Design method for enhancing toughness of local area of disordered mechanical metamaterial

Abstract

The invention relates to a design method for enhancing the toughness of a local area of a disordered mechanical metamaterial, which breaks through the limitation that the toughness of the disordered mechanical metamaterial can only be enhanced from a global level in a traditional method, can carry out targeted reinforcement on a potential fracture area, avoids the waste of materials, and completely eradicates the influence on the established performance of areas outside the fracture area. The design method comprises the following steps: firstly, generating a disordered mechanical metamaterial by using a generation algorithm, and then continuously searching a shortest path between an initial node and a target node. Then, the GEBC values of different keys in the shortest path are counted, and the GEBC values of the same keys are summed; then, two types of bonds with the highest GEBC value are regarded as potential broken bonds; and if no communicated path exists between the first row of nodes and the last row of nodes, ending the fracture area prediction. And finally, enhancing the toughness of the local area of the disordered mechanical metamaterial by increasing the average node connectivity or short key frequency of the structure in the fracture area.

Description

(I) Technical field

[0001] The invention belongs to the field of mechanics, and in particular relates to a design method for enhancing the toughness of a local area of ​​a disordered mechanical metamaterial. (II) Background technology

[0002] Mechanical metamaterials have surpassed the physical limitations of traditional materials and exhibited a series of outstanding properties, such as negative Poisson's ratio, negative effective modulus, negative compressibility, and high toughness. As an important branch, disordered mechanical metamaterials have also attracted widespread attention in recent years. Disordered mechanical metamaterials are not only lightweight, but also have unique properties such as energy focusing, avoiding catastrophic damage, shape reconstruction, and preventing stress concentration. However, due to the random distribution of internal bonds, disordered mechanical metamaterials inevitably produce local fracture-prone areas. The relatively low bearing capacity of the bonds in these fracture-prone areas may cause the disordered mechanical metamaterial to suddenly break during loading, greatly reducing the reliability of the material. Previous studies have explored the fracture characteristics of disordered mechanical metamaterials based on friction particle packing or Voronoi technology. They focused on the key role of disorder in the transition of metamaterials from brittle to ductile. According to Griffith's theory, the stress applied to a brittle material is usually concentrated in a small area, leading to crack formation and subsequent fracture. When the degree of disorder increases, the stress can be effectively dispersed throughout the material. However, adjusting the disorder of the entire metamaterial is usually a cumbersome task. Furthermore, the increase in disorder comes at the expense of the metamaterial's strength. (III) Summary of the invention

[0003] Purpose of the invention: The purpose of the present invention is to propose a design method for enhancing the toughness of local areas of disordered mechanical metamaterials, to overcome the limitation that existing design methods cannot control the easy-to-fracture areas in disordered mechanical metamaterials, and to achieve accurate prediction and targeted reinforcement of the easy-to-fracture areas of disordered mechanical metamaterials without changing the original performance of areas outside the easy-to-fracture areas.

[0004] Technical solution: The present invention provides a design method for enhancing the toughness of a local area of ​​a disordered mechanical metamaterial, comprising the following steps:

[0005] Step 1), using a growth algorithm to generate a type of disordered mechanical metamaterial (6) containing N nodes (1).

[0006] Step 2), define an N×N matrix A ij Stores the Euclidean distances between all adjacent nodes (1) where a key exists.

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

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

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

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

[0011] Furthermore, GEBC refers to geodesic edge betweenness centrality, which counts the frequency of occurrence of bonds (4) in the shortest path and is used to measure the importance of a bond (4) relative to other bonds (4) in disordered mechanical metamaterials. The calculation method of GEBC is:

[0012]

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

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

[0015] Step 3.1), the initial node (1) is iterated from the first node (1) to the last node (1) in sequence, and 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), all paths from the initial node (1) to the target node (1) need to be calculated and all shortest paths need to be identified. The GEBC values ​​of all keys (4) in the shortest path are calculated. 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 breaking 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 breaking bonds (8). 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 of nodes (1) and the last row of nodes (1), the prediction of the fractured region (7) ends.

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

[0020] Step 4.1), extract the predicted fracture area that needs to be strengthened (7).

[0021] Step 4.2), delete all bond patterns (5) in the predicted fracture region (7), and 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] In 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 a new design space (2).

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

[0024] In step 4.5), the structure is customized in the new design space (2) with the help of probabilistic combination and logical constraints to achieve local toughening.

[0025] Furthermore, the method for realizing local toughening of the present invention mainly includes adjusting probability combination and modifying logic constraints. The probability combination is adjusted so that the structure in the local area has a greater average node connectivity, and the logic constraints are modified to increase the frequency of short bonds.

[0026] Furthermore, the average node connectivity refers to the average number of bonds (4) connected to a single node (1). The bond 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] The present invention uses GEBC values ​​to predict the fracture-prone regions of disordered mechanical metamaterials, which can avoid the complexity of achieving toughening by optimizing disordered mechanical metamaterials at the global level, while avoiding the waste of materials and the change of performance of regions outside the fracture-prone regions. In addition, the present invention customizes the structure in the fracture-prone region to achieve local toughening, breaking the limitation that traditional methods cannot modify the structure while ensuring the connectivity and compatibility of bonds in the local region of disordered mechanical metamaterials. The method for toughening the local region of disordered mechanical metamaterials provided by the present invention provides inspiration for constructing artificial building materials with excellent performance. (IV) Description of the drawings

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

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

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

[0032] Figure 4 It is a disordered mechanical metamaterial used in the present invention;

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

[0034] Figure 6 It is the customized design method of the present invention;

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

[0036] Figure 8 This is an example of the local toughening of disordered mechanical metamaterials by changing the average node connectivity of the present invention;

[0037] Fig. 9 This is an example of the local toughening of disordered mechanical metamaterials by changing the bond length of the present invention;

[0038] Among them: 1-node, 2-design space, 3-lattice, 4-bond, 5-bond pattern, 6-disordered mechanical metamaterial, 7-predicted fracture region, 8-potential fracture bond, 9-predicted fracture region upper boundary, 10-predicted fracture region lower boundary, 11-inflection point, 12-bond length. (V) Specific implementation methods

[0039] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is specifically described below with reference to examples. It should be understood that the following text is only used to describe one or several specific implementations of the present invention, and does not strictly limit the scope of protection of the specific claims of the present invention.

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

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

[0042] like Figure 2 , 3 and 4, the present invention introduces the construction process of disordered mechanical metamaterials (6) used. Such disordered mechanical metamaterials (6) are guided by nodes (1), design space (2), probabilistic combinations and logical constraints.

[0043] Figure 2 The invention shows nodes (1), design space (2) and the first logical constraint. The invention shows that the design space (2) specifies the size of the final disordered mechanical metamaterial (6), and the node (1) serves as the positioning element of the bond (4). The first logical constraint is expressed as the node (1) can only move within the corresponding lattice (3).

[0044] Figure 3 The present invention shows the key (4) constructed by the node (1), the key pattern (5) constructed by the key (4), the second logical constraint and the third logical constraint. The present invention shows that the key (4) is used to connect two adjacent nodes (1). The second logical constraint is expressed as the node (1) can only construct a key (4) to the node (1) in the adjacent lattice (3), but cannot construct a key (4) to the node (1) in the lattice (3) on the diagonal. In order to illustrate the third logical constraint, the present invention introduces the binary representation of the lattice (3). Using a 3×3 matrix N 3×3 to represent the bond (4) state of the lattice (3). "0" in the matrix means that the current direction cannot construct a bond (4), and "1" means that the current direction can construct a bond (4). "0 / 1" means that the current position can be either "0" or "1". The number of "1" in the matrix is ​​at least three, 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 in the lattice (3). 3×3 [2,2] represents the center position of the lattice (3), which is the starting point for the generation of the bond (4). 上 , N 下 , N 左 and N 右 Respectively represent the four boundaries of the lattice (3). With the above definition, the present invention shows that the third logical constraint is: ||N 左 –N右 ||2=0 or ||N 下 –N 上 ||2=0. According to the number of bonds (4) in a single node (1), the bond pattern (5) is divided into three categories: Class I contains 4 bonds (4), Class II has 3 bonds (4), and Class III has only 2 bonds (4). The present invention states that if the directions of bonds (4) in different lattices are different but the number is the same, they belong to the same class of bonds (4).

[0045] Figure 4 The present invention presents probabilistic combinations and disordered mechanical metamaterials (6). In order to describe the possible bond patterns (5) on a single node (1), the present invention introduces probabilistic combinations (p1, p2, p3). i Refers to the probability of the i-th type key pattern (5), p1+p2+p3=1. Figure 4 A disordered mechanical metamaterial with the probability combination (0.1, 0.6, 0.3) is shown in (6).

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

[0047] like Figure 5 , the present 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 the disordered mechanical metamaterial (6) are arranged in 25 rows and 25 columns. The present invention constructs a 625×625 matrix A ij , which stores the Euclidean distances of adjacent nodes (1). For example, the first row and second column of the matrix stores the Euclidean distances 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), the matrix A ij The corresponding position in will store 0. ij is a symmetric matrix.

[0048] The present invention first sets the initial node (1) as the node (1) in the first row and first column, and the target node (1) is iterated from the first row and first column to the 25th row and 25th column. Each iteration of the target node (1) needs to calculate the shortest path. If the target node (1) is the same as the initial node (1), it is not necessary to calculate the shortest path, and the next iteration is directly performed. The GEBC values ​​of the keys (4) contained in the shortest path are calculated, and the GEBC values ​​of the same keys (4) are directly summed. When the iteration of the target node (1) is completed, the initial node (1) is moved to the first row and second column, and then the iteration of the target node (1) is continued. 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 bond (8) is completed.

[0049] In order to avoid missing potential break bonds (8) at the beginning, the present invention regards the 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 always used as potential break bonds (8), an area far exceeding the actual break area will be obtained. Therefore, in the 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 regarded as a potential break bond (8), the matrix A ij The number of the corresponding position in 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 fracture area prediction ends, otherwise the complete iteration of the initial node (1) will continue. Figure 5 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 is an experimental effect diagram of the actual fracture region. Among them, the light red straight line marks the potential fracture bond (8). The present invention shows that the predicted fracture region (7) and the actual fracture region are highly consistent.

[0050] like Figure 6 The present invention shows a process of customizing the structure in the predicted fracture region (7). First, the predicted fracture region (7) is accurately marked, and then all the bond patterns (5) therein are deleted. Then, the bond pattern (5) connecting the upper boundary (9) and the lower boundary (10) of the fracture region is fixed. For example Figure 6 The predicted fracture region (7) in is from row 3 to row 7, then the key patterns (5) in row 2 and row 8 are fixed. Then the upper boundary of the predicted fracture region (7) is expanded upward by one row, and the lower boundary is expanded downward 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, the structure is customized in the new design space (2) using new probability combinations or logical constraints.

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

[0052] The present invention shows that the peak strength and modulus of toughness (MOT) can be used as quantitative indicators of the toughness of the disordered mechanical metamaterial (6). The peak strength is used to measure the compressive strength of the disordered mechanical metamaterial (6) when subjected to external loads, and the modulus of toughness is used to measure the energy absorption capacity of the disordered mechanical metamaterial (6) before destruction. The peak strength is expressed as the maximum strength of the stress-strain curve, and the modulus of toughness is quantified using the area of ​​the stress-strain curve. The present invention further shows 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 , the present invention states that the bond length (12) does not simply refer to the length of a single bond (4), but the distance between two adjacent inflection points (11). For example, chamber k contains only four bonds (4), namely: i-ii, i-IV, ii-III and III-IV. In order to increase the frequency of short bonds (4), the present invention rejects the generation of long bonds (4) by modifying the third logic. Specifically, the present invention further restricts the third logical 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. The present invention shows that the use of the modified logical constraints will reject the generation of i-IV and ii-III.

[0054] like Figure 8 A, the present invention generates an original sample K under the probability combination (0.1, 0.4, 0.5) O , the potential fracture area (7) was predicted by calculating the GEBC value of the bond (4). Figure 8 B. The present invention adjusts the probability combination in the predicted fracture area (7) 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 C The present invention shows sample K O and K R Peak strength and toughness modulus of sample K O The peak strength and toughness modulus are 0.202MPa and 11.98KJ / m 3 , sample K R 0.239MPa and 12.79KJ / m 3 It is obvious that the local toughening effect can be achieved by increasing the average node connectivity of the structure in the local area.

[0055] like Fig. 9 A, the present invention generates an original sample N under the probability combination (0.2, 0.5, 0.3) O , the potential fracture area (7) was predicted by calculating the GEBC value of the bond (4). Fig. 9 B. The present invention uses the modified logical constraints to regrow the bond pattern (5) in the predicted fracture region (7). The modified sample is defined as N R The present invention shows that the original sample N O The longest key (4) can reach 14mm, modifying sample N R The bond lengths (12) in the samples are all lower than 10 mm, and the bond lengths (12) are significantly controlled. Fig. 9 C The present invention shows sample N O and NR Peak strength and toughness modulus. Sample N O The peak strength and toughness modulus are 0.695MPa and 16.89KJ / m 3 , sample N R 0.735MPa and 17.94KJ / m 3 It is clear that the local toughening effect can be achieved by increasing the short bond frequency of the structure in a local area.

[0056] The present invention provides a design method for enhancing the toughness of a local area of ​​a disordered mechanical metamaterial, which is a method for accurately predicting the easily broken area of ​​a disordered mechanical metamaterial and achieving targeted reinforcement. In addition, the present invention only modifies the structure in the easily broken area, avoiding the performance impact on areas outside the easily broken area. This design method effectively solves the technical problems existing in the background technology.

[0057] Although the embodiments of the present invention are described in detail in conjunction with the accompanying drawings, it should be understood by those skilled in the art that the above embodiments are merely explanations of the exemplary implementations of the present invention, and are not intended to limit the scope of the present invention. The details in the embodiments do not limit the scope of the present invention. Without departing from the spirit and scope of the present invention, any obvious changes such as equivalent transformations and simple replacements based on the technical solutions of the present invention fall within the protection scope of the present invention.

Claims

1. A design method for enhancing the toughness of a local region of a disordered mechanical metamaterial, characterized by: The steps include: Step 1), using a growth algorithm to generate a type of disordered mechanical metamaterial (6) containing N nodes (1). Step 2), define an N×N matrix A ij Stores the Euclidean distances between all adjacent nodes (1) where a key exists. Step 3), based on matrix A ij The GEBC value of the bond (4) is calculated, and the predicted fracture region (7) is determined based on the GEBC value. Step 4) is to re-customize the structure within the predicted fracture region (7) to achieve the toughening effect.

2. The design method according to claim 1, characterized in that: The growth algorithm used in the present invention is a graph-based search algorithm, which is established in a design space (2) based on nodes (1). It needs to construct a disordered mechanical metamaterial (6) under the joint guidance of probability combination and three logical constraints. The node (1) is used as a positioning element, the design space (2) determines the final size of the disordered mechanical metamaterial (6), the probability combination is used to specify the occurrence probability of the bond pattern (5), and the logical constraint is used to ensure the connectivity of the bond (4).

3. The design method according to claim 1, characterized in that: Matrix A ij is a symmetric matrix. If there is a bond (4) between adjacent nodes (1), then in A ij The corresponding position of A stores the Euclidean distance of the adjacent node (1). If there is no key (4) between the adjacent nodes (1), then ij Store 0 in .

4. The design method according to claim 1, characterized in that: GEBC refers to geodesic edge betweenness centrality, which counts the frequency of occurrence of bonds (4) in the shortest path and is used to measure the importance of a bond (4) relative to other bonds (4) in disordered mechanical metamaterials. The calculation method of GEBC is: where g(e) refers to the GEBC value of bond (4)e, δ st represents the number of shortest paths from the initial node (1)s to the target node (1)t, δ st The meaning of (e) is the number of keys (4)e contained in the shortest path.

5. The design method according to claim 1, characterized in that: The detailed steps of step 3) are as follows: Step 3.1), the initial node (1) is iterated from the first node (1) to the last node (1) in sequence, and 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. Step 3.2), in each iteration of the target node (1), all paths from the initial node (1) to the target node (1) need to be calculated and all shortest paths need to be identified. The GEBC values ​​of all keys (4) in the shortest path are calculated. The GEBC values ​​of the same key (4) need to be summed. 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 breaking 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 breaking bonds (8). The Aij value set as the potential breaking bond (8) 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 (1) and the last row of nodes (1), the prediction of the fractured region (7) ends.

6. The design method according to claim 1, characterized in that: The detailed steps of step 4) are as follows: Step 4.1), extract the predicted fracture area that needs to be strengthened (7). Step 4.2), delete all bond patterns (5) in the predicted fracture region (7), and set the bond pattern (5) connecting the upper (9) and lower boundaries (10) of the predicted fracture region (7) as a fixed bond pattern (5). In 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 a new design space (2). In step 4.4), the top row and the bottom row in the new design space (2) are used to accommodate the fixed key pattern (5). In step 4.5), the structure is customized in the new design space (2) with the help of probabilistic combination and logical constraints to achieve local toughening.

7. The design method according to claim 6, characterized in that: The method for realizing local toughening of the present invention mainly comprises adjusting probability combination and modifying logic constraints. The probability combination is adjusted so that the structure in the local area has a greater average node connectivity, and the logic constraints are modified to increase the frequency of short bonds.

8. The design method according to claim 7, characterized in that: Average node connectivity refers to the average number of bonds (4) connected to a single node (1). Bond length (12) refers to the distance between two inflection points (11).

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