A metamaterial with bidirectional functional gradient topological properties and its equivalent stiffness evaluation method

Abstract

The present invention discloses a metamaterial with a bidirectional functional gradient topological structure and a method for evaluating its equivalent stiffness. The bidirectional functional gradient topological structure design method of the material is as follows: first, a cell is selected; then, two types of gradient distribution configurations along a certain direction, symmetrical gradient change and asymmetrical gradient change, are constructed: the length of any cell is calculated; then, a symmetrical gradient or asymmetrical gradient topology is selected in the y and z directions respectively, a bidirectional gradient topological structure is generated in the yz plane, and uniformly changes in the x direction, the number of cells in the x direction is determined, and then a 3D bidirectional functional gradient topological structure is formed in the x, y, and z directions in sequence. Four bidirectional functional gradient topological structures can be obtained according to the different gradient distributions selected in the y and z directions. The bidirectional functional gradient metamaterial structure designed by the present invention has the advantages of high stiffness, significant impact energy absorption effect, and controllable deformation.

Description

Technical Field

[0001] The present invention relates to the technical field of metamaterials, in particular to a metamaterial with bidirectional functional gradient topological characteristics and an equivalent stiffness evaluation method thereof. Background Art

[0002] The impact energy absorption and mechanical properties of metamaterial structures are closely related to their cell topology. Functionally graded metamaterials are a new type of metamaterial structure whose component materials, structural topology, or dimensions gradually change spatially, resulting in corresponding changes in the mechanical properties of the overall structure. As an important component of lattice structure research, functionally graded metamaterial structures have better mechanical properties, damage behavior, and energy absorption than traditional uniform lattice topology structures. More importantly, gradient metamaterial structures have predictable performance that can simultaneously meet the needs of different parts of the structure under complex operating conditions. Currently, gradient metamaterial structure design is mainly achieved by changing the diameter, thickness, and type of cell rods, or by compressing and stretching the cell size.

[0003] According to the relationship between the density gradient direction and the loading direction of gradient metamaterials, there are two typical unidirectional gradient metamaterial structural topological configurations: the first type is the unidirectional functional gradient metamaterial (PG) structure in which the density gradient direction is parallel to the loading direction. The total energy absorption of this structure before the densification of the last layer is significantly higher than that of the uniform topological metamaterial structure, and the specific strength and specific energy absorption are also higher than those of the uniform topological metamaterial structure. The second type is the unidirectional functional gradient metamaterial (VG) structure in which the unidirectional density gradient direction is perpendicular to the loading direction. The stiffness and platform stress of this structure are higher than those of the PG structure, and the lattice topological structure with the density gradient perpendicular to the loading direction shows better stiffness and energy absorption capacity. Studies have shown that both unidirectional gradient designs can effectively improve the impact resistance and energy absorption characteristics of metamaterials, but this unidirectional gradient design is difficult to comprehensively improve the performance of all aspects of the metamaterial structure, including mechanical properties, energy absorption, etc. Summary of the Invention

[0004] In view of the deficiency that existing metamaterials with unidirectional gradient design are difficult to comprehensively improve the performance of all aspects of the metamaterial structure, the present invention provides a metamaterial with bidirectional functional gradient topological characteristics.

[0005] The metamaterial with bidirectional functional gradient topological characteristics provided by the present invention is designed with a bidirectional functional gradient topological structure by the following method:

[0006] Step S1: Select a cell, for example, an RD cell or an Octet cell.

[0007] The relative density of the cell is calculated as follows:

[0008]

[0009] Step S2: construct two types of gradient distribution configurations along a certain direction: symmetrical gradient change and asymmetrical gradient change:

[0010] In a certain direction, calculate the length l of any cell i The formula is as follows:

[0011]

[0012] Among them, α represents the central factor, that is, l0=αl; l is the cell size; λ=±1 represents the gradient direction; β is the gradient coefficient; χ is the gradient change rate, and n represents the number of cells;

[0013] Step S3: Select symmetric gradient or asymmetric gradient topology in the y and z directions respectively, generate a bidirectional gradient topology structure in the yz plane, and change it uniformly in the x direction, determine the number of cells in the x direction, and then array them in the x, y, and z directions in sequence to form a 3D bidirectional functional gradient topology structure.

[0014] In step S3, one of the following four bidirectional functional gradient topologies is obtained according to the different gradient distributions selected in the y and z directions:

[0015] Type I structure: the density gradient direction is the positive direction of the z-axis parallel to the loading direction and the positive direction of the y-axis perpendicular to the loading direction;

[0016] Type II structure: the direction of the density gradient is from the origin to the positive and negative z-axis and from the origin to the positive and negative y-axis;

[0017] Type III structure: the density gradient direction is the positive direction of the z-axis and the origin changes in the positive and negative directions of the y-axis;

[0018] Type IV structure: The direction of the density gradient is from the origin to the positive and negative z-axis and the positive y-axis.

[0019] The present invention also provides a method for evaluating the equivalent stiffness of the metamaterial having a bidirectional functional gradient topological structure, comprising the following steps:

[0020] S1. Determine the stiffness C of each cell in the bidirectional gradient metamaterial structure ij and volume fraction L ij , and draw the stiffness and volume fraction distribution of the structure;

[0021] S2. Determine the equivalent stiffness of each layer in turn based on the layer and equivalent volume fraction

[0022] Equivalent volume fraction of each layer Equal to the sum of the volume fractions of each cell;

[0023] The equivalent stiffness of each layer Equivalent volume fraction The product of is equal to the stiffness C of each cell in this layer ij and volume fraction L ij The product is summed and the equivalent stiffness of each layer is calculated based on this relationship.

[0024] S3. Calculate the equivalent stiffness C of the overall structure hom , the formula is as follows:

[0025]

[0026] Where n represents the number of each layer in the overall structure, which are numbered 0, 1, 2, 3, ..., n in sequence.

[0027] Compared with the prior art, the present invention is beneficial in that:

[0028] The bidirectional gradient topology designed in this invention significantly improves mechanical properties such as structural stiffness and its ability to absorb impact energy. It also shares the controllable deformation advantages of the PG topology, offering advantages in designing mechanical metamaterials with ideal post-yield strength. When loaded in the gradient direction, the bidirectional gradient topology significantly improves its bearing capacity compared to the unidirectional gradient topology, absorbing more impact energy. When the loading direction is at an angle to the gradient direction, its mechanical properties and energy absorption capacity are also superior to those of the unidirectional gradient topology.

[0029] Other advantages, objectives and features of the present invention will be reflected in part through the following description, and in part will be understood by those skilled in the art through study and practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 , structural design flow chart of bidirectional gradient metamaterials.

[0031] Figure 2 , Octet cell structure diagram.

[0032] Figure 3 , RD cell structure diagram.

[0033] Figure 4 , schematic diagram of the configuration distribution of symmetrical gradient changes (stretching / compression along the y direction).

[0034] Figure 5 , schematic diagram of the configuration distribution of asymmetric gradient changes (stretching / compression along the y direction).

[0035] Figure 6 、 Ⅰ Figure 1 shows the bidirectional gradient topology structure (Bi-GⅠ).

[0036] Figure 7 、 Ⅱ Diagram of bidirectional gradient topology structure (Bi-GⅡ).

[0037] Figure 8 、 Ⅲ Diagram of bidirectional gradient topology structure (Bi-GⅢ).

[0038] Figure 9 、 Ⅳ Diagram of bidirectional gradient topology structure (Bi-GⅣ).

[0039] Figure 10 , schematic diagram of the structural stiffness distribution of bidirectional gradient metamaterial (type I structure). DETAILED DESCRIPTION

[0040] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0041] The metamaterial with bidirectional functional gradient topological characteristics provided by the present invention has a specific structural design method as follows (eg Figure 1 shown):

[0042] Step S1, select a cell, for example, select Octet cell or RD cell. The structures of these two cells are shown in Figure 2 and Figure 3 .

[0043] The relative density of the cell is calculated as follows:

[0044]

[0045] Therefore, the relative density corresponding to the Octet cell and RD cell can be calculated as follows:

[0046]

[0047]

[0048] Step S2: construct two types of gradient distribution configurations along a certain direction: symmetrical gradient change and asymmetrical gradient change:

[0049] (1) Configurations with symmetrical gradient changes, such as Figure 4 As shown (taking Octet cell as an example). Calculate the length l of any cell according to the following formula i :

[0050]

[0051] Where α represents the center factor, i.e., l0 = αl; l is the cell size; λ = ±1 represents the gradient direction; β is the gradient coefficient; χ is the gradient rate of change; and n is the number of cells. The central octet cell generates 2(n+1) octet cells in a gradient-symmetric array in the y direction.

[0052] In this embodiment, the symmetric gradient change parameters are n=2, α=1, λ=-1, β=0.4, χ=0.5; the cell size is l=10 mm; and the lengths of the cells are l0=10 mm, l1=6 mm, and l2=4 mm.

[0053] (2) Configurations with asymmetric gradient changes, such as Figure 5 As shown (taking Octet cell as an example). It can be seen that the overall structure generates n+1 Octet cells in the y direction according to the gradient array, and the length of each cell is l i It can also be calculated using the formula above.

[0054] In this embodiment, the asymmetric gradient change parameters are n=4, α=1, λ=-1, β=0.2, χ=1; the cell size l=10 mm; and the lengths of each cell are: l0=10 mm, l1=8 mm, l2=6 mm, l3=4 mm, l4=2 mm.

[0055] Step S3: Select symmetric gradient or asymmetric gradient topology in the y and z directions respectively, generate a bidirectional gradient topology structure in the yz plane, and array it n+1 times of equal size in the x direction to form a 3D bidirectional functional gradient topology structure.

[0056] Depending on the gradient distribution selected in the y and z directions, one of the following four bidirectional functional gradient topologies is obtained:

[0057] Type I bidirectional gradient topology (Bi-GⅠ): Figure 6 As shown, the overall size of the structure is 30×30×30mm 3 The density gradient direction is the positive z-axis (parallel to the loading direction) and the positive y-axis (perpendicular to the loading direction). The RD cell size changes from -z to +z are 10mm, 8mm, 6mm, 4mm, and 2mm; the RD cell size changes from -y to +y are 10mm, 8mm, 6mm, 4mm, and 2mm. The cell size in the x-direction remains unchanged. The number of cells is 5×5×3.

[0058] Type II bidirectional gradient topology (Bi-GⅡ): Figure 7 As shown, the overall size of the structure is 30×30×30mm 3The density gradient direction changes from the origin to the positive and negative z-axis (parallel to the loading direction) and the origin to the positive and negative y-axis (perpendicular to the loading direction). The RD cell size changes from -z to +z as 4mm, 6mm, 10mm, 6mm, and 4mm; the RD cell size changes from -y to +y as 4mm, 6mm, 10mm, 6mm, and 4mm. The cell size in the x-direction remains unchanged. The number of cells is 5×5×3.

[0059] Type III bidirectional gradient topology (Bi-GⅢ): Figure 8 As shown, the overall size of the structure is 30×30×30mm 3 The density gradient direction is in the positive z-axis (parallel to the loading direction) and changes from the origin to the positive and negative y-axis (perpendicular to the loading direction). The RD cell size changes from -z to +z as 10mm, 8mm, 6mm, 4mm, and 2mm; the RD cell size changes from -y to +y as 4mm, 6mm, 10mm, 6mm, and 4mm. The cell size in the x-direction remains unchanged. The number of cells is 5×5×3.

[0060] Type IV bidirectional gradient topology (Bi-GIV): Figure 9 As shown, the overall size of the structure is 30×30×30mm 3 The density gradient direction changes from the origin to the positive and negative z-axis (parallel to the loading direction) and the positive y-axis (perpendicular to the loading direction). The RD cell size changes from -z to +z as 4mm, 6mm, 10mm, 6mm, and 4mm; the RD cell size changes from -y to +y as 10mm, 8mm, 6mm, 4mm, and 2mm. The cell size in the x-direction remains unchanged. The number of cells is 5×5×3.

[0061] The following method is used to evaluate the equivalent stiffness of the designed metamaterial with a bidirectional functional gradient topological structure.

[0062] Since there is no gradient change in the x-direction, it can be considered that the stiffness of the structure in the x-direction is uniform. The following mainly examines the equivalent stiffness in the yz plane. The method is as follows:

[0063] S1. Determine the stiffness C of each cell in the bidirectional gradient metamaterial structure ij and volume fraction L ij , and draw the stiffness and volume fraction distribution of the structure, such as Figure 10 The figure shows a schematic diagram of the stiffness distribution of type I structure.

[0064] S2. Determine the equivalent stiffness of each layer in turn based on the layer and equivalent volume fraction

[0065] Equivalent volume fraction of each layer is equal to the sum of the volume fractions of each cell. For example, according to Figure 10 The distribution diagram shown is calculated

[0066] The equivalent stiffness of each layer Equivalent volume fraction The product of is equal to the stiffness C of each cell in this layer ij and volume fraction L ij The product is summed and the equivalent stiffness of each layer is calculated based on this relationship. according to Figure 10 The distribution plot shown yields:

[0067] Similarly, the equivalent stiffness of other layers along the z direction can be calculated in turn and equivalent volume fraction

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075]

[0076] Finally, the equivalent stiffness C of the overall structure hom It can be expressed as:

[0077]

[0078] The same method can be used to obtain the equivalent stiffness expressions of type II, III, and IV structures.

[0079] The energy absorption characteristics of several structures are compared in Table 1. It can be seen from the comparison that the energy absorption per unit mass (specific energy absorption) of the designed bidirectional gradient metamaterial is significantly better than that of the PG and VG metamaterial configurations.

[0080] Table 1. Comparison of impact energy absorption characteristics of several gradient metamaterial structures

[0081]

[0082] The bidirectional functionally gradient metamaterial structure of this invention combines the advantages of both PG and VG topologies, offering greater practicality in areas such as impact energy absorption, lightweight design, vibration control, and noise reduction. Its high stiffness, effective impact energy absorption, and controllable deformation make it an ideal structure for vibration reduction in aerospace and civil engineering applications.

[0083] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with this profession can make some changes or modifications to equivalent embodiments of the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A metamaterial with a bidirectional functional gradient topological structure, characterized in that: The design method of the bidirectional functional gradient topology structure is as follows: Step S1, selecting a cell; Step S2: construct two types of gradient distribution configurations along a certain direction: symmetrical gradient change and asymmetrical gradient change: Among them, in a certain direction, calculate the length of any cell l i The formula is as follows: in, represents the central factor, i.e. ; is the cell size; represents the gradient direction; is the gradient coefficient; is the gradient change rate, n represents the number of cells; Step S3: Selecting a symmetric gradient or an asymmetric gradient topology in the y and z directions, respectively, to generate a bidirectional gradient topology structure in the yz plane, and uniformly changing it in the x direction, determining the number of cells in the x direction, and then sequentially arraying them in the x, y, and z directions to form a 3D bidirectional functional gradient topology structure; Among them, according to y 、 z The gradient distribution selected in the direction is different, and one of the following four bidirectional functional gradient topologies is obtained: Type I structure: the density gradient direction is the positive direction of the z-axis parallel to the loading direction and the positive direction of the y-axis perpendicular to the loading direction; Type II structure: the direction of the density gradient is from the origin to the positive and negative z-axis and from the origin to the positive and negative y-axis; Type III structure: the density gradient direction is the positive direction of the z-axis and the origin changes in the positive and negative directions of the y-axis; Type IV structure: The direction of the density gradient is from the origin to the positive and negative z-axis and the positive y-axis.

2. The metamaterial having a bidirectional functional gradient topological structure according to claim 1, wherein: In step S1, an RD cell or an Octet cell is selected.

3. The metamaterial having a bidirectional functional gradient topological structure according to claim 2, wherein: The relative density of the cell is calculated as follows: 。 4. A method for evaluating the equivalent stiffness of a metamaterial having a bidirectional functional gradient topological structure according to claim 1, characterized in that: Here are the steps: S1. Determine the stiffness of each cell in the bidirectional gradient metamaterial structure C ij and volume fraction L ij , and draw the stiffness and volume fraction distribution of the structure; S2. Determine the equivalent stiffness of each layer in turn based on the layer and equivalent volume fraction : Equivalent volume fraction of each layer Equal to the sum of the volume fractions of each cell; The equivalent stiffness of each layer Equivalent volume fraction The product is equal to the stiffness of each cell in this layer C ij and volume fraction L ij The product is summed and the equivalent stiffness of each layer is calculated based on this relationship. ; S3. Calculate the equivalent stiffness of the overall structure , the formula is as follows: Where n represents the number of each layer in the overall structure, which are numbered 0, 1, 2, 3, ..., n in sequence.

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