Design method of novel mechanical metamaterial database

Abstract

The invention discloses a design method of a novel mechanical metamaterial database. The novel mechanical metamaterial database comprises a large number of novel dot matrix metamaterials. The minimum repetitive units of the novel dot matrix metamaterial are building blocks; the method comprises the steps that representative units are formed by component blocks through symmetric operation of graphic transformation, and the representative units are periodically and densely laid to form the novel dot matrix metamaterial; wherein the building block comprises three structural features, namely a boundary node, an internal node and a rod piece; the plane space occupied by the building blocks is square; the number of boundary nodes of the building block is four, and the boundary nodes are located on the four boundaries of the square respectively. The number of the internal nodes of the building block is at least one, and the internal nodes are distributed in a quadrilateral area defined by the four boundary nodes of the building block; and determining a boundary node position, an internal node position and a rod piece connection relation between the nodes of the building block based on a boundary node position rule, a uniform distribution rule of the internal nodes and a rod piece connectivity rule. A large number of novel dot matrix metamaterials can be efficiently generated.

Description

Technical Field

[0001] The invention relates to a design method for a novel mechanical metamaterial database. Background Art

[0002] Metamaterials are materials with artificially designed structures and extraordinary physical properties that natural materials do not have. Among them, lattice metamaterials are a type of truss-like porous structure composed of periodic repeating units with unusual mechanical properties. They are composed of periodic patterns or geometric networks based on the transformation of building block graphics. They have attracted practical engineering attention due to their design flexibility and unique performance. Building blocks are the smallest repeating units of lattice metamaterials. The mechanical properties of lattice metamaterials depend on the structural form of building blocks and the arrangement and connection mode of graphic transformation. The design flexibility of building blocks gives lattice metamaterials a broad structural design space, which can achieve extraordinary properties such as high stiffness and negative Poisson's ratio. Stiffness refers to the ability of lattice metamaterials to resist elastic deformation when subjected to force, and is a characterization of the difficulty of elastic deformation of the structure. High stiffness is crucial for engineering applications such as ensuring gear meshing and machine tool processing accuracy. Stiffness is usually measured by elastic modulus. Lattice metamaterials with high elastic modulus achieve lightweight while ensuring high stiffness, and have high application value. Poisson's ratio is the ratio of the lateral positive strain to the axial positive strain when the lattice metamaterial is subjected to unidirectional tension or compression. It is an elastic constant that reflects the lateral deformation of the lattice metamaterial. Most common engineering materials only have positive Poisson's ratios, such as metals, ceramics, and polymers. Negative Poisson's ratio materials with functions such as energy absorption and buffering and deformation control are very rare. Negative Poisson's ratio metamaterials can gather at the impact point when impacted to avoid catastrophic collapse and resist deformation. Therefore, they can be used to manufacture special vehicle tires, sports protective equipment, safety helmets and other engineering equipment. In addition, negative Poisson's ratio metamaterials have tensile and expansion properties consistent with the skin, and can be used to develop wearable devices such as flexible skin.

[0003] Existing design methods for lattice metamaterials mainly involve inspired design. Inspired design mainly comes from crystal structure, molecular structure and biological structure, as well as combination design based on these structures. However, since inspired design relies on the designer's experience and intuition, it can only design a limited number of lattice metamaterials and requires a lot of repeated calculations and verifications. Therefore, this design strategy still leaves a huge unexplored structural space.

[0004] Therefore, in the absence of expert knowledge and design guidelines, and lack of design methods to efficiently generate a large number of new mechanical metamaterials, the structural design of new mechanical metamaterials remains extremely challenging and there is a huge gap. Summary of the invention

[0005] The purpose of this application is to provide a design method for a novel mechanical metamaterial database, which can efficiently generate a large number of novel lattice metamaterials.

[0006] The technical solutions provided in this application are:

[0007] The technical solution adopted by the present invention to solve the above problems is:

[0008] In a first aspect, a design method for a novel mechanical metamaterial database includes a large number of novel lattice metamaterials; the smallest repeating unit of the novel lattice metamaterial is a building block; the method comprises: the building block is formed into a representative unit through a symmetric operation of a graphic transformation, and the representative unit is periodically densely laid to form a novel lattice metamaterial;

[0009] Wherein, the building block includes three structural features, namely, boundary nodes, internal nodes and rods;

[0010] The plane space occupied by the building block is a square with a side length of D; the building block has 4 boundary nodes, which are respectively located on the 4 boundaries of the square; the building block has at least 1 internal node, which is distributed inside the quadrilateral area surrounded by the 4 boundary nodes of the building block;

[0011] The boundary node positions, internal node positions and the rod connection relationships between nodes of the building blocks are determined based on the boundary node position rules, the uniform distribution rules of the internal nodes and the rod connectivity rules.

[0012] In one possible implementation, there are 11 symmetry operation modes of graphic transformation, forming 11 representative units respectively; the 11 representative units are respectively recorded as p1, p2, p4, p4g, pm, pmm, pg, pgg, pmg, cm and cmm, respectively representing a simple translation transformation group, a double rotation transformation group, a quadruple rotation transformation group, a quadruple rotation sliding transformation group, a reflection transformation group, a double reflection transformation group, a sliding transformation group, a double sliding transformation group, a reflection sliding transformation group, a center reflection transformation group and a double center reflection transformation group.

[0013] In a possible implementation, the boundary node position rule is: boundary nodes in a single building block do not overlap, and boundary nodes between adjacent building blocks overlap;

[0014] The boundary node position rules include global boundary node position rules applicable to 11 representative units and boundary node position rules in groups applicable to different representative units;

[0015] Assume that in the building block, the position scale factor of the i-th boundary node is k Ai,i=1,2,3,4, this scale factor is used to measure the position of the boundary node, which is equal to the ratio of the distance from the boundary node to the nearest vertex in the counterclockwise direction to the length of the building block edge;

[0016] The global boundary node position rule is: This rule ensures that boundary nodes in the same building block do not overlap with each other;

[0017] The boundary node position rules in the group include a first rule and a second rule; the first rule is the connectivity of the boundary nodes between adjacent building blocks in the representative unit; the second rule is the connectivity of the boundary nodes between the representative units when the lattice metamaterial is constructed by plane paving; the boundary node position rules in each group are expressed by the following formula:

[0018] p1: p2: p4: p4g: pm:k A1 +k A3 =1;

[0019] pmm:none; pg: pgg: pmg:k A2 =k A4 =1 / 2; cm:k A1 =k A3 ; cmm: k A2 = 1 / 2; the unmentioned proportionality coefficients have no restrictions in the corresponding groups;

[0020] According to the boundary node position rules, the feasible boundary node coordinates are determined.

[0021] In a possible implementation, the uniform distribution rule of the internal nodes is: the internal nodes of the building block are uniformly distributed inside a quadrilateral region surrounded by four boundary nodes of the building block;

[0022] According to the uniform distribution rule of internal nodes, the feasible internal node coordinates are determined, including:

[0023] Generate feasible internal node coordinates through the intersection of bisectors inside the quadrilateral area enclosed by the four boundary nodes of the building block;

[0024] A complete set of coordinate positions of internal nodes of different building blocks is generated by systematically traversing all feasible internal node coordinates, and the positions of each internal node do not overlap.

[0025] The coordinates of each set of feasible boundary nodes and internal nodes can form a node coordinate matrix. The dimension of the node coordinate matrix is ​​2 rows × number of nodes. The first row is the horizontal coordinate of the node, and the second row is the vertical coordinate of the node. The first four columns are the coordinates of the boundary nodes A1 to A4, and the fifth to the last columns are the coordinates of the internal nodes.

[0026] In a possible implementation, all adjacency matrices are generated as a lookup table for rod connections by traversing and folding a base number system with n as the base number, where the value of n is N·(N-1) / 2, and N is the total number of nodes; the elements in the adjacency matrix are all natural numbers, and non-zero element values ​​indicate that there is a rod connection between corresponding nodes, different non-zero element values ​​indicate different rod materials, and an element value of zero indicates that there is no rod connection between corresponding nodes, that is, there is no connectivity between corresponding nodes;

[0027] The bar connectivity rule includes a first connectivity rule and a second connectivity rule;

[0028] The first connectivity rule requires that connectivity must be ensured between boundary nodes A1 and A3, and between boundary nodes A2 and A4 in the building block, that is, there is a continuous rod structure between boundary nodes A1 and A3, and between boundary nodes A2 and A4.

[0029] The second connectivity rule requires that the internal nodes must be connected to at least two boundary nodes through rods to ensure the non-independence of the internal nodes, that is, there should be at least two non-zero elements in the corresponding row in the adjacency matrix. If the corresponding row of the internal node in the adjacency matrix contains only one non-zero element, the internal node is only connected to another node alone. This independent internal node cannot transfer loads, resulting in redundancy of the rod. Therefore, the second connectivity rule requires that there should be at least two non-zero elements in the corresponding row of the internal node in the adjacency matrix. Through the second connectivity rule, the non-independence of the internal nodes can be guaranteed to ensure the mechanical contribution of all rods.

[0030] The adjacency matrix that satisfies the first connectivity rule and the second connectivity rule is a feasible adjacency matrix.

[0031] In a possible implementation, the first connectivity rule is based on the p-th power N of the adjacency matrix C p To determine, p ranges from 1 to the total number of rods in the building block; N C p The value of (i,j) represents the connectivity between nodes i and j, N C p (i,j)≠0 means that there is connectivity between nodes i and j consisting of p rods, N C p(i, j) = 0 means that there is no connectivity between nodes i and j.

[0032] Therefore, the first connectivity rule is that for any value of p, as long as there exists N C p (i,j)≠0, the boundary nodes i and j are connected.

[0033] In a possible implementation, a feasible node coordinate matrix set and a feasible adjacency matrix set are generated, wherein the feasible node coordinate matrix set includes a plurality of feasible node coordinate matrices, each feasible node coordinate matrix includes a set of feasible boundary nodes and internal node coordinates; the feasible adjacency matrix set includes a plurality of feasible adjacency matrices;

[0034] Generate building blocks based on a feasible set of node coordinate matrices and a feasible set of adjacency matrices;

[0035] The generated building blocks are verified to exclude the situations of bar crossing, bar overlap and nodes on bars.

[0036] The verified building blocks are densely laid on a plane to achieve the design of new mechanical metamaterial structures.

[0037] In a second aspect, the present application provides an electronic device, including: a memory and a processor;

[0038] The memory is used to store computer programs;

[0039] The processor is used to call the computer program to execute the method as described above.

[0040] In a third aspect, the present application provides a computer-readable storage medium, in which a computer program is stored. When the computer program is executed on an electronic device, the electronic device implements the method as described above.

[0041] In a fourth aspect, the present application provides a computer program product, including a computer program, and when the computer program is executed on an electronic device, the electronic device implements the method as described above.

[0042] The specific implementation methods of the second to fourth aspects of the present application can refer to the implementation methods of the first aspect, which will not be repeated here.

[0043] Beneficial effects:

[0044] Based on the design method of the present invention, a large number of new lattice metamaterials can be constructed quickly and efficiently without relying on the designer's experience and knowledge, greatly reducing the trial and error and calculation costs in the design process. The generated large-scale new mechanical metamaterial database will further promote the practical engineering application of lattice metamaterials, and can support the rapid design and search customization of various modulus and Poisson's ratio engineering requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is the framework of the lattice metamaterial design method in the embodiment of this application;

[0046] Figure 2 Symmetry operations for four graphical transformations and 11 planar crystal groups based on square building blocks;

[0047] Figure 3 It is the boundary node location rule in the embodiment of this application;

[0048] Figure 4 This is the uniform distribution rule of internal nodes in the embodiment of the present application;

[0049] Figure 5 The connectivity rule of the rod connection in the embodiment of the present application;

[0050] Figure 6 This is the design result of the lattice metamaterial structure in the embodiment of this application. DETAILED DESCRIPTION

[0051] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution of the present application will be further described in detail below in conjunction with the embodiments and drawings of the present application.

[0052] The present invention determines the boundary node positions, internal node positions and the rod connection relationship between nodes of the building blocks by designing boundary node position rules, uniform distribution rules of internal nodes and rod connectivity rules, and realizes the design of new mechanical metamaterial structures by plane paving of the building blocks. Through the method of the present invention, a large number of lightweight lattice metamaterials with unique and novel structures can be efficiently designed. The structure of the lattice metamaterial generated by the present invention is a periodic two-dimensional truss-type porous structure formed by multiple rods fixedly connected at nodes, and its constituent materials are common engineering materials. The present invention can guide and expand the practical engineering applications of metamaterials, and belongs to a functional material structure design method.

[0053] Specific embodiments according to the present application will be described below with reference to the accompanying drawings.

[0054] The present application relates to a design method for a novel mechanical metamaterial database, wherein the novel mechanical metamaterial database includes a large number of novel lattice metamaterials; the smallest repeating unit of the novel lattice metamaterial is a building block; the method comprises: the building block forms a representative unit through a symmetric operation of a graphic transformation, and the representative unit is periodically densely laid to form a novel lattice metamaterial;

[0055] Wherein, the building block includes three structural features, namely, boundary nodes, internal nodes and rods;

[0056] The plane space occupied by the building block is a square with a side length of D; the building block has 4 boundary nodes, which are respectively located on the 4 boundaries of the square; the building block has at least 1 internal node, which is distributed inside the quadrilateral area surrounded by the 4 boundary nodes of the building block;

[0057] The boundary node positions, internal node positions and the rod connection relationships between nodes of the building blocks are determined based on the boundary node position rules, the uniform distribution rules of the internal nodes and the rod connectivity rules.

[0058] The design object of the method described in the present invention involves a truss-like porous structure composed of periodic repeating units, which is called a lattice metamaterial. Figure 1 As shown in part (a), the three design levels of building blocks, representative units (RVEs), and lattice metamaterials can be transformed into each other based on the symmetry and periodicity of graphical transformations. The plane space occupied by the building block is a square with a side length of D. The four boundary nodes are located on the four sides of the square. The boundary nodes have one degree of freedom along the direction of the edge, and the overlap between boundary nodes is prohibited. At least one internal node is located in the distribution area surrounded by the boundary nodes. The structure connecting the nodes is called a rod. The length of the rod is the distance between the nodes. The in-plane width and out-of-plane thickness of the cross-section of the rod are b and t respectively. The constituent materials of the connecting rod between different nodes can be different.

[0059] like Figure 1 As shown in part (b), the design concept of the method described in the present invention draws on the method of constructing a planar crystal group, which is a method of constructing a planar crystal group with a square pattern that periodically covers the entire plane. In this application, the plane space occupied by the building block is a square with a side length of D. The building blocks form representative units through symmetric operations of graphic transformation, and the representative units are periodically densely laid to form metamaterials. The pattern corresponding to the representative unit is periodically densely laid along the horizontal and vertical basis vectors in the plane, which is a planar crystal group. Figure 1 As shown in part (c), the basic framework of the method described in the present invention is from basic structural features to building blocks, then to representative units (RVEs), and finally to lattice metamaterials.

[0060] Based on the three basic structural features of boundary nodes, internal nodes and rods, the present invention establishes boundary node position rules, uniform distribution rules and connectivity rules to generate building blocks. The present invention establishes boundary node position rules to determine feasible boundary node coordinates in building blocks. The design concept of boundary node position rules comes from 11 plane crystal groups based on squares. Planar crystal groups include all symmetry operations related to two-dimensional graphics, namely translation, reflection, rotation and sliding. Figure 2 As shown in the figure, the 11 planar crystal groups based on squares can be named P1, P2, P4, P4g, PM, PMM, PG, PGG, PMG, CM, CMM, respectively, which include the combination of all symmetry operations of square tiling in the plane. Embedding building blocks in the square lattice of the planar crystal group is the basic design concept of this method.

[0061] Correspondingly, in the present application, the building blocks form representative units through the symmetry operations of graphic transformations. By adopting 11 symmetry operations of graphic transformations, 11 representative units can be formed, which are respectively recorded as p1, p2, p4, p4g, pm, pmm, pg, pgg, pmg, cm and cmm, respectively representing simple translation transformation group, double rotation transformation group, quadruple rotation sliding transformation group, reflection transformation group, double reflection transformation group, sliding transformation group, double sliding transformation group, reflection sliding transformation group, center reflection transformation group and double center reflection transformation group.

[0062] This application mathematically converts the symmetry operation of the graph transformation into boundary node position rules to ensure the precise connection of boundary nodes between adjacent building blocks. The boundary node position rules can be divided into two aspects, including global boundary node position rules applicable to 11 representative units and boundary node position rules in groups applicable to different representative units; the boundary node position rules in groups include the first rule and the second rule. The first rule is the connectivity of boundary nodes between adjacent building blocks within the representative unit; the second rule is the connectivity of boundary nodes between representative units when constructing lattice metamaterials by planar tiling. Figure 3 The square in part (a) represents a general building block with orientation, where points and vectors in homogeneous coordinates are represented as a three-dimensional vector [xyw] on a plane. T , where x and y are derived from Cartesian coordinates, w is an extra dimension (w = 1 for a point on the plane, w = 0 for a vector on the plane), and the superscript T indicates the transpose. The positions of the boundary nodes are represented by Figure 3 The proportionality factor k shown in part (a) Ai (i=1,2,3,4) indicates that the position vectors of its boundary nodes and vertices A1, A2, A3, A4, O1, O2, O3 and O4 are expressed in the homogeneous coordinate system as:

[0063]

[0064] Where L x and L y is the side length of the building block, and L x =L y = D. Position vector X = [x X y X 1] T The graphic transformation is achieved by calculating the left dot product with the transformation matrix.

[0065] To prevent the boundary nodes in the same building block from overlapping, the global boundary node position rule is:

[0066]

[0067] In the formula, {} represents a set. Figure 3 In parts (b) to (e), groups p1, p4, pgg and pmm are used as representatives to describe the mathematical description of the boundary node position rules. The analysis of other groups is similar. Figure 3 As shown in part (b), the building blocks of group p1 are consistent with RVE, and its boundary nodes only need to satisfy the first rule. The translation matrix corresponding to the basis vectors of the horizontal and vertical plane tiling is:

[0068]

[0069] In the horizontal translation, points O2 and O1′ coincide, and points A2 and A′4 coincide, and the corresponding position vectors satisfy:

[0070]

[0071] In vertical translation, points O1 and O′4′ coincide, and points A1 and A′3′ coincide, and the corresponding position vectors satisfy:

[0072]

[0073] Combining formulas (4) and (5) we can get the boundary node location rule of group p1:

[0074]

[0075] like Figure 3 As shown in part (c), the building blocks of group p4 are first formed by vertices The RVE is constructed by four-fold rotational symmetry, with a rotation angle of ψ of 90 degrees. The rotation transformation matrix of this process is:

[0076]

[0077] According to the first rule, the points that need to coincide during the rotation process include and as well as and The corresponding position vector satisfies:

[0078]

[0079] According to the second rule, during the translation process, the corresponding position vector of the node overlap is calculated as:

[0080]

[0081] Where, the horizontal and vertical translation matrices are:

[0082]

[0083] Combining formulas (8) and (9), the boundary node position rule of group p4 is:

[0084]

[0085] like Figure 3 As shown in part (d), the RVE of group pgg is formed by two sliding transformations of building blocks. The sliding transformation is a special basic transformation that is first reflected and then translated. The median line of the building block is the reflection axis and the translation direction. The sliding transformation matrices in the horizontal and vertical directions are calculated as:

[0086]

[0087] The translation transformation matrix T G And the reflection transformation matrix M is:

[0088]

[0089] Auxiliary transformation matrix and It is used to handle the situation where the sliding axis does not pass through the origin. In this process, it is expressed as:

[0090]

[0091] Where d x and d y They represent the projection lengths of the distance between the sliding axis and the origin of the coordinate system in the horizontal and vertical directions, respectively. Formula (12) shows the basic process of sliding transformation. The point and the reflection axis are translated by the auxiliary transformation matrix to the position where the sliding axis and the origin intersect for reflection transformation. Then the transformed point and the reflection axis are moved back to the initial position, and finally a translation transformation is performed along the reflection axis.

[0092] The above process requires points and and and and coincide, the corresponding position vectors satisfy:

[0093]

[0094] The boundary nodes of group pgg automatically satisfy the second rule while satisfying the first rule represented by formula (15). Therefore, the boundary node position rule of group pgg is:

[0095]

[0096] In group pmm, boundary nodes naturally overlap during reflection and translation transformations. As long as the boundary nodes comply with global rules, their positions are arbitrary, so group pmm does not impose additional constraints on boundary nodes. The complete boundary node position rules are shown in Table 1. The proportional coefficients not mentioned in the table are not restricted in the corresponding group. So far, the method of the present invention has completed the construction of boundary nodes.

[0097] Table 1 Boundary node location rules

[0098]

[0099]

[0100] The present invention establishes a uniform distribution rule to determine the feasible internal node coordinate positions in the building block. Figure 4 As shown in part (a), the white rectangle surrounded by the dotted line represents a building block. The boundary nodes on the four sides are marked A1 to A4 in sequence. The area surrounded by the quadrilateral A1A2A3A4 is called the distribution area, and the internal nodes are distributed in the distribution area. Figure 4 Part (b) shows equidistant points on the edge of the distribution area. Figure 4 In part (c), equidistant lines are drawn by connecting equidistant points on these opposite sides. The positions of the internal nodes are determined by the intersection of these equidistant lines. Figure 4 As shown in part (d), when the number of equally divided points is 3, there are 9 equally divided points, named p1 to p9. The complete coordinate position set of the internal nodes of different building blocks is generated by systematically traversing all feasible internal node coordinates, and the positions of the internal nodes cannot overlap. Figure 4 Part (e) is an example of a building block with two internal nodes.

[0101] For any building block with K internal nodes, the coordinates of the internal nodes are stored in the node set along with the boundary nodes:

[0102]

[0103] The present invention establishes connectivity rules to determine all feasible rod connection modes in a building block. The connectivity between nodes is determined using an adjacency matrix. This matrix, as a lookup table, is used to indicate whether there is a rod connection between nodes in corresponding rows and columns. The elements in the adjacency matrix are all natural numbers, wherein non-zero element values ​​indicate that there is a rod connection between the nodes, different non-zero element values ​​indicate different rod materials, and an element value of zero indicates that there is no connectivity between the nodes. The adjacency matrix is ​​a symmetric matrix and can be represented by an upper (or lower) triangular matrix that does not include the main diagonal. Since the elements are all natural numbers, all potential adjacency matrices are generated by traversing and folding a base number system with n as the base, where the value of n is N·(N-1) / 2, and N is the total number of boundary nodes and internal nodes. For example, for a building block with four boundary nodes, two internal nodes, and two materials, the ternary number corresponding to an adjacency matrix may be "001001022000202". As Figure 5 As shown in part (a), the ternary number is folded into segments to form an adjacency matrix, and further combined with the node set to generate a building block. The connectivity rule of the present invention includes two aspects. The first connectivity rule is to make the generated building block have a continuous structure to transmit mechanical loads; the second connectivity rule is that all rods contribute to force transmission, that is, there are no redundant rods. The connectivity rule can be judged without relying on specific node coordinates.

[0104] The first connectivity rule requires that in the building block, a continuous rod structure must be ensured between the boundary nodes A1 and A3, and A2 and A4. This rule is based on the p-th power N of the adjacency matrix. C p To determine, p ranges from 1 to the total number of members in the building block. C p The value of (i,j) represents the connectivity between nodes i and j, N C p (i,j)≠0 means that there is connectivity between nodes i and j consisting of p rods, N C p (i, j) = 0. Therefore, the first connectivity rule is that for any value of p, as long as there are N C p (i,j)≠0, the boundary nodes i and are connected. Figure 5Part (b) shows the adjacency matrix that satisfies the first connectivity rule in the horizontal and vertical directions. Adjacency matrices that do not satisfy the first connectivity rule are excluded in the design process. The second connectivity rule requires the non-independence of internal nodes to ensure the mechanical contribution of all rods. If the corresponding row of the internal node in the adjacency matrix contains only one non-zero element, the internal node is only connected to another node alone. This independent internal node cannot transfer loads, resulting in redundancy of the rod. Therefore, there should be at least two non-zero elements in the corresponding row of the internal node in the adjacency matrix. Figure 5 Part (c) shows a dependent internal node and an independent internal node (highlighted by the dashed line). The adjacency matrix with independent internal nodes is excluded in the design.

[0105] At this point, according to the boundary node position rule, uniform distribution rule and connectivity rule, a feasible node coordinate matrix set and a feasible adjacency matrix set can be obtained. When combining the two sets to generate building blocks, it is necessary to exclude Figure 5 In part (d), there are three cases: bars cross, bars overlap, and nodes are on bars. Further embedding the building blocks into a planar crystal group and performing planar tiling can realize the design of a new type of lattice metamaterial.

[0106] Experimental verification:

[0107] (1) Set the design parameters. Four boundary nodes and one internal node are used in the experiment, and the cross-sectional dimensions of the rod are

[0108] 1.5mm×1.5mm, the plane space square occupied by the building block is 20.0mm×20.0mm. The 5 feasible positions of each boundary node are specified at five equally divided points on one boundary of the square. The representative units selected are p2, pm, pmm and cm. The number of uniformly distributed positions of the internal nodes of group p2 is 25, and the number of uniformly distributed positions of the internal nodes of the other three groups is 9. The component material of the rod is acrylonitrile butadiene styrene (ABS) plastic.

[0109] (2) Generate new lattice metamaterials. Generate lattice metamaterials based on design parameters and design framework. The design results of group p2 are 91956, the design results of group pm are 161432, the design results of group pmm are 897094, and the design results of group cm are 181669. Most of the metamaterials are unprecedented new designs. Each group shows 10 design results, such as Figure 6 shown.

[0110] Manufacturability of new lattice metamaterials. A new lattice metamaterial was selected from each of the four groups for sample fabrication. The samples were prepared using an Ultimaker S5 fused deposition modeling 3D printer, using red ABS plastic as the material.

[0111] like Figure 6 As shown, the four red samples are all well formed, which can verify the manufacturability of the design results and the feasibility of the method described in the present invention.

[0112] An embodiment of the present application also provides an electronic device, including: a memory and a processor;

[0113] The memory is used to store computer programs;

[0114] The processor is used to call the computer program to execute the method as described above.

[0115] An embodiment of the present application further provides a computer-readable storage medium, in which a computer program is stored. When the computer program is executed on an electronic device, the electronic device implements the method as described above.

[0116] An embodiment of the present application further provides a computer program product, including a computer program. When the computer program is executed on an electronic device, the electronic device implements the method described above.

[0117] The embodiments of the present application also provide a system, an electronic device, a computer-readable storage medium, and a computer program product. The specific implementation methods can refer to the specific embodiments of the above methods and will not be repeated here.

[0118] Obviously, those skilled in the art should understand that the above-mentioned units or steps of the present application can be implemented by a general-purpose computing device, they can be concentrated on a single computing device, or distributed on a network composed of multiple computing devices, and optionally, they can be implemented by a program code executable by a computing device, so that they can be stored in a storage device and executed by the computing device, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. In this way, the present application is not limited to any specific combination of hardware and software.

[0119] The above description of the embodiments of the present application is only a partial embodiment of the present application, which is used to enable professionals in the field to implement or use the content of the present application, and is not used to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. A design method for a new mechanical metamaterial database, characterized in that: The novel mechanical metamaterial database includes a large number of novel lattice metamaterials; the smallest repeating unit of the novel lattice metamaterial is a building block; the method is: the building block forms a representative unit through a symmetric operation of graphic transformation, and the representative unit is periodically densely laid to form a novel lattice metamaterial; Wherein, the building block includes three structural features, namely, boundary nodes, internal nodes and rods; The plane space occupied by the building block is a square with a side length of D; the building block has 4 boundary nodes, which are respectively located on the 4 boundaries of the square; the building block has at least 1 internal node, which is distributed inside the quadrilateral area surrounded by the 4 boundary nodes of the building block; The boundary node positions, internal node positions and the rod connection relationships between nodes of the building blocks are determined based on the boundary node position rules, the uniform distribution rules of the internal nodes and the rod connectivity rules.

2. The method according to claim 1, characterized in that: There are 11 symmetry operation modes of graphic transformation, forming 11 representative units respectively; the 11 representative units are respectively recorded as p1, p2, p4, p4g, pm, pmm, pg, pgg, pmg, cm and cmm, respectively representing simple translation transformation group, double rotation transformation group, quadruple rotation sliding transformation group, reflection transformation group, double reflection transformation group, sliding transformation group, double sliding transformation group, reflection sliding transformation group, center reflection transformation group and double center reflection transformation group.

3. The method according to claim 2, characterized in that The boundary node position rule is: the boundary nodes in a single building block do not overlap, and the boundary nodes between adjacent building blocks overlap; The boundary node position rules include global boundary node position rules applicable to 11 representative units and boundary node position rules in groups applicable to different representative units; Assume that in the building block, the position scale factor of the i-th boundary node is k Ai ,i=1,2,3,4, this scale factor is used to measure the position of the boundary node, which is equal to the ratio of the distance from the boundary node to the nearest vertex in the counterclockwise direction to the length of the building block edge; The global boundary node position rule is: Used to ensure that the boundary nodes in the same building block do not overlap with each other; The boundary node position rules in the group include a first rule and a second rule; the first rule is the connectivity of the boundary nodes between adjacent building blocks in the representative unit; the second rule is the connectivity of the boundary nodes between the representative units when the lattice metamaterial is constructed by plane paving; the boundary node position rules in each group are expressed by the following formula: pm:k A1 +k A3 =1; pmm: none; pmg:k A2 =k A4 =1 / 2; cm:k A1 =k A3 ; cmm: k A2 = 1 / 2; the unmentioned proportionality coefficients have no restrictions in the corresponding groups; According to the boundary node position rules, the feasible boundary node coordinates are determined.

4. The method according to claim 3, characterized in that The uniform distribution rule of the internal nodes is: the internal nodes of the building block are uniformly distributed inside the quadrilateral area surrounded by the four boundary nodes of the building block; According to the uniform distribution rule of internal nodes, the feasible internal node coordinates are determined, including: Generate feasible internal node coordinates through the intersection of bisectors inside the quadrilateral area enclosed by the four boundary nodes of the building block; A complete set of coordinate positions of internal nodes of different building blocks is generated by systematically traversing all feasible internal node coordinates, and the positions of each internal node do not overlap.

5. The method according to claim 4, characterized in that All adjacency matrices are generated as the lookup table of the rod connection by traversing and folding the base n number system, where the value of n is N·(N-1) / 2, and N is the total number of nodes; the elements in the adjacency matrix are all natural numbers, and the non-zero element value indicates that there is a rod connection between the corresponding nodes, different non-zero element values ​​indicate different rod materials, and the element value of zero indicates that there is no rod connection between the corresponding nodes; The bar connectivity rule includes a first connectivity rule and a second connectivity rule; The first connectivity rule requires that connectivity between boundary nodes A1 and A3, and between boundary nodes A2 and A4 must be ensured in the building block; The second connectivity rule requires that the internal nodes must be connected to at least two boundary nodes through rods to ensure the non-independence of the internal nodes; The adjacency matrix that satisfies the first connectivity rule and the second connectivity rule is a feasible adjacency matrix.

6. The method according to claim 5, characterized in that The first connectivity rule is based on the p-th power N of the adjacency matrix C p To determine, p ranges from 1 to the total number of rods in the building block; N C p The value of (i,j) represents the connectivity between nodes i and j, N C p (i,j)≠0 means that there is connectivity between nodes i and j consisting of p rods, N C p (i,j)=0 means there is no connectivity between nodes i and j; The second connectivity rule is based on the fact that there should be at least two non-zero elements in the row corresponding to the internal node in the adjacency matrix.

7. The method according to claim 1, characterized in that Generate the building blocks, including: Generate a feasible node coordinate matrix set and a feasible adjacency matrix set, wherein the feasible node coordinate matrix set includes a plurality of feasible node coordinate matrices, each feasible node coordinate matrix includes a set of feasible boundary nodes and internal nodes; the feasible adjacency matrix set includes a plurality of feasible adjacency matrices; Generate building blocks based on a feasible set of node coordinate matrices and a feasible set of adjacency matrices; The generated building blocks are verified to exclude the situations of bar crossing, bar overlap and nodes on bars.

8. An electronic device, characterized in that: include: Memory and processor; The memory is used to store computer programs; The processor is configured to call the computer program to execute the method according to any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed on an electronic device, the electronic device implements the method according to any one of claims 1 to 7.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed on an electronic device, the electronic device implements the method according to any one of claims 1 to 7.

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