a side of a triangle to a micro-beam. C2) remove each micro-beam where neither of the two nodes belongs to the first subdomain, C3) identify and remove each micro-beam where only one of the two nodes belongs to the first subdomain, the node belonging to the first subdomain then being identified as the boundary node of the first subdomain, 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 subdomain, 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 where neither of the two nodes belongs to the second subdomain, D3) identify and remove each micro-beam where only one of the two nodes belongs to the second subdomain, the node belonging to the second subdomain being identified as the boundary node of the second subdomain; E) connect the second micro-trellis to the first micro-trellis. The design phase also involves defining a shape and associated transverse dimensions for each micro-beam, then: - to manufacture the architecture thus conceived.
[0022] The process according to the invention may include at least one of the following additional steps, taken alone or in combination:
[0023] - step Bl) is implemented from a random arrangement of marbles identical diameters;
[0024] - step Bl) is implemented by a Lubachevsky-Stillinger algorithm, an al force bias algorithm, an algorithm derived from these, or any succession of these different algorithms;
[0025] - Step E) comprises the following steps: E1) for each identified micro-beam then deleted obtained in step C3), redefine the boundary node of the first subdomain at the point of intersection of the identified and then deleted micro-beam with the boundary of the first subdomain, 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 subdomain, find the closest boundary node of the first subdomain and connect these two nodes with a micro-beam; E3) for each boundary node of the first subdomain that has not been connected at the end of step E2), find the closest boundary node of the second subdomain and connect these two nodes with a micro-beam;
[0026] - after step El), an additional step consisting of connecting each boundary node of the first subdomain with the nearest border node of the first subdomain;
[0027] - step E) comprises the following steps: E' 1) for each micro-beam obtained identified and then deleted in step D3), redefine the boundary node of the second subdomain at the point of intersection of the identified and then deleted micro-beam with the boundary of the second subdomain, then define a new micro-beam between the old boundary node and the redefined boundary node; E'2) for each boundary node of the first subdomain, find the nearest boundary node of the second subdomain and connect these two nodes with a micro-beam; E'3) for each boundary node of the second subdomain that has not been connected at the end of step E'2), find the nearest boundary node of the first subdomain and connect these two nodes with a micro-beam;
[0028] - the method comprises a step, implemented at the end of the design step and consisting of creating a mesh for each micro-trellis 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 subdomain being connected to a boundary node of the first subdomain and vice versa. Brief description of the figures
[0031] Other objects and features of the invention will become clearer in the following description, made with reference to the accompanying figures, in which:
[0032] Fig. 1 is a schematic representation of the main steps of a process according to the invention for manufacturing a two- or three-dimensional part having a composite architecture with at least two different micro-lattices connected to each other;
[0033] Figure 2 represents a domain separated into two subdomains obtained after the implementation in the implementation of a first step of the process according to the invention;
[0034] Figure 3 represents a compact random stacking of rigid balls almost identical diameters, obtained after implementing by computer a subsequent step of the process according to the invention;
[0035] [Fig.4] represents a cloud of nodes obtained after implementing by computer a step of the process according to the invention carried out from the arrangement of [Fig.3];
[0036] [Fig.5] represents the micro-lattice obtained throughout the domain after implementing by computer another step of the process according to the invention carried out from the node cloud of [Fig.4];
[0037] Figure 6 represents the micro-lattice obtained after computer implementation another step of the process according to the invention carried out from the micro-lattice of [Fig.5];
[0038] Figure 7 represents the micro-lattice obtained after computer implementation another step of the process according to the invention, within the second subdomain;
[0039] Figure 8 is an enlarged view of Figure 7 at a boundary zone between the two subdomains visible in [Fig.2];
[0040] Figure 9 represents the micro-lattice obtained for the first subdomain after having implemented by computer another step of the process according to the invention which can be carried out from the micro-lattice of [Fig.6];
[0041] Figure 10 represents the micro-lattice finally obtained within the whole of the area shown in [Fig.2] after implementing by computer an additional step of the process according to the invention carried out from the micro-lattice of [Fig.8];
[0042] Figure 11 is an enlarged view of Figure 10 at a boundary zone between the two subdomains visible in [Fig.2];
[0043] Figure 12 shows in two dimensions the Young's modulus (E) of the architecture composite as a whole as a function (on the x-axis) of the material density, 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) with respect to "hard zones" (Delaunay). Detailed description of the invention
[0045] Fig. 1 is a schematic representation of the different main steps of the process 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 computer-implemented design steps; then • to manufacture 200 of the architecture thus conceived.
[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 a second sub-domain, complementary to the first sub-domain, 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] Bl) from a random two- or three-dimensional arrangement 100BINIT of rigid balls of given diameters in the whole of said domain, to realize 100B1 a random compact packing of said balls within said domain,
[0052] B2) for each ball of the two- or three-dimensional random close packing of said domain, determine 100B2 the coordinates of the center of the ball, then
[0053] B3) for each ball of the two- or three-dimensional random close packing of said domain, associate 100B3 the coordinates of the center of the ball with those of a generating center for either of the first or second micro-lattice,
[0054] Step C) consists of defining the first micro lattice delimited by the first subdomain as follows:
[0055] Cl) perform 100C1 a Delaunay triangulation with the generating centers (in this case, nodes) and then associate two nodes connected by a side of a triangle to a micro-beam,
[0056] C2) remove 100C2 each micro-beam of which neither of the two nodes belongs to the first subdomain,
[0057] C3) identify and remove 100C3 each micro-beam of which one of the two nodes only belongs to the first subdomain, the node belonging to the first subdomain then being 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 subdomain, as follows:
[0059] Dl) generate 100D1 a Voronoi diagram using said generating centers as seeds of said diagram and then, associate two nodes connected by the Voronoi diagram to a micro-beam,
[0060] D2) remove 100D2 each micro-beam of which neither of the two nodes belongs in the second subdomain,
[0061] D3) identify and remove 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 to connect the second micro-lattice to the first micro-lattice, which will be detailed later.
[0063] The design stage also includes defining a shape and associated transverse dimensions for each micro-beam.
[0064] We will explain this process with the support of an example of its implementation. For the sake of clarity of representation, we have chosen to do so in 2 dimensions, but the extrapolation to 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, intended to delimit a second micro-lattice different from the first micro-lattice.
[0066] An example of a domain split into a first subdomain (in white) and a second subdomain (in grey) is provided in [Fig.2]. Step B)
[0067] We start 100BINIT from a three-dimensional random arrangement of undeformable 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 process 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 with an arrangement of beads having similar diameters, typically with a variation not exceeding 30% from an average value, or identical diameters to minimize the standard deviation from the average length of the microbeams present in the microtruss that one seeks to manufacture. The homogeneity of the microbeam lengths, along with the random nature of the bead distribution within the three-dimensional close-packed bead arrangement, contributes to defining an isotropic architecture.
[0071] From this initial state, the step aims to obtain 100B1 a random compact stacking of said balls within the entire domain.
[0072] There are various types of algorithms in the literature that allow 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 Anglo-Saxon terminology), an algorithm derived from these, or 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, Z.A. Rycerz & P.W.M. 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 marbles within said domain and thus implement step 100B1.
[0076] We used the algorithm developed by Vasili Baranau, available 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 rate of contraction, 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 beads.
[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 taken into consideration.
[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 bead stack.
[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 the marbles in the container.
[0083] The algorithm (called PackingGeneration.exe) is then executed in "fba" mode (it is a "Forced-Biased" algorithm). The pre-stacking obtained after implementing this algorithm is given in a file packing.xyzd containing the X, Y positions and diameters D of each ball. Attached to this packing.xyzd file is another file, packing.nfo, containing various parameters characteristic of the pre-stacking (e.g., compactness).
[0084] These last two files are then used as inputs to the same algorithm (PackingGeneration.exe) but executed in "1s" mode (indicating a Lu-bachevsky-Stillinger algorithm). This produces a new file, packing.xyzd, containing the X, Y, Z positions and the diameters D updated after compaction, and also a new file, packing.nfo, containing information on the pre-stacking thus obtained.
[0085] These new files, packing.xyzd and packing.nfo, are used as inputs to the same algorithm (PackingGeneration.exe), but now in "Isgd" mode (an algorithm derived from the Lubachevsky-Stillinger 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 close packing, and the file contains various information about the packing, and in particular, its compactness. The compactness obtained in this embodiment 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 values mentioned by a scaling factor F defined as follows: [Maths 1] \ 1 / 3 UpJ where the parameters pfin and pth are both given in packing.info. In this particular case, the F-factor for scaling is F = 1.0842. The implementation of this correction is related to the implementation of the computer program chosen to illustrate the process according to the invention, but is not systematic in implementing step 101 of the process according to the invention.
[0087] Figure 3 represents the close random packing of rigid balls of almost identical diameters (the variability of the diameters does not exceed 20% compared to to an average diameter), obtained after implementing step 100B1 of the process according to the invention by computer. The 2D geometry of the stack imposes a statistical distribution of diameters to prevent crystallization. Here, this distribution is log-normal with a mean value set at 1 and a standard deviation of 0.2.
[0088] Next, step 100B2 consists, for each ball of the two- or three-dimensional random compact stacking of said domain, of determining 100B2 the coordinates of the center of each ball.
[0089] In this particular case, the coordinates of the center of each ball are 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 stacking of the domain, of associating the coordinates of the center of the ball with those of a generating center for any one of the first or second microlattice.
[0091] Fig. 4 represents the cloud of generating centers obtained after implementing step 100B3 by computer. Step C)
[0092] The objective of step 100C is to define a first micro-lattice delimited by the first subdomain.
[0093] During a step 100C1, a Delaunay triangulation is performed with the generating centers obtained at the end of step B3).
[0094] This triangulation defines the triangles with the closest nodes, which allows for a certain homogeneity in the side lengths of each triangle. This homogeneity is important because, as will be seen later in the description, it defines the homogeneity in the length of the microbeams. Defining microbeams with homogeneous lengths (low dispersion) within the microtruss to be manufactured is important for obtaining good mechanical properties, particularly with regard to stiffness (E / q ratio). A Delaunay triangulation was implemented in the following embodiment. More specifically, the following document provides the algorithm: https: / / docs.scipy.org / doc / scipy / reference / generated / scipy.spatial.Delaunay.html (Python). This is what was used in the embodiment described here.
[0095] 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.
[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 diameter chosen for the balls before the implementation of the process according to the invention and step 100B1 of implementation of random compact stacking within said domain.
[0097] The shape of the micro-beams and the associated cross-sectional 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 step 100 of the design. This data only becomes useful for proceeding with the actual manufacturing.
[0099] In particular, once the shape is fixed, determining the transverse dimensions allows for adjusting the final relative density of the micro-truss. These transverse dimensions can vary from one micro-beam to another. However, choosing a cross-section with identical shape and the same transverse dimensions for all micro-beams makes it easy to control the relative density of the structure to be built. Thus, for example, in two dimensions (2D), if these transverse dimensions are significantly smaller than the length of the micro-beams (a situation that results in a low relative density), the relative density of the structure to be built varies 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 shape of a plate can be provided. In 3D, a cylindrical shape can be provided, for example.
[0101] Fig. 5 represents the micro-lattice obtained at the end of step 100C1.
[0102] Next, we implement a step 100C2 consisting of removing each microbeam of which neither of the two nodes belongs to the first subdomain.
[0103] Then, a step 100C3 is implemented, consisting of identifying and removing each micro-beam where only one of the two nodes belongs to the first subdomain. The node belonging to the first subdomain is then identified as the boundary node of the first subdomain.
[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 subdomain, 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 packing of, advantageously monodisperse, marbles. This triangulation guarantees, for a given domain of size consistent with those of a triangle (namely, a domain of much larger size than the triangles), that the connectivity at every 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 marble packing. This micro-lattice therefore exhibits a substantially well-defined Young's modulus and Poisson's modulus, and high stiffness. The stiffness then varies substantially linearly with the density in both 2D and 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 subdomain. The second subdomain is complementary to the first subdomain within the domain.
[0107] Here, starting 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 connecting two nodes of the Voronoi diagram with a microbeam. In other words, each edge of the polygons (in two dimensions) or polyhedra (in three dimensions) defined by the Voronoi diagram is associated with a microbeam, and each vertex of these polygons or polyhedra with a node.
[0108] Next, in step 100D2, each micro-beam where neither of the two nodes belongs to the second subdomain should be removed.
[0109] Then, it is necessary to identify and remove 100D3 each micro-beam of which only one of the two nodes belongs to the second subdomain, the node belonging to the subdomain then being identified as the boundary node of the second subdomain.
[0110] The result of the Voronoi tessellation performed in the second subdomain is shown in Figures 7 and 8. Figure 8 is an enlarged view of Figure 7, at a boundary zone 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 subdomain with a globally amorphous, isotropic architecture and a minimal E / p ratio. The construction of this micro-lattice is based on a Voronoi tessellation applied to a random compact stacking of beads, advantageously monodisperse. The Voronoi tessellation guarantees that the connectivity at each 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 bead stacking. This micro-lattice therefore exhibits a substantially well-defined Young's modulus and Poisson's modulus, and low stiffness. 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 subdomain since the configuration of Fig.7 to match the Delaunay triangulation with the limits of the first subdomain.
[0114] Figures 10 and 11 show more precisely the connection between the two subdomains.
[0115] At step C3), each micro-beam of which only one of the two nodes belonged to the first subdomain was identified before being removed.
[0116] Thus, initially, for each micro-beam thus identified and then deleted at the end of step C3), we can redefine 100E1 the boundary node of the first subdomain at the point of crossing of the micro-beam identified and then deleted with the boundary of the first subdomain, and then define a new micro-beam between the old boundary node and the boundary node thus redefined.
[0117] In this particular case, an optional step 100E1B is also provided after step 100E1, during which each border node of the first subdomain is connected to the nearest border node of the first subdomain. This increases the connectivity of the border nodes of the first subdomain. This step 100E1B can be performed immediately after step 100E1, but can also be performed later during step 100E.
[0118] Fig. 9 represents the micro-lattice obtained at the end of step 100E1B.
[0119] For each boundary node of the second subdomain identified in step 100D3, it is necessary to search in step 100E2 for the boundary node of the first subdomain that is closest to it and to connect these two nodes by a micro-beam.
[0120] Then, for each boundary node of the first subdomain that has not been connected at the end of step 100E2, it is then necessary to search during step 100E3 for the boundary node of the second subdomain that 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] Figure 10 shows what is obtained at the end of step E) as described above. Figure 11 is an enlarged view of Figure 10 at a boundary zone between the two subdomains.
[0123] The design is now 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, which consists of creating a mesh representative of the micro-lattice obtained at the end of step 100E. This mesh is typically created 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 bifacial micro-lattice. 2D, or a cylindrical 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 conceivable.
[0127] One can, for example, proceed as follows.
[0128] At step D3), each micro-beam of which only one of the two nodes belonged to the second subdomain was identified before being removed.
[0129] Thus, initially, for each micro-beam thus identified and then deleted at the end of step D3), we can redefine IOOE'1 the boundary node of the second subdomain at the point of crossing of the micro-beam identified and then deleted with the boundary of the second subdomain, and then define a new micro-beam between the old boundary node and the boundary node thus redefined.
[0130] For each boundary node of the first subdomain identified in step 100C3, it is necessary to search during step 100E'2 for the boundary node of the second subdomain which is closest to it and to connect these two nodes by a micro-beam.
[0131] Then, for each border node of the second subdomain that has not been connected at the end of step 100E'2, it is necessary to search during step 100E'3 for the border node of the first subdomain that is closest to it and to connect these two nodes by a micro-beam.
[0132] It is conceivable to provide an additional (optional) step, for example after step 100E' 1, aimed at increasing the connectivity of the nodes on the border of the two subdomains, in order to be able to achieve a smoother transition with the other subdomain.
[0133] Furthermore, it should also be noted that the order of the steps, from step A) to step E) following alphabetical order in the previously provided embodiment example, can be adapted. Thus, steps C) and D) can be interchanged.
[0134] It is finally understood that if, in the example implementation provided earlier, the first subdomain in which the Delaunay triangulation is performed is the larger of the two subdomains (see figures), this is merely a choice for illustrative purposes. Thus, depending on the desired result, the first subdomain in which the Delaunay triangulation is performed could very well be the smaller of the two subdomains.
[0135] Within the framework of the invention, it is possible to fabricate a composite architecture composed of hard zones (Delaunay triangulation) and soft zones (Voronoi tessellation) over a domain capable of exhibiting any geometry, whether in two or three dimensions. The density of each of these micro-lattices is adjustable over a wide range, as is their elastic modulus, and also 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 nacre giving it hardness and toughness for example).
[0137] Furthermore, within the framework of the present invention, an amorphous architecture is generated for each microlattice of the composite architecture without starting from a periodic lattice, and which consequently exhibits a lack of order over the medium and long spans. Within each microlattice, the mechanical behavior is therefore globally isotropic. Moreover, the mechanical performance obtained is optimal (for example, maximum E / p ratio in hard areas and minimum E / p ratio in soft areas).
[0138] Finally, depending on the prescribed distribution of hard and soft zones, the local mechanical behavior in the total micro-lattice is modulated.
[0139] Figure 12 shows, for example, the modularity of the Young's modulus (E) of the composite architecture as a whole as a function (on the x-axis) of the material's density (d), for several values of the relative proportion of "soft zones" (Voronoi) to "hard zones" (Delaunay). In particular, the figure shows a line representing the evolution of Young's modulus as a function of density in pure Voronoi, and conversely, another line representing the same evolution but in pure Delaunay. Between these two lines, it can be observed that by varying the material's density and the proportion of the different soft and hard zones, it is possible to tile a wide range of Young's modulus values.
[0140] Figure 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 x-axis) of the material's density (d), for several values of the relative proportion of "soft zones" to "hard zones." In particular, the figure shows a line representing the evolution of the G / K ratio as a function of density in pure Voronoi, and conversely, another line representing the same evolution but in pure Delaunay. Between these two lines, it can be observed that by varying the material's density and the proportion of the different zones, it is possible to modularly obtain a material that preferentially resists either compressive or shear deformation.
[0141] It is also possible to subdivide the domain during step A) into more than two subdomains to delimit as many micro-lattices as there are different from each other. Thus, for example, the domain can be subdivided into N subdomains, with N being a natural number greater than or equal to 3, in which the different subdomains are complementary to each other within the domain.
[0142] It is then simply a matter of adapting the process with additional steps. For example, if we consider N = 3 subdomains during step A), we continue with steps B) and C), then we add a step C') on another subdomain similar to step C) before proceeding with step D) for the last subdomain. The connection between two subdomains 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 subdomain being connected to a boundary node of the first subdomain and vice versa.
[0144] This part is the one that is directly obtained by implementing steps A) to E) described above.
Claims
Demands
1. 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 comprising the following steps: A) define (100A) 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 a second sub-domain, complementary to the first sub-domain, 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 micro-lattice and the second micro-lattice, as follows: (11) from a random two- or three-dimensional arrangement (100BINIT) of rigid balls of given diameters in the whole of said domain, realize (100B1) a random compact packing of said balls within said domain, B2) for each ball in the two- or three-dimensional random close packing of said domain, determine (100B2) the coordinates of the center of the ball, then B3) for each ball in the two- or three-dimensional random compact stacking of said domain, associate (100B3) the coordinates of the center of the ball with those of a generating center for any one of the first or second micro-lattice, C) define (100C) the first micro-lattice delimited by the first subdomain as follows: Cl) perform (100C1) a Delaunay triangulation with generating centers and then associate two nodes connected by a side of a triangle to a micro-beam, C2) remove (100C2) each micro-beam where neither of the two nodes belongs to the first subdomain, C3) identify and delete (100C3) each micro-beam where only one of the two nodes belongs to the first subdomain, the node ap- starting from the first subdomain being then identified as the boundary node of the first subdomain, 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 subdomain, as follows: D1) generate (100D1) 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 (100D2) each micro-beam of which neither of the two nodes belongs to the second subdomain, D3) identify and delete (100D3) each micro-beam of which only one of the two nodes belongs to the second subdomain, the node belonging to the second subdomain being identified as the boundary node of the second subdomain;E) connect (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: • manufacture (200) the architecture thus designed.;
2. A method according to claim 1, characterized in that step Bl) 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 Bl) 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. A method according to any one of the preceding claims, characterized in that step E) comprises the following steps: E1) for each identified and then deleted microbeam obtained in step C3), redefine (E1) the boundary node of the first subdomain at the point of intersection of the identified and then deleted microbeam with the boundary of the first subdomain, and then define a new microbeam between the old boundary node and the boundary node thus redefined; E2) for each boundary node of the second subdomain, search (100E2) the border node of the first subdomain that is closest to it and connect these two nodes with a micro-beam, E3) for each border node of the first subdomain that has not been connected at the end of step E2), search for (100E3) the border node of the second subdomain that is closest to it and connect these two nodes with a micro-beam.
5. A manufacturing method according to the preceding claim, characterized in that step E) comprises, after step El), an additional step (100E1B) consisting of linking each boundary node of the first subdomain with the nearest boundary node of the first subdomain.
6. A method according to any one of claims 1 to 3, characterized in that step E) comprises the following steps: E' 1) for each microbeam obtained (identified and then deleted in step D3), redefine (100E' 1) the boundary node of the second subdomain at the point where the identified and then deleted microbeam intersects the boundary of the second subdomain, and then define a new microbeam between the old boundary node and the boundary node thus redefined; E' 2) for each boundary node of the first subdomain, find (100E' 2) the nearest boundary node of the second subdomain and connect these two nodes with a microbeam; E' 3) for each boundary node of the second subdomain that has not been connected as a result of step E' 2), find (100E' 3) the nearest boundary node of the first subdomain and connect these two nodes with a micro-beam.
7. A method according to any 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 creating a mesh of each micro-lattice before implementing the manufacturing step.
8. A method according to the preceding claim, characterized in that the manufacturing step is carried out by additive manufacturing.
9. 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 forming Delaunay triangles and the second micro-lattice, also isotropic, having an architecture made with micro-beams connected to each other in forming Voronoi cells, each boundary node of the second subdomain being connected to a boundary node of the first subdomain and vice versa.