Method for generating and predicting plate-beam hybrid metamaterials based on topological-geometric coding

Abstract

The application discloses a kind of plate rod hybrid metamaterial generation and prediction method based on topology-geometry coding, belong to mechanical metamaterial design, additive manufacturing structure optimization and computational mechanics analysis field.This method first establishes periodic three-dimensional cell space model, for rod-shaped lattice structure, according to the one-dimensional connection between cell nodes Establish two-dimensional topology adjacency matrix;For plate lattice structure, according to the topology relationship of the surface element formed by non-collinear node combination to establish three-order adjacency tensor.Rod structure topology matrix, plate structure topology tensor and rod diameter, plate thickness and other geometric parameters are jointly coded, and a topology-geometry unified parameterization description model is established.Combined with entity fusion and Boolean operation method, the automatic generation of plate-rod hybrid mechanical metamaterial structure with different topological forms is realized.The application can realize the rapid design and performance evaluation of mechanical metamaterial structure, and provide technical support for the generation, performance optimization and intelligent design of lightweight structure in additive manufacturing.

Description

Technical Field

[0001] This invention belongs to the fields of mechanical metamaterial design, additive manufacturing structure optimization and computational mechanics analysis, and specifically relates to a method for generating and predicting plate-rod hybrid metamaterials based on topology-geometric coding. Background Technology

[0002] With the increasing demand for lightweight, high-strength, and multifunctional structures in aerospace, energy equipment, biomedicine, and advanced manufacturing, mechanical metamaterials are gradually becoming an important development direction for advanced structural materials because they can achieve macroscopic mechanical property control through artificially designed microstructures.

[0003] Lattice structures, as an important component of mechanical metamaterials, mainly include rod-shaped lattices, plate-shaped lattices, and three-period minimal surface structures. Among these, rod-shaped lattices, typically composed of nodes and connecting rods, offer advantages such as simple structure, easy manufacturing, and high material utilization. However, because their load-bearing paths rely on discrete rods, they are prone to problems such as nodal stress concentration, local yielding of rods, and insufficient load transfer efficiency, limiting their application in high-strength and high-reliability load-bearing structures. Plate-shaped lattices, by forming continuous load-bearing paths through continuous curved surfaces or solid thin walls, can effectively improve structural stability and energy absorption capacity. Compared to rod-shaped structures, which typically possess complex spatial curved surface features, their geometric construction process relies on complex modeling methods, and the inconsistent parameter representation methods restrict the degree of freedom in structural design, while also increasing the difficulty of computational analysis and optimization design.

[0004] Currently, mechanical metamaterial structure design methods mainly target single-type lattice structures, constructing rod-like, plate-like, or curved structures through predefined geometric templates or specific mathematical functions. These methods typically rely on manually designing existing configurations, making it difficult to overcome the limitations of traditional topological forms. Furthermore, the lack of a unified data description method between different types of lattice structures hinders the automatic combination and collaborative design of rod and plate structures.

[0005] In recent years, plate-rod hybrid lattice structures, combining the lightweight advantages of rod lattices with the continuous load-bearing and high stability of plate lattices, have been considered an important structural form for achieving synergistic optimization of high stiffness, high strength, high toughness, and high energy absorption. However, existing plate-rod hybrid lattice structure designs mainly rely on artificially constructed specific cell models, which has the following shortcomings:

[0006] (1) There is a lack of a unified topological expression method.

[0007] Existing methods typically describe rod-like structures using node connections and plate-like structures using surface equations or solid boundaries. However, these methods lack a unified data encoding format, making it difficult to integrate the design of different structural types. Furthermore, it is challenging to achieve coordinated representation of plate and rod structures.

[0008] (2) The automation level of the structure generation process is insufficient.

[0009] Existing plate-rod hybrid structures typically rely on manual modeling and parameter adjustment, making it difficult to quickly generate a large number of structural models with different topological forms and geometric parameter combinations according to design requirements.

[0010] (3) The mapping relationship between structural parameters and mechanical properties is unclear.

[0011] Due to the lack of efficient structure generation and performance evaluation processes, it is difficult to systematically analyze the influence of different topological features, geometric parameters, and relative densities on macroscopic mechanical properties.

[0012] (4) There is a lack of an integrated design method that combines high-throughput generation of structures with performance prediction.

[0013] Existing methods typically separate structural modeling, finite element analysis, and performance evaluation, which makes it difficult to meet the needs of high-throughput design and rapid optimization of mechanical metamaterials.

[0014] Therefore, there is an urgent need to establish a unified coding method that can simultaneously describe the topological information of rod structures and the spatial combination relationship of plate structures, establish a joint expression model that combines topological information and geometric parameters, realize the automatic generation of plate-rod hybrid mechanical metamaterial structures, and combine the finite element homogenization method to quickly predict their equivalent mechanical properties, so as to provide an efficient technical approach for the design and optimization of mechanical metamaterial structures. Summary of the Invention

[0015] The purpose of this invention is to address the problems in existing mechanical metamaterial structure design, such as the lack of a unified expression method for rod-shaped and plate-shaped lattice structures, low efficiency in generating hybrid structures, and long prediction cycles for mechanical properties. This invention provides a method for parameterized generation and homogenized performance prediction of plate-rod hybrid mechanical metamaterial structures based on topological-geometric joint encoding. This method establishes a unified topological and geometric parameter expression model to achieve the collaborative description, automatic combination, and parameterized generation of rod-shaped and plate-shaped lattice structures. Combined with homogenization calculation methods, it enables rapid prediction of the macroscopic mechanical properties of mechanical metamaterials.

[0016] The specific technical solution adopted in this invention is as follows:

[0017] This invention provides a method for generating and predicting hybrid metamaterials based on topological-geometric coding, as detailed below:

[0018] 1) Establish a periodic three-dimensional cell space model, and define the node set, node spatial coordinate information, and periodic boundary information;

[0019] 2) Based on step 1), a two-dimensional topological adjacency matrix is ​​established according to the connection relationship between cell nodes; wherein, the matrix elements are used to indicate whether there is a rod unit connection relationship between two cell nodes, realizing the encoding of the topological information of the rod lattice structure; the determined geometric parameters of the rod unit are encoded; by coupling the encoded topological information and geometric information, a joint encoding model of rod structure topology-geometry is established.

[0020] 3) Based on step 1), a third-order topological adjacency tensor is established according to the combination relationship between cell nodes; wherein, the tensor elements are used to represent whether the three nodes together constitute a plate unit, realizing the topological information encoding of the plate lattice structure; by coupling the encoded topological information and geometric information, a joint encoding model of plate structure topology and geometry is established.

[0021] 4) Based on the topology-geometric joint coding model of the rod structure and the topology-geometric joint coding model of the plate structure, construct a unified topology-geometric joint coding model;

[0022] 5) Based on the unified topology-geometric joint coding model, a plate-rod hybrid mechanical metamaterial structure is automatically generated through entity fusion and Boolean operations;

[0023] 6) The plate-rod hybrid mechanical metamaterial structure is discretized by finite element method and periodic boundary conditions are applied. The equivalent mechanical properties of the structure are obtained through homogenization calculation.

[0024] Preferably, in step 1), the node set includes cell vertex nodes, boundary nodes, face nodes, and body-centered nodes. By adjusting the number and spatial position of the selected nodes, mechanical metamaterial structures with different topologies can be generated.

[0025] Preferably, step 2) is as follows:

[0026] For rod-shaped lattice structures, a second-order topological adjacency matrix A is used. rod ∈{0,1} n×n Describe the topological relationships of the rod structure, where the matrix element is A. ij Let i,j=1, ...,n, where n is the total number of nodes; the adjacency matrix serves as a lookup table, and when node v... i With node v j When there is a link element connection relationship between A ij =1, otherwise A ij =0;

[0027] Establish the geometric parameters of the rod structure =(R b ,Rm ,R e ,L), where R b R is the initial cross-sectional radius of the rod. m R is the radius of the cross section at the middle of the rod. e R is the radius of the end section of the rod, and L is the length of the rod; using R b ,R m ,R e The three parameters are used to geometrically encode the cross-sectional radii of the start, mid, and end points of the rod structure to achieve cross-sectional changes;

[0028] By coupling the topological and geometric information of the rod structure, a joint topological-geometric encoding tensor of the rod structure is formed. =(A rod , );according to The node connection relationships are automatically extracted and assigned corresponding geometric parameters to generate a rod-shaped lattice solid structure, resulting in a rod structure topology-geometric joint coding model.

[0029] Alternatively, the effective rod element length threshold can be set to L. min For lengths less than L min The rod elements are deleted to improve the generation efficiency of the rod structure topology-geometric joint coding model.

[0030] Preferably, step 3) is as follows:

[0031] For plate-like lattice structures, a three-dimensional topological adjacency tensor T is used. plate ∈{0,1} n × n× n Describe the topological relationships of the plate structure, where the tensor element is T. ijk Let i,j = 1, ..., n, where n is the total number of nodes; the adjacency tensor serves as a lookup table, and when node v... i Node v j and node v k When they together form a plate unit, T ijk =1, otherwise T ijk =0;

[0032] Establish the geometric parameters of the plate structure =(t,S), where t is the plate thickness and S is the plate area; by... With T plate Coupling forms a plate structure topology-geometric joint encoding tensor. =(T plate , Based on the preset topology parameters, the cell node connection relationship is selected to obtain the skeleton of the plate lattice unit model. The plate unit thickness parameter is further assigned to generate the plate lattice unit solid structure, and the plate structure topology-geometric joint coding model is obtained.

[0033] Alternatively, the plate unit area threshold can be set to S. min For areas smaller than S min The plate units are deleted to improve the efficiency of generating the topology-geometric joint coding model of the plate structure.

[0034] Preferably, step 4) is as follows:

[0035] The topological-geometric joint encoding tensor of rod structures and plate structures are uniformly expressed as C=( , By constructing a unified structural description model through node connection relationships and geometric parameters, a unified topology-geometric joint coding model is obtained, enabling data fusion of different types of lattice structures.

[0036] Preferably, step 5) is as follows:

[0037] Based on the unified topology-geometric joint coding model, geometric Boolean operations, voxel reconstruction, and topological superposition are performed sequentially. Based on the topology-geometric information of the rod structure topology-geometric joint coding model and the plate structure topology-geometric joint coding model, the automatic combination of plate structure and rod structure is realized to generate plate-rod hybrid mechanical metamaterial structure.

[0038] The topological superposition methods include shared-node hybrid structures and interpenetrating hybrid structures; the shared-node hybrid structure refers to the rod structure and the plate structure sharing some or all of the nodes; the interpenetrating hybrid structure refers to the rod structure and the plate structure having independent topological information, and forming a hybrid structure through spatial fusion.

[0039] Preferably, step 6) is as follows:

[0040] The plate-rod hybrid mechanical metamaterial structure is periodically meshed to establish a finite element model. Periodic boundary conditions are applied to the finite element model, and the elastic modulus E and Poisson's ratio are input. The equivalent elastic matrix of the structure is obtained by finite element simulation calculation using the parameters of the parent material. Furthermore, the equivalent Young's modulus, shear modulus, Poisson's ratio, and local stress distribution of the finite element calculation model are obtained; based on the homogenization calculation results, the mechanical properties of plate-rod hybrid mechanical metamaterial structures under different topological structures, geometric parameters, and relative density conditions are predicted.

[0041] As a preferred embodiment, the method for constructing the finite element calculation model is as follows:

[0042] The 1 / 8_model of the first octant is truncated and discretized into three-dimensional solids using tetrahedral, hexahedral, or voxel elements to obtain the 1 / 8_mesh. The 1 / 8_mesh is then symmetric along the XOY plane to obtain the 1 / 8_mesh_mirror. The 1 / 8_mesh and 1 / 8_mesh_mirror are summed using Boolean to obtain the 1 / 4_mesh. The 1 / 4_mesh is then symmetric along the YOZ plane to obtain the 1 / 4_mesh_mirror. The 1 / 4_mesh and 1 / 4_mesh_mirror are summed using Boolean to obtain the 1 / 2_mesh. Finally, the 1 / 2_mesh is symmetric along the XOZ plane to obtain the 1 / 2_mesh_mirror. The 1 / 2_mesh and 1 / 2_mesh_mirror are summed using Boolean to obtain the final periodic mesh, thus constructing the finite element computation model.

[0043] Compared with the prior art, the present invention has the following advantages:

[0044] (1) This invention establishes a unified topology-geometric joint encoding method, which describes the node connection relationship of the rod structure through a two-dimensional topological matrix and describes the topological relationship of the surface unit of the plate structure through a third-order topological adjacency tensor based on the node combination relationship, thereby realizing a unified digital expression of rod lattice structure, plate lattice structure and plate-rod hybrid lattice structure, and solving the problem of lack of a unified description method for different types of mechanical metamaterial structures.

[0045] (2) This invention breaks through the limitations of traditional single lattice structure design. By jointly controlling the node topology relationship and geometric parameters, it can realize the rapid and automatic generation of plate-rod hybrid mechanical metamaterial structures with different topological forms, different geometric dimensions and different relative densities, thereby improving the degree of freedom of structural design and the efficiency of parameter search.

[0046] (3) This invention combines the structural parameterization generation method with the finite element periodic homogenization analysis method, which can quickly obtain the equivalent elastic matrix, equivalent mechanical performance parameters and local stress distribution law of plate-rod hybrid mechanical metamaterial structure, realize the integration of structural design and performance evaluation, reduce the cost of traditional experimental verification and improve design efficiency.

[0047] (4) The method proposed in this invention has good versatility and scalability. It does not depend on a specific material system and can be applied to the mechanical metamaterial structure design of various material systems such as metal materials, ceramic materials, polymer materials and composite materials.

[0048] (5) The present invention uses a parametric coding method to establish data association between structural topology, geometric parameters and mechanical properties, which can be further combined with structural optimization algorithms, machine learning algorithms and intelligent design methods to provide a data foundation for high-throughput design and performance optimization of mechanical metamaterial structures. Attached Figure Description

[0049] Figure 1 This is a roadmap for the parametric design and homogenization property prediction technology of plate-rod hybrid structures based on topological-geometric joint coding, as described in this invention.

[0050] Figure 2 This is a schematic diagram of a variable cross-section rod system model driven by the geometric parameter encoding of the rod structure cross-section in this invention; wherein, (a) is a variable cross-section rod with thickened ends, (b) is a variable cross-section rod with thickened middle, and (c)-(d) are variable cross-section rods with thickened ends.

[0051] Figure 3 This is a schematic diagram of the plate-rod hybrid structure generation strategy proposed in this invention, including a shared node hybrid method based on node sharing and an interpenetrating hybrid method based on independent topology superposition.

[0052] Figure 4 The rod-shaped lattice structure model P1 generated based on topological encoding in Example 1 has a volume fraction of 20%.

[0053] Figure 5 The plate-like lattice structure model T1 generated based on topological encoding in Example 1 has a volume fraction of 20%.

[0054] Figure 6 The diagram shows the generation of the plate-rod hybrid structure driven by geometric parameter encoding in Example 1 (keeping the volume fraction constant at 20%); where (a) is the base rod diameter structure, (b) the rod diameter increase type structure, (c) the plate thickness increase type structure, and (d) the rod diameter and plate thickness coordinated control type structure.

[0055] Figure 7 The above are homogenized simulation von Mises stress distribution diagrams of different lattice structures in Example 1 under a strain of 0.02; where (a1)-(a6) is the rod-shaped lattice structure model P1, (b1)-(b6) is the plate-shaped lattice structure model T1, and (c1)-(c6) is the plate-rod hybrid structure model PT-1.

[0056] Figure 8 The diagram shows the generation of the plate-rod hybrid structure driven by geometric parameter encoding in Example 1 (keeping the plate thickness constant and changing the rod diameter; where (a) volume fraction is 0.15, (b) volume fraction is 0.2, (c) volume fraction is 0.25, (d) volume fraction is 0.3, and (e) volume fraction is 0.35). Detailed Implementation

[0057] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. Technical features in various embodiments of the present invention can be combined accordingly without mutual conflict.

[0058] like Figure 1 As shown, this invention provides a method for generating and predicting hybrid metamaterials based on topological-geometric coding. This method first establishes a periodic three-dimensional cell space model, defining the set of cell nodes, node coordinate information, and spatial topological relationships. For the rod-shaped lattice structure, a two-dimensional topological adjacency matrix A is established based on the one-dimensional connection relationships between cell nodes. rod This enables the parameterized expression of the topological information of rod elements; for plate-like lattice structures, a third-order adjacency tensor T is established based on the topological relationship of surface elements formed by the combination of non-collinear nodes. plate This paper aims to achieve a digital description of the spatial topological relationships of plate elements. Based on this, the topological matrix of the rod structure, the topological tensor of the plate structure, and geometric parameters such as rod diameter and plate thickness are jointly encoded to establish a unified topological-geometric parametric description model. Combining entity fusion and Boolean operations, the automatic generation of plate-rod hybrid mechanical metamaterial structures with different topological forms is achieved. Furthermore, the generated plate-rod hybrid mechanical metamaterial structures are discretized using the finite element method, periodic boundary conditions are applied, and the equivalent elastic matrix, local stress distribution, and macroscopic mechanical response of the structure are obtained through homogenization calculations.

[0059] The specific steps of this method are as follows:

[0060] S1: Establish a periodic three-dimensional cell space model.

[0061] Establish a standardized three-dimensional periodic cell model (e.g., a cube cell), and define the set of cell nodes: ={v0, v1, ... v n}, where n is the total number of nodes; define the spatial coordinates of the nodes: =( , , ), used to describe the positional information of nodes inside and at the boundaries of a cell.

[0062] As a preferred embodiment of the present invention, the node set mainly includes cell vertex nodes, boundary nodes, face nodes and body-centered nodes. By adjusting the number and spatial position of the selected nodes, mechanical metamaterial structures with different topologies can be generated.

[0063] S2: Based on the node set and node coordinate information of S1, establish a joint coding model of rod structure topology and geometry.

[0064] For rod-shaped lattice structures, a second-order topological adjacency matrix A is used. rod ∈{0,1} n × n Describe the node connection relationship, where matrix element A ij (i,j = 1, ...,n), where n is the total number of nodes. The adjacency matrix serves as a lookup table, where A... ij =1 indicates node v i With node v j There are bar elements present, when A ij =0 indicates that there is no connection between the two nodes. Establish the geometric parameters of the rod structure. =(R b ,R m ,R e ,L), where R b R is the initial cross-sectional radius of the rod. m R is the radius of the cross section at the middle of the rod. e The three parameters—radius of the end section of the rod, the radius of the cross-section at the start, midpoint, and end points—are used to geometrically encode the cross-sectional changes, such as... Figure 2 As shown; L is the rod length. By coupling the topological and geometric information of the rod structure, the adjacency matrix A is... rod and list of geometric parameters Combined, a rod-structured topological-geometric joint encoding tensor is formed. =(A rod , According to the encoding information The node connection relationships are automatically extracted and assigned corresponding geometric parameters to generate a rod-shaped lattice solid structure, resulting in a rod structure topology-geometric joint coding model.

[0065] S3: Screening for the effectiveness of bar structures.

[0066] Set the effective link element length threshold to L. min Link elements with lengths less than a threshold are deleted. Deleting invalid short links improves the efficiency of generating the joint topological-geometric coding model for link structures.

[0067] S4: Establish a joint coding model of plate structure topology and geometry.

[0068] For plate-like lattice structures, a three-dimensional topological adjacency tensor T is used. plate ∈{0,1} n × n× n Describe the topological relationships of the plate structure, where the tensor element is T. ijk Let i, j = 1, ..., n, where n is the total number of nodes. The adjacency tensor serves as a lookup table; when node v... i Node v j and node v k When they together form a plate unit, T ijk =1, otherwise T ijk =0. Establish the geometric parameters of the plate structure. =(t,S), where t is the plate thickness and S is the plate area. By... With T plate Coupling forms a plate structure topology-geometric joint encoding tensor. =(T plate , Based on preset topological parameters, the cell node connection relationship is selected to obtain the skeleton of the plate-shaped lattice unit model. Then, the plate unit thickness parameter is further assigned to generate the plate-shaped lattice unit solid structure, resulting in the plate structure topology-geometric joint encoding model.

[0069] In this embodiment, a plate element is defined by three or more nodes, and its topology is a planar plate element. Three nodes are used to define the plate element in this example.

[0070] S5: Screening for the effectiveness of plate structures.

[0071] Set the plate unit area threshold to S. min For areas smaller than S min The plate elements are deleted, and the efficiency of generating the plate structure topology-geometry joint coding model is improved by deleting unstable surfaces.

[0072] S6: Establish a unified topology-geometric joint coding model.

[0073] Joint encoding tensor of rod structure topology and geometry Joint encoding tensor of plate structure topology and geometry To express C in a unified way , By constructing a unified structural description model using node connectivity and geometric parameters, a unified topology-geometric joint coding model is obtained, enabling data fusion of different types of lattice structures.

[0074] As a preferred embodiment of the present invention, when the plate structure and the rod structure are mixed, the method includes common node connection and non-common node embedded connection.

[0075] S7: Automatic generation of plate-rod hybrid mechanical metamaterial structures.

[0076] Based on a unified topology-geometric joint coding model, and through geometric Boolean operations, voxel reconstruction, and topological superposition, the automatic combination of plate and rod structures is achieved using the topological-geometric joint coding models of rod and plate structures, generating a plate-rod hybrid mechanical metamaterial structure. For example... Figure 3 As shown, in response to the differences in the topology of the two structures, the hybrid superposition methods include: (1) Shared node hybrid structure: the rod structure and the plate structure share some or all of the nodes. (2) Interpenetrating hybrid structure: the rod structure and the plate structure each have independent topological information, and form a hybrid structure through spatial fusion.

[0077] As a preferred embodiment of the present invention, the structural performance of the plate-rod hybrid mechanical metamaterial structure can be controlled by adjusting the following parameters: (1) number of nodes; (2) number of rod units; (3) cross-sectional dimensions of rod units; (4) number of plate units; (5) thickness of plate units; (6) plate-rod combination ratio; (7) relative density of the structure.

[0078] S8: Establish a finite element homogenization model.

[0079] A finite element method (FEM) model is established by periodically discretizing a plate-rod hybrid mechanical metamaterial structure using a mesh. This model can be discretized using voxel elements, hexahedral solid elements, or tetrahedral solid elements.

[0080] As a preferred embodiment of the present invention, the step is as follows:

[0081] The 1 / 8_model of the first octant is truncated and discretized into a 3D solid using tetrahedral, hexahedral, or voxel elements to obtain a 1 / 8_mesh. This 1 / 8_mesh is then symmetric along the XOY plane to obtain a 1 / 8_mesh_mirror. A Boolean sum of the 1 / 8_mesh and 1 / 8_mesh_mirror yields a 1 / 4_mesh. This 1 / 4_mesh is then symmetric along the YOZ plane to obtain a 1 / 4_mesh_mirror. A Boolean sum of the 1 / 4_mesh and 1 / 4_mesh_mirror yields a 1 / 2_mesh. Finally, this 1 / 2_mesh is symmetric along the XOZ plane to obtain a 1 / 2_mesh_mirror. A Boolean sum of the 1 / 2_mesh and 1 / 2_mesh_mirror yields the final, periodic mesh. In other words, a periodic mesh corresponding to the solid model is obtained through three symmetries, thus constructing the finite element computation model.

[0082] S9: Apply periodic boundary conditions to the obtained finite element calculation model and input the parent material parameters (including elastic modulus E and Poisson's ratio). The equivalent elastic matrix of the structure was obtained through finite element simulation calculation. (Including equivalent elastic constants such as elastic modulus, Poisson's ratio, and shear modulus) and the local stress distribution of the model.

[0083] S10: Based on the homogenization calculation results, the mechanical properties of plate-rod hybrid mechanical metamaterial structures under different topological structures, geometric parameters and relative density conditions are predicted.

[0084] The above-described method of the present invention is applicable to the mechanical metamaterial structure design of metal, ceramic, polymer and composite material systems. It can also be further combined with optimization algorithms or data-driven methods to achieve structural parameter search under the constraint of target mechanical properties.

[0085] The effects of the method of the present invention will be specifically illustrated through the following examples.

[0086] Example

[0087] This embodiment provides a method for generating and predicting hybrid metamaterials based on topological-geometric coding, specifically following these steps:

[0088] For a 27-node cube cell, the vertices of the cell are classified into sets of 8 corner vertices. ={v0, v1, v2, v3, v4, v5, v6, v7}, a set of 12 edge nodes. ={ e0, e1, e2, e3, e4, e5, e6, e7, e8, e9, e 10 e 11}, a collection of 6 face nodes ={f0, f1, f2, f3, f4, f5}, and the cell center single-cell node C={c0}.

[0089] The cube cell size is set to 0.5, and the coordinates of the 27 nodes are as follows: n0 = (0,0,0); n1 = (0,0.25,0); n2 = (0,0.5,0); n3 = (0.25,0.5,0); n4 = (0.25,0.25,0); n5 = (0.25,0,0); n6 = (0.5,0,0); n7 = (0.5,0.25,0); n8 = (0.5,0.5,0); n9 = (0,0,0.25); n 10 =(0,0.25,0.25); n 11 =(0,0.5,0.25); n 12 =(0.25,0.5,0.25); n 13 =(0.25,0.25,0.25); n 14=(0.25,0,0.25); n 15 =(0.5,0,0.25); n 16 =(0.5,0.25,0.25); n 17 =(0.5,0.5,0.25); n 18 =(0,0,0.5); n 19 =(0,0.25,0.5); n 20 =(0,0.5,0.5); n 21 =(0.25,0.5,0.5); n 22 =(0.25,0.25,0.5); n 23 =(0.25,0,0.5); n 24 =(0.5,0,0.5); n 25 =(0.5,0.25,0.5); n 26 =(0.5,0.5,0.5).

[0090] Select nodes n1, n9, n 17 n 25 The coordinates of the four nodes are n1 (0, 0.25, 0); n9 (0, 0, 0.25); n 17 (0.5, 0.5, 0.25); n 25 (0.5, 0.25, 0.5). Nodes are connected in pairs to form rods, and the rod numbers and lengths are denoted as {L}. 1-9 ,L 17-25}: ;{L 1-17 ,L 9-25}: ;{L 1-25 ,L 9-17}: Let P be the triangle formed by any three nodes. 1-9-17 ;P 1-9-25 ;P 1-17-25 ;P 9-17-25 The area size is Set L min for The valid rods retained are {L} 1-17 ,L 9-25 ,L 1-25 ,L 9-17};S min The value is 0.1, and the valid triangles retained are {P}. 1-9-17 ;P 1-9-25 ;P 1-17-25 ;P 9-17-25}. The target volume fraction is set to 0.2, and the rod-shaped lattice structure model P1 ( Figure 4 The radius R of the rod, the plate-like lattice structure model T1 ( Figure 5 The thickness t of the plate and the plate-rod hybrid structure models PT-1, PT-2, PT-3 and PT-4 ( Figure 6 The geometric information of the rod diameter and plate thickness is shown in Table 1.

[0091] Table 1 Summary of Model Geometric Parameters

[0092]

[0093] The homogenization performance of the established rod-shaped lattice structure, plate-shaped lattice structure, and plate-rod hybrid lattice structure was calculated. First, the generated structural models were periodically discretized into 64×64×64 voxel units, dividing the computational domain into 64×64×64 voxel units. The number of voxel units and volume fractions of the rod-shaped lattice structure model P1, the plate-shaped lattice structure model T1, and the different plate-rod hybrid structure models (PT-1, PT-2, PT-3, and PT-4) are listed in Table 1.

[0094] Subsequently, periodic boundary conditions were applied to the aforementioned periodic mesh model. TC4 titanium alloy was selected as the matrix material, with its elastic modulus (E) set to 110 GPa and Poisson's ratio (…). The value was set to 0.34. The stress response and equivalent mechanical properties of different structural models were calculated using finite element homogenization, obtaining the equivalent elastic modulus of each structural model along the three principal directions. To eliminate the influence of different structural volume fractions on the evaluation of elastic performance, the ratio of elastic modulus to volume fraction was further normalized, and the specific elastic modulus results are shown in Table 2. Furthermore, taking the rod-like lattice structure model P1, the plate-like lattice structure model T1, and the plate-rod hybrid structure model PT-1 as examples, uniaxial tensile loads were applied along the X, Y, and Z directions, respectively, and shear loads were applied in XOY, XOZ, and YOZ. The von Mises stress distribution inside the structure under different loading conditions was analyzed, and the results are shown in Table 2. Figure 7 As shown.

[0095] Depend on Figure 7 Comparing (a1), (b1), and (c1), it can be seen that when a 2% strain is applied along the X direction, the maximum von Mises stresses of models P1, T1, and PT-1 are 3222 MPa, 6152 MPa, and 3031 MPa, respectively. Among them, the plate-rod hybrid structure model PT-1 has the lowest maximum von Mises stress. Along the Y ( Figure 7 (a2), (b2) and (c2) in the middle and Z ( Figure 7When a 2% strain is applied in the (a3), (b3), and (c3) directions, the stress responses of the models show similar patterns, with PT-1 exhibiting relatively low local maximum stress. In the XOY (… Figure 7 (a4), (b4) and (c44) in XOZ Figure 7 (a5), (b5) and (c5) in the YOZ ( Figure 7 Under the planar shear conditions (a6), (b6) and (c6) in the figure, PT-1 also exhibits a low degree of local stress concentration.

[0096] The above results demonstrate that, under the same loading conditions, the plate-rod hybrid structure can integrate the load transfer characteristics of both rod and plate structures, resulting in a more continuous and uniform load transfer path within the structure. This reduces local stress concentration areas and lowers the maximum von Mises stress. Therefore, the topological fusion of rod and plate structures can effectively improve the load transfer behavior within the lattice structure, enhance the structural load-bearing stability, and provide a basis for the structural design and mechanical property control of plate-rod hybrid mechanical metamaterials.

[0097] Table 2 Summary of Model Specific Elastic Modulus

[0098]

[0099] To further verify the ability of the method of the present invention to control structural parameters, while keeping the plate structure thickness parameter t=0.05 constant, plate-rod hybrid lattice structure models with volume fractions of 0.15, 0.20, 0.25, 0.30, and 0.35 were constructed by adjusting the rod structure radius parameter; the corresponding rod structure radii were set to R=0.015, 0.06, 0.07, 0.083, and 0.091, respectively. The models were constructed using... Figure 8 The method is presented here. By changing the geometric parameters of the rod structure, the automatic generation of plate-rod hybrid structures with different relative densities can be achieved.

[0100] The above results show that the method based on topological-geometric joint encoding proposed in this invention can realize the automatic generation of different types of lattice structures, and can effectively predict the equivalent mechanical properties and local stress distribution of complex mechanical metamaterial structures by combining periodic homogenization analysis methods, providing an effective technical means for the design and optimization of plate-rod hybrid mechanical metamaterial structures.

[0101] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A method for generating and predicting hybrid metamaterials based on topological-geometric coding, characterized in that, Specifically as follows: 1) Establish a periodic three-dimensional cell space model, and define the node set, node spatial coordinate information, and periodic boundary information; 2) Based on step 1), a two-dimensional topological adjacency matrix is ​​established according to the connection relationship between cell nodes; wherein, the matrix elements are used to indicate whether there is a rod unit connection relationship between two cell nodes, realizing the encoding of the topological information of the rod lattice structure; the determined geometric parameters of the rod unit are encoded; by coupling the encoded topological information and geometric information, a joint encoding model of rod structure topology-geometry is established. 3) Based on step 1), a third-order topological adjacency tensor is established according to the combination relationship between cell nodes; wherein, the tensor elements are used to represent whether the three nodes together constitute a plate unit, realizing the topological information encoding of the plate lattice structure; by coupling the encoded topological information and geometric information, a joint encoding model of plate structure topology and geometry is established. 4) Based on the topology-geometric joint coding model of the rod structure and the topology-geometric joint coding model of the plate structure, construct a unified topology-geometric joint coding model; 5) Based on the unified topology-geometric joint coding model, a plate-rod hybrid mechanical metamaterial structure is automatically generated through entity fusion and Boolean operations; 6) The plate-rod hybrid mechanical metamaterial structure is discretized by finite element method and periodic boundary conditions are applied. The equivalent mechanical properties of the structure are obtained through homogenization calculation.

2. The method for generating and predicting plate-rod hybrid metamaterials based on topological-geometric coding according to claim 1, characterized in that, In step 1), the node set includes cell vertex nodes, boundary nodes, face nodes, and body-centered nodes. By adjusting the number and spatial position of the selected nodes, mechanical metamaterial structures with different topologies can be generated.

3. The method for generating and predicting plate-rod hybrid metamaterials based on topological-geometric coding according to claim 1, characterized in that, Step 2) is as follows: For rod-shaped lattice structures, a second-order topological adjacency matrix A is used. rod ∈{0,1} n×n Describe the topological relationships of the rod structure, where the matrix element is A. ij Let i,j=1, ...,n, where n is the total number of nodes; the adjacency matrix serves as a lookup table, and when node v... i With node v j When there is a link element connection relationship between A ij =1, otherwise A ij =0; Establish the geometric parameters G of the rod structure r =(R b ,R m ,R e ,L), where R b R is the initial cross-sectional radius of the rod. m R is the radius of the cross section at the middle of the rod. e R is the radius of the end section of the rod, and L is the length of the rod; using R b ,R m ,R e The three parameters are used to geometrically encode the cross-sectional radii of the start, mid, and end points of the rod structure to achieve cross-sectional changes; By coupling the topological and geometric information of the rod structure, a rod structure topology-geometric joint encoding tensor C is formed. b =(A rod G r According to C b The node connection relationships are automatically extracted and assigned corresponding geometric parameters to generate a rod-shaped lattice solid structure, resulting in a rod structure topology-geometric joint coding model.

4. The method for generating and predicting hybrid metamaterials based on topological-geometric coding according to claim 3, characterized in that, Alternatively, the effective rod element length threshold can be set to L. min For lengths less than L min The rod elements are deleted to improve the generation efficiency of the rod structure topology-geometric joint coding model.

5. The method for generating and predicting plate-rod hybrid metamaterials based on topological-geometric coding according to claim 3, characterized in that, Step 3) is as follows: For plate-like lattice structures, a three-dimensional topological adjacency tensor T is used. plate ∈{0,1} n × n× n Describe the topological relationships of the plate structure, where the tensor element is T. ijk Let i,j = 1, ..., n, where n is the total number of nodes; the adjacency tensor serves as a lookup table, and when node v... i Node v j and node v k When they together form a plate unit, T ijk =1, otherwise T ijk =0; Establish the geometric parameters G of the plate structure p =(t, S ), where t is the plate thickness and S is the plate area; by using G p With T plate Coupling forms the plate structure topology-geometric joint encoding tensor C. p =(T plate G p Based on the preset topology parameters, the cell node connection relationship is selected to obtain the skeleton of the plate lattice unit model. The plate unit thickness parameter is further assigned to generate the plate lattice unit solid structure, and the plate structure topology-geometric joint coding model is obtained.

6. The method for generating and predicting plate-rod hybrid metamaterials based on topological-geometric coding according to claim 5, characterized in that, You can also set the plate unit area threshold to S min For areas smaller than S min The plate units are deleted to improve the efficiency of generating the topology-geometric joint coding model of the plate structure.

7. The method for generating and predicting plate-rod hybrid metamaterials based on topological-geometric coding according to claim 5, characterized in that, Step 4) is as follows: The topology-geometric joint encoding tensor of rod structures and plate structures are uniformly expressed as C=(C b C p By constructing a unified structural description model through node connection relationships and geometric parameters, a unified topology-geometric joint coding model is obtained, enabling data fusion of different types of lattice structures.

8. The method for generating and predicting hybrid metamaterials based on topological-geometric coding according to claim 1, characterized in that, Step 5) is as follows: Based on the unified topology-geometric joint coding model, geometric Boolean operations, voxel reconstruction, and topological superposition are performed sequentially. Based on the topology-geometric information of the rod structure topology-geometric joint coding model and the plate structure topology-geometric joint coding model, the automatic combination of plate structure and rod structure is realized to generate plate-rod hybrid mechanical metamaterial structure. The topological superposition methods include shared-node hybrid structures and interpenetrating hybrid structures; the shared-node hybrid structure refers to the rod structure and the plate structure sharing some or all of the nodes; the interpenetrating hybrid structure refers to the rod structure and the plate structure having independent topological information, and forming a hybrid structure through spatial fusion.

9. The method for generating and predicting plate-rod hybrid metamaterials based on topological-geometric coding according to claim 1, characterized in that, Step 6) is as follows: The plate-rod hybrid mechanical metamaterial structure is periodically meshed to establish a finite element model. Periodic boundary conditions are applied to the finite element model, and the elastic modulus E and Poisson's ratio are input. The equivalent elastic matrix C of the structure is obtained through finite element simulation calculation based on the parameters of the parent material. ij Furthermore, the equivalent Young's modulus, shear modulus, Poisson's ratio, and local stress distribution of the finite element calculation model are obtained; based on the homogenization calculation results, the mechanical properties of plate-rod hybrid mechanical metamaterial structures under different topological structures, geometric parameters, and relative density conditions are predicted.

10. The method for generating and predicting plate-rod hybrid metamaterials based on topological-geometric coding according to claim 9, characterized in that, The specific method for constructing the finite element calculation model is as follows: The 1 / 8_model of the first octant is truncated and discretized into three-dimensional solids using tetrahedral, hexahedral, or voxel elements to obtain the 1 / 8_mesh. The 1 / 8_mesh is then symmetric along the XOY plane to obtain the 1 / 8_mesh_mirror. The 1 / 8_mesh and 1 / 8_mesh_mirror are summed using Boolean to obtain the 1 / 4_mesh. The 1 / 4_mesh is then symmetric along the YOZ plane to obtain the 1 / 4_mesh_mirror. The 1 / 4_mesh and 1 / 4_mesh_mirror are summed using Boolean to obtain the 1 / 2_mesh. Finally, the 1 / 2_mesh is symmetric along the XOZ plane to obtain the 1 / 2_mesh_mirror. The 1 / 2_mesh and 1 / 2_mesh_mirror are summed using Boolean to obtain the final periodic mesh, thus constructing the finite element computation model.

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