A design method to enhance the local toughness of disordered mechanical metamaterials

Abstract

This invention relates to a design method for enhancing the local toughness of disordered mechanical metamaterials. It overcomes the limitations of traditional methods that can only enhance the toughness of disordered mechanical metamaterials at a global level, allowing for targeted reinforcement of potential fracture regions, avoiding material waste and preventing the predetermined properties of regions outside the fracture region from being affected. The design method first uses a generative algorithm to generate a class of disordered mechanical metamaterials, then continuously searches for the shortest path between the initial node and the target node. Next, it calculates the GEBC values ​​of different bonds in the shortest path and sums the GEBC values ​​of identical bonds. Subsequently, the two classes of bonds with the highest GEBC values ​​are considered potential fracture bonds. If no connected path exists between the nodes in the first row and the last row, the fracture region prediction ends. Finally, the toughness of the local region of the disordered mechanical metamaterial is enhanced by increasing the average node connectivity or short bond frequency of the structure in the fracture region.

Description

(I) Technical Field

[0001] This invention belongs to the field of mechanics, specifically relating to a design method for enhancing the local toughness of disordered mechanical metamaterials. (II) Background Technology

[0002] Mechanical metamaterials have surpassed the physical limitations of traditional materials, exhibiting a series of outstanding properties such as negative Poisson's ratio, negative effective modulus, negative compressibility, and high toughness. Disordered mechanical metamaterials, as an important branch, have also attracted widespread attention in recent years. Disordered mechanical metamaterials are not only lightweight but also possess unique properties such as energy focusing, avoidance of catastrophic failure, shape reconstruction, and prevention of stress concentration. However, due to the random distribution of internal bonds, disordered mechanical metamaterials inevitably generate localized fracture-prone regions. The bonds in these fracture-prone regions have relatively low load-bearing capacity, which may lead to sudden fracture of the disordered mechanical metamaterial during loading, significantly reducing the material's reliability. Previous studies have explored the fracture characteristics of disordered mechanical metamaterials based on friction particle fillers or Voronoi techniques. They focused on the crucial role of disorder in the transition of metamaterials from brittle to ductile. According to Griffith's theory, stress applied to brittle materials is usually concentrated in a small area, leading to crack formation and subsequent fracture. When the degree of disorder increases, stress can be effectively dispersed throughout the material. However, adjusting the overall disorder of a metamaterial is often a daunting task. Furthermore, the increase in disorder comes at the cost of sacrificing the strength of the metamaterial. (III) Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to propose a design method to enhance the local toughness of disordered mechanical metamaterials, overcome the limitation of existing design methods that cannot control the easily fractured regions in disordered mechanical metamaterials, and achieve accurate prediction and targeted reinforcement of the easily fractured regions of disordered mechanical metamaterials without changing the original properties of regions outside the easily fractured regions.

[0004] Technical solution: This invention provides a design method for enhancing the local toughness of disordered mechanical metamaterials, comprising the following steps:

[0005] Step 1) Use a growth algorithm to generate a class of disordered mechanical metamaterials (6) containing N nodes (1).

[0006] Step 2), define an N×N matrix A ij Store the Euclidean distance between all adjacent nodes (1) of the key.

[0007] Step 3), based on matrix A ij Calculate the GEBC value of the bond (4) and determine the predicted fracture region (7) based on the GEBC value.

[0008] Step 4) Re-customize the structure within the predicted fracture region (7) to achieve a toughening effect.

[0009] Furthermore, the growth algorithm used in this invention is a graph-based search algorithm, built on a node-based design space (2). It needs to construct the disordered mechanical metamaterial (6) under the joint guidance of probabilistic combination and three logical constraints. The node (1) serves as the positioning element, the design space (2) determines the final size of the disordered mechanical metamaterial (6), the probabilistic combination is used to specify the probability of occurrence of the bond pattern (5), and the logical constraints are used to ensure the connectivity of the bond (4).

[0010] Furthermore, matrix A ij It is a symmetric matrix. If there is a key (4) between adjacent nodes (1), then in A ij The corresponding position stores the Euclidean distance between adjacent nodes (1). If there is no key (4) between adjacent nodes (1), then in A ij Store 0.

[0011] Furthermore, GEBC refers to geodesic edge intermediate centrality, which statistically analyzes the frequency of occurrence of bonds (4) in the shortest path, and is used to measure the importance of a particular bond (4) in a disordered mechanical metamaterial relative to other bonds (4). The calculation method for GEBC is as follows:

[0012]

[0013] Where g(e) refers to the GEBC value of bond (4)e, δ st δ represents the number of shortest paths from the initial node (1)s to the target node (1)t. st (e) means the number of keys (4)e contained in the shortest path.

[0014] Furthermore, the detailed steps of step 3) are as follows:

[0015] Step 3.1) The initial node (1) iterates sequentially from the first node (1) to the last node (1). Each iteration of the initial node (1) is accompanied by a complete iteration of the target node (1) (from the first node (1) to the last node (1)). They form a nested loop.

[0016] Step 3.2): In each iteration of the target node (1), it is necessary to calculate all paths from the initial node (1) to the target node (1) and identify all shortest paths. Calculate the GEBC value of all keys (4) in the shortest path. The GEBC values ​​of the same key (4) need to be summed.

[0017] Step 3.3): In the first complete iteration of the initial node (1), the four types of bonds (4) with the largest GEBC values ​​are set as potential breakable bonds (8). In subsequent complete iterations of the initial node, the two types of bonds (4) with the largest GEBC values ​​are set as potential breakable bonds (8). The A bonds set as potential breakable bonds (8) are... ij The value is updated to 0.

[0018] Step 3.4), repeat steps 3.1-3.3), if there is no longer a connected path between the first row node (1) and the last row node (1), then the prediction of the broken region (7) ends.

[0019] Furthermore, the detailed steps of step 4) are as follows:

[0020] Step 4.1), extract the predicted fracture regions that need to be reinforced (7).

[0021] Step 4.2) Delete all bond patterns (5) in the predicted fracture region (7). Set the bond pattern (5) connecting the upper and lower boundaries (9, 10) of the predicted fracture region (7) as a fixed bond pattern (5).

[0022] Step 4.3) The upper boundary (9) of the predicted fracture region (7) is expanded upward by one row, and the lower boundary (10) is expanded downward by one row. The expanded predicted fracture region (7) is defined as the new design space (2).

[0023] Step 4.4), the top and bottom rows in the new design space (2) are used to accommodate the fixed key pattern (5).

[0024] Step 4.5) With the help of probabilistic combinations and logical constraints, the structure is customized in the new design space (2) to achieve local toughening.

[0025] Furthermore, the method for achieving local toughening in this invention mainly includes adjusting the probability combination and modifying the logical constraints. Adjusting the probability combination results in a larger average node connectivity within the local region, while modifying the logical constraints aims to increase the frequency of short bonds.

[0026] Furthermore, average node connectivity refers to the average number of keys (4) connected to a single node (1). Key length (12) refers to the distance between two inflection points (11).

[0027] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0028] This invention uses GEBC values ​​to predict the fracture-prone regions of disordered mechanical metamaterials, avoiding the complexity of achieving toughening at the global level by optimizing the disordered mechanical metamaterial, while also avoiding material waste and changes in performance outside the fracture-prone regions. Furthermore, this invention overcomes the limitation of traditional methods that cannot modify the structure while maintaining bond connectivity and compatibility in localized regions of disordered mechanical metamaterials by customizing structures within the fracture-prone regions to achieve localized toughening. The method for localized toughening of disordered mechanical metamaterials provided by this invention offers inspiration for constructing artificial building materials with superior performance. (iv) Description of the attached drawings

[0029] Figure 1 This is a flowchart of the method of the present invention;

[0030] Figure 2 These are the nodes, design space, and lattice of this invention;

[0031] Figure 3 This is the binary representation of the present invention;

[0032] Figure 4 This invention uses disordered mechanical metamaterials;

[0033] Figure 5 This is the predicted and experimental fracture region of the present invention;

[0034] Figure 6 This invention relates to a customized design method;

[0035] Figure 7 This is the bond length definition of the present invention;

[0036] Figure 8 This is an example of how the present invention alters the average node connectivity to locally toughen disordered mechanical metamaterials;

[0037] Figure 9 This is an example of how changing bond lengths in this invention locally toughens disordered mechanical metamaterials;

[0038] Wherein: 1-node, 2-design space, 3-lattice, 4-bond, 5-bond mode, 6-disordered mechanical metamaterial, 7-predicted fracture region, 8-potential fracture bond, 9-upper boundary of predicted fracture region, 10-lower boundary of predicted fracture region, 11-inflection point, 12-bond length. (V) Detailed Implementation

[0039] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to examples. It should be understood that the following text is merely used to describe one or more specific embodiments of this invention and does not strictly limit the scope of protection specifically claimed by this invention.

[0040] Combination Figure 1 The design method for disordered mechanical metamaterials includes the following steps:

[0041] Step 1: Construct a class of disordered mechanical metamaterials.

[0042] like Figure 2 In paragraphs 3 and 4, this invention describes the construction process of the disordered mechanical metamaterial (6) used. This type of disordered mechanical metamaterial (6) is guided by nodes (1), design space (2), probabilistic combination, and logical constraints.

[0043] Figure 2 This invention illustrates a node (1), a design space (2), and a first logical constraint. The invention shows that the design space (2) specifies the dimensions of the final disordered mechanical metamaterial (6), with the node (1) serving as a positioning element for the bond (4). The first logical constraint states that the node (1) can only move within its corresponding lattice (3).

[0044] Figure 3 This invention demonstrates a key (4) constructed by a node (1), a key pattern (5) constructed by the key (4), a second logical constraint, and a third logical constraint. This invention shows that the key (4) is used to connect two adjacent nodes (1). The second logical constraint states that a node (1) can only construct a key (4) to a node (1) in an adjacent lattice (3), but cannot construct a key (4) to a node (1) in a diagonal lattice (3). To illustrate the third logical constraint, this invention introduces a binary representation of the lattice (3). A 3×3 matrix N is used. 3×3 To represent the bond (4) state of the lattice (3). In the matrix, "0" indicates that a bond (4) cannot be formed in the current direction, and "1" indicates that a bond (4) can be formed in the current direction. "0 / 1" means that the current position can be either "0" or "1". The matrix contains at least three "1"s, and "1" can only appear in the following five positions: N 3×3 [1,2],N 3×3 [2,1],N 3×3 [2,2],N 3×3 [2,3] and N 3×3 [3,2]. N 3×3 [i,j] (i,j = 1,2,3) refers to the number in the i-th row and j-th column of the lattice (3). N 3×3 [2,2] represents the center position of the lattice (3), which is the starting point for bond (4) formation. N 上 N 下 N 左 and N 右 These represent the four boundaries of the lattice (3). Using the above definition, this invention demonstrates that the third logical constraint is: ||N 左 –N右 ||2 = 0 or ||N 下 –N 上 ||2=0. Based on the number of bonds (4) in a single node (1), the bond pattern (5) is divided into three categories: Category I contains 4 bonds (4), Category II contains 3 bonds (4), and Category III contains only 2 bonds (4). This invention declares that if the orientation of bonds (4) is different but the number is the same in different lattices, they belong to the same category of bonds (4).

[0045] Figure 4 This invention presents probabilistic combinations and disordered mechanical metamaterials (6). To describe the possible bond modes (5) on a single node (1), this invention introduces probabilistic combinations (p1, p2, p3). i This refers to the probability of the i-th type of key pattern (5), p1+p2+p3=1. This invention... Figure 4 The figure shows a disordered mechanical metamaterial with a probability combination of (0.1, 0.6, 0.3) (6).

[0046] Step 2: Prediction of fracture-prone regions in disordered mechanical metamaterials.

[0047] like Figure 5 This invention generates a disordered mechanical metamaterial (6) containing 625 nodes (1) under the probability combination (0.1, 0.4, 0.5). The nodes (1) in this disordered mechanical metamaterial (6) are arranged in a 25x25 row and 25 column configuration. This invention constructs a 625×625 matrix A. ij The matrix A stores the Euclidean distance between adjacent nodes (1). For example, the first row and second column of the matrix stores the Euclidean distance between the node (1) in the first row and first column and the node (1) in the first row and second column. If there is no key (4) between two adjacent nodes (1), matrix A... ij The corresponding position in matrix A will be stored as 0. ij It is a symmetric matrix.

[0048] This invention first sets the initial node (1) as the node (1) in the first row and first column. The target node (1) iterates from the first row and first column to the 25th row and 25th column. The shortest path needs to be calculated for each iteration of the target node (1). If the target node (1) and the initial node (1) are the same, the shortest path does not need to be calculated, and the next iteration is performed directly. The GEBC value of the key (4) contained in the shortest path is calculated, and the GEBC values ​​of the same key (4) are directly summed. After the iteration of the target node (1) is completed, the initial node (1) is moved to the first row and second column, and the iteration of the target node (1) continues. When the initial node (1) moves to the 25th row and 25th column, it indicates a complete iteration, and the first prediction of the potential broken key (8) ends.

[0049] To avoid missing potential break bonds (8) at the beginning, this invention considers all four types of bonds (4) with the largest GEBC values ​​as potential break bonds (8) after the first prediction. However, if the four types of bonds (4) with the largest GEBC values ​​are used as potential break bonds (8) indefinitely, a region far exceeding the actual break region will be obtained. Therefore, in subsequent complete iterations, the two types of bonds (4) with the largest GEBC values ​​are used as potential break bonds (8). Once a bond (4) is considered a potential break bond (8), matrix A... ij The corresponding number in the table needs to be updated to 0. If there is no longer a connected path between the first row node and the 25th row node, the broken region prediction ends; otherwise, the complete iteration of the initial node (1) will continue. Figure 5 Figure A shows the predicted fracture region (7) of the disordered mechanical metamaterial (6). Figure 5 B shows the actual fracture region of the disordered mechanical metamaterial (6). Figure 5 C represents the experimental results of the actual fracture region. The light red straight line marks the potential fracture bonds (8). This invention demonstrates that the predicted fracture region (7) and the actual fracture region are highly consistent.

[0050] like Figure 6 This invention demonstrates a process for customizing the structure in a predicted fracture region (7). First, the predicted fracture region (7) is precisely marked, and then all bond patterns (5) within it are deleted. Next, the bond patterns (5) connecting the upper boundary (9) and lower boundary (10) of the fracture region are fixed. For example… Figure 6 If the predicted break region (7) is from row 3 to row 7, then the key patterns (5) in rows 2 and 8 are fixed. Then, the upper boundary of the predicted break region (7) is expanded upwards by one row, and the lower boundary is expanded downwards by one row to construct a new design space (2). The first and last rows in the new design space (2) are used to accommodate the fixed key patterns (5). Finally, a new probabilistic combination or logical constraint is used to customize the structure in the new design space (2).

[0051] Step 3: Local toughening of disordered mechanical metamaterials.

[0052] This invention demonstrates that the toughness of disordered mechanical metamaterials (6) can be quantified using peak strength and toughness modulus (MOT). Peak strength measures the compressive strength of the disordered mechanical metamaterial (6) under external loads, while toughness modulus measures the energy absorption capacity of the disordered mechanical metamaterial (6) before failure. Peak strength is expressed as the maximum strength of the stress-strain curve, and toughness modulus is quantified using the area under the stress-strain curve. This invention further demonstrates that increasing the average node connectivity or short bond frequency of the disordered mechanical metamaterial (6) can increase the toughness of the disordered mechanical metamaterial (6).

[0053] like Figure 7 This invention declares that the bond length (12) does not simply refer to the length of a single bond (4), but rather the distance between two adjacent inflection points (11). For example, chamber k contains only four bonds (4): i-ii, i-IV, ii-III, and III-IV. To increase the frequency of short bonds (4), this invention modifies the third logic to reject the generation of long bonds (4). Specifically, this invention further restricts the third logic constraint: in the same chamber, at least one of the bond patterns (5) between two adjacent nodes (1) has an inflection point (11) in the chamber. This invention shows that using the modified logic constraint will reject the generation of i-IV and ii-III.

[0054] like Figure 8 A, this invention generates an original sample K under the probability combination (0.1, 0.4, 0.5). O The potential fracture region (7) was predicted by calculating the GEBC value of bond (4). Figure 8 B. In this invention, the probability combination in the predicted fracture region (7) is adjusted to (0.6, 0.2, 0.2), and the corresponding average node connectivity increases from 2.68 to 3.31. The modified sample is defined as K. R . Figure 8 In C, this invention demonstrates sample K. O and K R The peak strength and toughness modulus. Sample K O The peak strength and toughness modulus are 0.202 MPa and 11.98 KJ / m, respectively. 3 Sample K R The values ​​are 0.239 MPa and 12.79 KJ / m. 3 Clearly, local toughening can be achieved by increasing the average node connectivity of the structure in a local region.

[0055] like Figure 9 A, this invention generates an original sample N under the probability combination (0.2, 0.5, 0.3). O The potential fracture region (7) was predicted by calculating the GEBC value of bond (4). Figure 9 B, In this invention, modified logic constraints are used to regenerate the bond pattern (5) in the predicted fracture region (7), and the modified sample is defined as N. R This invention shows that the original sample N O The longest bond (4) in the sample can reach 14mm. R The bond lengths (12) in the samples are all less than 10 mm, and the bond lengths (12) are significantly controlled. Figure 9 In C, this invention demonstrates sample N. O and NR The peak strength and toughness modulus. Sample N O The peak strength and toughness modulus are 0.695 MPa and 16.89 KJ / m, respectively. 3 Sample N R The values ​​are 0.735 MPa and 17.94 KJ / m. 3 Clearly, increasing the frequency of short bonds in a localized region can achieve a localized toughening effect.

[0056] This invention provides a design method for enhancing the local toughness of disordered mechanical metamaterials. It is a method for accurately predicting the fracture-prone regions of disordered mechanical metamaterials and achieving targeted reinforcement. Furthermore, the structural modifications of this invention are limited to the fracture-prone regions, avoiding impact on the performance of areas outside the fracture-prone regions. This design method effectively solves the technical problems existing in the prior art.

[0057] Although the embodiments of the present invention have been described in detail with reference to the accompanying drawings, those skilled in the art should understand that the above embodiments are merely illustrative explanations of the implementation of the present invention and are not intended to limit the scope of the present invention. The details in the embodiments do not constitute a limitation on the scope of the present invention. Any obvious changes, such as equivalent transformations or simple substitutions, based on the technical solutions of the present invention without departing from the spirit and scope of the present invention fall within the protection scope of the present invention.

Claims

1. A design method for enhancing the local toughness of disordered mechanical metamaterials, characterized in that; Includes the following steps: Step 1), use a growth algorithm to generate a class containing N The disordered mechanical metamaterial (6) with nodes (1) is a graph-based search algorithm based on a node-based design space (2). The algorithm needs to construct the disordered mechanical metamaterial under the joint guidance of probability combination and three logical constraints. The nodes serve as positioning elements, the design space determines the final size of the disordered mechanical metamaterial, the probability combination is used to specify the probability of occurrence of the bond pattern (5), and the logical constraints are used to ensure the connectivity of the bond (4). Step 2), define a N × N Matrix A ij Stores the Euclidean distance between all adjacent nodes of the key; Step 3), based on matrix A ij Calculate the GEBC value of the bond, where GEBC refers to the geodesic edge median centrality, and the frequency of the bond in the shortest path is statistically analyzed to measure the importance of a certain bond in the disordered mechanical metamaterial relative to other bonds; determine the predicted fracture region based on the GEBC value (7), including the following steps: Step 3.1) The initial node iterates sequentially from the first node to the last node. Each iteration of the initial node is accompanied by a complete iteration of the target node. That is, the target node needs to iterate from the second node to the last node, forming a nested loop. Step 3.2) In each iteration of the target node, it is necessary to calculate all paths from the initial node to all target nodes, identify all shortest paths, calculate the GEBC value of all keys in the shortest path, and sum the GEBC values ​​of the same keys. Step 3.3): In the first complete iteration of the initial node, the four types of bonds with the largest GEBC values ​​are set as potential breakable bonds (8). In subsequent complete iterations of the initial node, the two types of bonds with the largest GEBC values ​​are set as potential breakable bonds. The A bonds set as potential breakable bonds... ij The value is updated to 0; Step 3.4), repeat steps 3.1)-3.3), if there is no longer a connected path between the first row of nodes and the last row of nodes, then the prediction of the broken region ends; Step 4), re-customizing the predicted fracture area to achieve a toughening effect; includes the following steps: Step 4.1) Extract the predicted fracture regions that need to be reinforced; Step 4.2) Delete all bond patterns in the predicted fracture region; set the bond patterns connecting the upper and lower boundaries of the predicted fracture region as fixed bond patterns; Step 4.3) Expand the upper boundary of the predicted fracture region upward by one row and the lower boundary downward by one row; the expanded predicted fracture region is defined as the new design space; Step 4.4) The top and bottom rows in the new design space are used to accommodate fixed-bond patterns. With the help of probabilistic combinations and logical constraints, the structure is customized in the new design space to achieve local toughening.

2. The design method for enhancing the local toughness of disordered mechanical metamaterials according to claim 1, characterized in that; Matrix A ij Given a symmetric matrix, if there is a key between two nodes, then in A... ij The corresponding positions store their Euclidean distance; if there is no key between two nodes, then in A ij Store 0.

3. The design method for enhancing the local toughness of disordered mechanical metamaterials according to claim 1, characterized in that... The method for calculating GEBC is as follows: in, g(e ) refers to the key e GEBC value, δ st Represents the initial node s To the target node t The number of shortest paths in the data. δ st ( e The meaning of ) is that the shortest path contains a key. e The quantity.

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