Grid local dynamic self-adaptive encryption method suitable for continuous and discontinuous method

Abstract

The invention discloses a grid local dynamic self-adaptive encryption method suitable for a continuous and discontinuous method, which comprises the following steps of: S1, extracting a grid of a current continuous and discontinuous model, and degenerating the grid into a state before a bonding unit is inserted; s2, grid encryption is carried out, and the grid encryption process specifically comprises the steps that S2.1, the crack tip position in a current grid is searched, and triangular units needing to be re-divided are marked according to the preset re-division range radius; s2.2, carrying out grid re-division processing on the marked triangular units; s2.3, suspended node elimination processing is carried out on all the units to be processed; and S3, re-inserting a bonding unit into the grid processed in the step S2, and carrying out variable inheritance and node position correction on the bonding unit. According to the method, on the premise of eliminating suspension nodes and ensuring the quality of the grid, local dynamic reconstruction of the grid containing the bonding unit area is realized, the consistency before and after re-division is effectively maintained, and the calculation efficiency is improved.

Description

A local dynamic adaptive mesh refinement method applicable to continuous and discontinuous methods Technical Field

[0001] This invention relates to the field of continuous and discontinuous computational mechanics, and more specifically to a local dynamic adaptive mesh refinement method applicable to continuous and discontinuous methods. Background Technology

[0002] Continuous-discontinuous methods are a class of numerical methods used to simulate the fracture behavior of quasi-brittle materials. They can precisely characterize the entire process of material fracture, from continuous deformation and crack initiation to propagation and eventual complete breakage, and have been widely applied in structural design and safety assessment in fields such as geotechnical engineering, automotive engineering, and aerospace engineering. However, in these methods, cracks are only allowed to occur along element boundaries, inevitably exhibiting significant mesh dependence. Overly sparse meshes will limit crack propagation paths and reduce stress calculation accuracy, leading to distorted simulation results; while overly dense meshes will significantly increase computational scale and time. Therefore, how to improve computational efficiency while maintaining computational accuracy using adaptive mesh refinement techniques has become a key problem that needs to be solved in continuous-discontinuous methods.

[0003] A currently effective strategy is to dynamically track the crack tip during crack propagation and refine the mesh locally only within its neighborhood. This strategy not only improves the accuracy of stress calculation near the crack tip but also significantly expands the crack development space, thereby improving the overall accuracy of crack propagation simulation with relatively low computational cost. This type of method has been widely used in phase-field methods and element elimination-based fracture simulation methods, but its application within the framework of continuous and discontinuous methods still faces significant challenges. The fundamental reason is that the presence of bonding elements significantly increases the complexity of mesh re-division.

[0004] Bonded elements are a type of thicknessless element existing between adjacent solid elements sharing edges, used to describe the crack propagation zone during material cracking. Since bonded elements are attached to the boundaries of solid elements, they must also be re-meshed when the solid elements are re-meshed. However, the inconsistency in topology and data organization between bonded elements and solid elements makes synchronous re-meshing extremely challenging at the program implementation level, and related research and mature technologies are still relatively scarce. Furthermore, to preserve the morphology of formed and evolving cracks, nodes and boundaries in continuous-discontinuous methods cannot be freely adjusted during mesh re-meshing as in traditional finite element methods; they can only be locally reconstructed based on the original mesh. Simultaneously, since bonded elements need to be inserted at element boundaries, dangling nodes are not allowed in the mesh. These constraints further increase the difficulty of implementing local adaptive mesh refinement techniques in continuous-discontinuous methods.

[0005] Existing research largely focuses on splitting and refining a small number of elements near the crack tip. Scholars both domestically and internationally have proposed a series of dynamic splitting adaptive refinement methods for elements at the crack tip, improving crack path simulation by increasing the potential crack propagation directions. Some studies have further introduced tensile and shear failure criteria to control the splitting direction, thus more accurately describing crack propagation behavior. This type of local refinement method based on splitting a small number of elements can be considered a weakened adaptive refinement strategy. Its advantage lies in avoiding the re-subdivision problem of bonded elements by not involving the subdivision of existing element boundaries, and also avoiding the element distortion problem that may be caused by multi-level local refinement. However, the improvement in crack simulation accuracy by this type of method is relatively limited, mainly reflected in a slight increase in crack propagation directions, with no significant improvement in the accuracy of the stress field near the crack tip.

[0006] Another type of research circumvents the re-meshing problem of bonded elements by introducing an external bonding element strategy. This method does not pre-place bonded elements in the initial model; instead, it dynamically identifies potential cracking regions during computation based on failure criteria, first re-meshes these regions locally, and then inserts the corresponding bonded elements. This strategy, through a "re-mesh first, then insert" approach, effectively avoids the complex process of synchronously updating bonded elements during mesh re-meshing. However, this method typically assumes that cracked regions will not experience secondary failure, making it impossible to re-mesh regions with inserted bonded elements. Therefore, its applicability is significantly limited under complex stress paths and multi-crack evolution conditions.

[0007] Therefore, existing technologies lack a local dynamic adaptive encryption technology for grids applicable to continuous and discontinuous method frameworks. Summary of the Invention

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] This invention provides a local dynamic adaptive encryption method for grids based on continuous and discontinuous methods, comprising the following steps:

[0010] S1. Extract the mesh of the current continuous and discontinuous model and degenerate it to the state before inserting the bonding element. The mesh is a triangular mesh, which includes multiple triangular solid elements, called triangular elements.

[0011] S2. Perform mesh encryption. The mesh encryption process specifically includes:

[0012] S2.1 Search for the crack tip location in the current mesh, and mark the triangular elements that need to be re-divided according to the preset re-division radius;

[0013] S2.2, Perform mesh re-division processing on the marked triangular elements;

[0014] S2.3 Perform dangling node elimination processing on all units to be processed. The meanings of the units to be processed and dangling nodes are as follows: If there is a node in any triangular unit that does not belong to the vertex of the triangular unit, then the triangular unit is called the unit to be processed, and such nodes are called dangling nodes.

[0015] S3. Reinsert the bonding elements into the mesh processed in step S2, and perform variable inheritance and node position correction on the bonding elements.

[0016] Furthermore, in step S2.1, after marking the triangular units that need to be re-divided, the target subdivision level is determined by the following formula. :

[0017]

[0018] in, It is a function that rounds up. The average mesh size for all currently labeled triangular cells. The value of the current partitioning level is the average size of the desired target mesh. Initially 0;

[0019] Following step S2.3, the following step is also included:

[0020] S2.4, Current hierarchical value Add 1, then check if the condition is met. If yes, proceed to step S3; otherwise, re-mark the triangular units that need to be re-divided according to the preset re-division radius, and then return to step S2.2.

[0021] Furthermore, in step S2, during the grid encryption process, the first method is combined with the second method.

[0022] The first method is to connect the midpoints of each side of the original triangular unit to subdivide the original triangular unit into four sub-triangular units;

[0023] The second method is to connect a vertex of the original triangular unit with the midpoint of its opposite side to divide the original triangular unit into two sub-triangular units.

[0024] The unprocessed original triangular unit or the triangular unit generated after processing by the first method is called the first unit, and the triangular unit generated after processing by the second method is called the second unit.

[0025] Furthermore, step S2.2 specifically includes the following steps:

[0026] During the mesh re-division process, if the marked triangular cell is the first cell, it is subdivided into four new first cells using the first method.

[0027] If the marked triangular unit is the second unit, it is first degenerated to its form before being processed by the second method, and then subdivided into four new first units by the first method.

[0028] Furthermore, step S2.3 specifically includes the following steps:

[0029] When eliminating dangling nodes, traverse all current triangular elements to find all elements to be processed;

[0030] If the unit to be processed is the first unit and the number of dangling nodes is one, then the second method is used to connect the dangling nodes of the unit to be processed and the vertices opposite to the dangling nodes, thereby generating two second units and eliminating the dangling nodes.

[0031] If the unit to be processed is the first unit and the number of suspended nodes is two or three, then the first method is used to subdivide the unit to be processed into four new first units;

[0032] If the unit to be processed is the second unit, it is first degenerated to the form before being processed by the second method, and then subdivided into four new first units by the first method.

[0033] After processing all the current units to be processed, traverse all the current triangular units again to determine whether there are still units to be processed and dangling nodes. If so, repeat the above steps until there are no more units to be processed and dangling nodes, indicating that all dangling nodes have been eliminated, and end step S2.3.

[0034] Furthermore, in step S1, each triangular unit and each node are also numbered;

[0035] In step S2, for each newly generated triangular unit, the number of the corresponding parent unit is also recorded, where the parent unit refers to the original triangular unit before processing in step S2.

[0036] Furthermore, for each newly generated edge, a linked list of edge midpoint information is constructed, which contains the numbers of the two endpoints and the midpoint of each edge.

[0037] Furthermore, after step S2 and before step S3, the stress and strain variables of the corresponding parent element are inherited according to the number of the parent element corresponding to the newly generated triangular element recorded in step S2.

[0038] Furthermore, in step S3, when performing variable inheritance on the bonding unit, specifically:

[0039] The new and old bonded elements are matched using the parent element number corresponding to the adjacent triangular element of the newly generated bonded element;

[0040] For category variables, newly generated bonding units directly inherit the variable values ​​of the corresponding old bonding units. The category variables include failure state and failure type.

[0041] For continuous numerical variables, interpolation inheritance is performed on the corresponding variables based on the newly generated local coordinate system of the bonding unit. The continuous numerical variables include energy and damage values.

[0042] Furthermore, in step S3, when correcting the node positions of the bonding unit, specifically:

[0043] By using the node numbers of the edges adjacent to the newly generated bonding unit, the node coordinates of the corresponding old bonding unit are directly inherited;

[0044] For each newly generated node, the coordinates of each node are gradually corrected to the average of the coordinates of its two corresponding endpoint nodes, following the order of the edge midpoint information linked list.

[0045] Furthermore, during the dynamic change of the mesh in the continuous and discontinuous model, each preset time interval is used to execute steps S1-S3 to process the mesh at the current moment, thereby achieving local dynamic adaptive densification of the mesh.

[0046] Compared with existing technologies, the mesh local dynamic adaptive refinement method for continuous and discontinuous methods provided by this invention achieves local dynamic reconstruction of the mesh including the bonded element region while eliminating dangling nodes and ensuring mesh quality. This effectively maintains the consistency of crack geometry and mechanical state before and after re-meshing, and improves the computational efficiency of continuous and discontinuous methods. Attached Figure Description

[0047] Figure 1 is a schematic diagram of a local dynamic adaptive encryption method for grids based on continuous and discontinuous methods provided by the present invention;

[0048] Figure 2 shows schematic diagrams of the first and second methods;

[0049] Figures 3a-3f are schematic diagrams of mesh re-division and dangling point elimination;

[0050] Figures 4a-4f are schematic diagrams of the processing of the bonding unit;

[0051] Figures 5a and 5b show the original mesh and the mesh effect after local refinement, respectively.

[0052] Figures 6a and 6b show the stress inheritance effect of the original mesh and the mesh after processing by the present invention, respectively.

[0053] Figures 7a and 7b show the effects of the opening degree and relative slip of the bonding elements in the original mesh and the mesh after processing according to the present invention, respectively.

[0054] Figures 8a and 8b show the damage values ​​of the bonding elements in the original mesh and the mesh after processing according to the present invention, respectively.

[0055] Figures 9a-9d are comparison diagrams of the processing effects of the present invention and existing global mesh generation methods. Detailed Implementation

[0056] To make the technical means, creative features, objectives and effects of this invention easier to understand, the following description, in conjunction with the accompanying drawings and specific embodiments, further explains how this invention is implemented.

[0057] Referring to Figure 1, in one specific embodiment, the present invention provides a local dynamic adaptive encryption method for grids based on continuous and discontinuous methods, comprising the following steps:

[0058] S1. Extract the mesh of the current continuous and discontinuous model and degenerate it to the state before the insertion of the bonding elements. The mesh is a triangular mesh, consisting of multiple triangular solid elements, called triangular elements. The mesh degeneration operation means: deleting the bonding elements that have been inserted into the model and restoring the original topological connections between the solid elements, without changing the node coordinates and element mesh of the solid elements.

[0059] S2. Perform mesh encryption. The mesh encryption process specifically includes:

[0060] S2.1 Search for crack tip locations in the current mesh and mark the triangular elements that need to be re-divided according to the preset re-division radius. It can be understood that the specific marking method is: if the minimum distance between the triangular element and the current crack tip location is less than the preset re-division radius, then the triangular element is marked.

[0061] S2.2 Perform mesh re-division processing on the marked triangular units.

[0062] S2.3 Perform dangling node elimination processing on all units to be processed. The meanings of units to be processed and dangling nodes are as follows: If there is a node in any triangular unit that does not belong to the vertex of the triangular unit, then the triangular unit is called a unit to be processed, and such a node is called a dangling node.

[0063] S3. Reinsert the bonding elements into the mesh processed in step S2, and perform variable inheritance and node position correction on the bonding elements.

[0064] Preferably, in step S2, the mesh encryption process employs a combination of the first and second methods. The first method involves connecting the midpoints of the sides of the original triangular unit to subdivide it into four sub-triangular units. The second method involves connecting a vertex of the original triangular unit to the midpoint of its opposite side to subdivide it into two sub-triangular units. Referring to Figure 2, subdividing the original unit into four sub-units in the lower left corner corresponds to the first method; subdividing the original unit into two sub-units in the lower right corner corresponds to the second method.

[0065] The original triangular units that have not been processed or the triangular units generated after processing by the first method are collectively referred to as the first unit, and the triangular units generated after processing by the second method are referred to as the second unit.

[0066] Step S2.2 specifically includes the following steps:

[0067] During the mesh re-division process, if the marked triangular unit is the first unit, it is subdivided into four new first units using the first method; if the marked triangular unit is the second unit, it is first degenerated to its original form before being processed by the second method, and then subdivided into four new first units using the first method.

[0068] Referring to Figure 2, for the two second units in the lower right corner, if at least one of the second units is marked, when performing mesh re-division processing, it is first degenerated into the shape of the original unit, and then subdivided into four first units in the lower left corner using the first method.

[0069] Understandably, the first element generated using the first method maintains geometric similarity to the original element, thus ensuring no reduction in mesh quality during any level of refinement. However, this method may introduce dangling nodes, requiring the second method for elimination. Referring to Figure 3a, assuming only triangular elements a and b are currently marked, after re-partitioning these two triangular elements using the first method, the state shown in Figure 3b is reached. At this point, dangling nodes appear on the edges of triangular elements c and d. Therefore, triangular elements c and d are elements to be processed and require subsequent dangling node elimination processing.

[0070] Step S2.3 specifically includes the following steps: During the dangling node elimination process, all current triangular units are traversed to find all units to be processed. If the unit to be processed is a first unit and has one dangling node, the second method is used to connect the dangling node of the unit to be processed and the vertex opposite the dangling node, thereby generating two second units and eliminating the dangling node; if the unit to be processed is a first unit and has two or three dangling nodes, the first method is used to subdivide the unit to be processed into four new first units; if the unit to be processed is a second unit, it is first degenerated to its form before the second method, and then subdivided into four new first units using the first method.

[0071] After processing all the current units to be processed, traverse all the current triangular units again to determine whether there are still units to be processed and dangling nodes. If so, repeat the above steps until there are no more units to be processed and dangling nodes, indicating that all dangling nodes have been eliminated, and end step S2.3.

[0072] For the units c and d to be processed in Figure 3b, both of them belong to the first unit and have only one dangling node. Therefore, the second method is used to process them and enter the state shown in Figure 3c, thereby eliminating the dangling node.

[0073] It is understood that, based on the above processing method of the present invention, dangling nodes will only appear at the midpoint of the sides of the triangle. Therefore, the unit to be processed can generate at most three dangling nodes, which is rare. If a unit to be processed is a first unit and has three dangling nodes, it means that the midpoints of its three sides are all dangling nodes. In this case, the first method is used to subdivide the unit to be processed into four new first units, thereby eliminating the three dangling nodes.

[0074] If a unit to be processed is the first unit and has two dangling nodes, as shown in Figure 3d, after processing the unit to be processed e using the first method, it enters the state shown in Figure 3e. Although the original two dangling nodes are eliminated, new dangling nodes are generated on the triangular unit f that originally did not have dangling nodes. The second method is then used to process unit f to further eliminate the dangling nodes, as shown in Figure 3f.

[0075] If a unit to be processed is a second unit, it is first degenerated to its state before processing by the second method (the state before processing belongs to the first unit), and then processed using the first method. This process may also introduce new dangling nodes.

[0076] It can be seen that if only one dangling point elimination process is performed for all units to be processed, it may not be possible to eliminate all dangling nodes. Therefore, after processing all units to be processed, it is necessary to traverse all triangular units again. If there are still units to be processed and dangling nodes, the processing needs to be performed again until all dangling nodes are eliminated, and then step S2.3 ends.

[0077] Furthermore, in the method described above, step S2 only performs one mesh refinement (although multiple dangling node elimination processes may be required, only one mesh re-division process is performed). In practical applications, a single mesh refinement may not meet the accuracy requirements, necessitating multi-mesh refinement.

[0078] Preferably, in step S2.1, after marking the triangular units that need to be re-divided, the target subdivision level is determined by the following formula. :

[0079]

[0080] in, It is a function that rounds up. The average mesh size for all currently labeled triangular cells. The value of the current partitioning level is the average size of the desired target mesh. It is initially set to 0. This is understandable. and The corresponding dimensions are all length dimensions. In this embodiment, "grid size" specifically refers to the average side length of the triangle, i.e. This refers to the average side length of the triangles corresponding to all marked grids; This refers to the average side length of the triangle corresponding to the desired target mesh.

[0081] Accordingly, after the processing in steps S2.2 and S2.3, the following steps are also included:

[0082] S2.4, Current hierarchical value Add 1, then check if the condition is met. If yes, proceed to step S3; otherwise, re-mark the triangular units that need to be re-divided according to the preset re-division radius, and then return to step S2.2.

[0083] Repeat this process. Secondary mesh refinement ensures that the refined mesh achieves the required accuracy, and dangling nodes generated during the refinement process are completely eliminated.

[0084] In addition, to achieve variable inheritance and node position correction in step S3, each triangle unit and each node is numbered in step S1; in step S2, for each newly generated triangle unit, the number of the corresponding parent unit is recorded, where the parent unit refers to the original triangle unit before processing in step S2; and for each newly generated edge, a linked list of edge midpoint information is constructed, which contains the numbers of the two endpoints and the midpoint of each edge.

[0085] After step S2 and before step S3, the stress and strain variables of the corresponding parent element are inherited based on the parent element number recorded in step S2 for the newly generated triangular element. Since the continuous-discontinuous method uses first-order constant-strain solid elements, this variable inheritance method can ensure that the stress field and strain field remain consistent before and after mesh remapping.

[0086] In step S3, when inheriting variables for the bonding unit, specifically: the new and old bonding units are matched using the number of the parent unit corresponding to the adjacent triangular unit of the newly generated bonding unit; since the parent-child relationship of the triangular unit remains unique and cross-parent unit recombination does not occur during the processing of step S2, the parent unit number of the adjacent entity unit of the newly generated bonding unit is consistent with the corresponding old bonding unit, thereby realizing the one-to-one correspondence between the new and old bonding units.

[0087] For categorical variables, newly generated bonding elements directly inherit the variable values ​​of the corresponding old bonding elements. Categorical variables include failure state and failure type. For continuous numerical variables, interpolation inheritance is performed on the corresponding variables based on the local coordinate system of the newly generated bonding elements. Continuous numerical variables include energy and damage values.

[0088] Furthermore, in step S3, when correcting the node positions of the bonding elements, specifically: the node numbers of the edges adjacent to the newly generated bonding elements are used to directly inherit the node coordinates of the corresponding old bonding elements. For newly generated nodes, the coordinates of each newly generated node are gradually corrected to the average of the coordinates of its two corresponding endpoint nodes according to the order of the edge midpoint information linked list. Since the newly added nodes in step S2 are all located at the midpoint of the line connecting their endpoints, the above-mentioned gradual correction process essentially constitutes a reverse backtracking of the node generation process. This allows the nodes on the copied edges of the new bonding elements to be gradually traced back to the geometric positions of the copied edges of the old bonding elements, ensuring the geometric consistency of the copied edges of the new and old bonding elements before and after mesh re-division, and achieving consistency between the normal aperture and tangential slip of the new and old bonding elements before and after re-division.

[0089] Since the bonding element is composed of the original boundary of the solid element and its copied edge, and its normal aperture and tangential slip are both zero at the initial generation, the newly generated bonding element needs to inherit the node coordinates of the copied edge of the old bonding element in order to retain the aperture information of the old bonding element and ensure the consistency of the crack geometry before and after mesh remapping.

[0090] Referring to Figures 4a-4f, in a specific case, the original mesh before step S1 is shown in Figure 4a, where edge ab represents the original boundary and a'-b' represents the copied edge. After step S1, as shown in Figure 4b, the mesh degenerates to the state before the insertion of the bonding element. Assuming that after mesh subdivision in step S2 and re-insertion of the bonding element, the mesh is shown in Figure 4c.

[0091] For the original nodes in the newly generated bonding unit copied edge (nodes a' and b' in Figure 4c, which already exist in Figure 4a and belong to the original nodes), after the matching of the new and old bonding units is completed, the coordinates of the corresponding old bonding unit nodes are directly inherited, as shown in Figure 4d.

[0092] For newly generated nodes in the copied edge (nodes c' and d' in Figure 4c), their positions are progressively corrected based on the constructed edge midpoint information linked list. Specifically, after the original node coordinates on the copied edge are inherited, the coordinates of each newly generated node are progressively corrected to the average of the coordinates of its two corresponding endpoint nodes according to the order of the edge midpoint information linked list. For example, the coordinates of the new node c' in the copied edge are first corrected based on the average coordinates of endpoints a' and b', as shown in Figure 4e; then the coordinates of the new node d' in the copied edge are corrected based on the average coordinates of endpoints a' and c', as shown in Figure 4f.

[0093] By comparing the aperture distribution of the bonded elements in the original mesh (as shown in Figure 4a) with the aperture distribution of the bonded elements after mesh remapping (as shown in Figure 4f), it can be seen that this method can maintain the consistency of the normal aperture and relative slip of the old and new bonded elements before and after mesh remapping.

[0094] For any continuous or discontinuous model mesh (which can be considered a static mesh), the complete process of steps S1-S3 described above can be used to achieve local adaptive refinement of the mesh at the current moment. That is, the method described above completes one round of local adaptive mesh refinement. During the dynamic changes of the mesh in the continuous or discontinuous model, steps S1-S3 can be executed every preset time interval to process the mesh at the current moment, thereby achieving local dynamic adaptive refinement of the mesh.

[0095] Understandably, during the entire dynamic processing, in the first round of processing, step S2.1 marks the triangular elements that need to be re-divided near the initial crack tip location. Since only the original triangular elements (belonging to the aforementioned first element) exist in the mesh in the initial state, only the first element can be marked. In subsequent rounds of processing, due to the dynamic changes in the mesh of the continuous and discontinuous model, the crack tip location will also change. Therefore, based on the changed crack tip location, the triangular elements are re-marked and processed. Thus, there may be a second element that is marked. In this case, the processing method corresponding to the different situations mentioned above can be applied.

[0096] In some specific cases, referring to Figures 5a and 5b, the original mesh and the mesh after local refinement using this method are shown respectively. It can be seen that the method provided by this invention eliminates all dangling points while achieving local refinement.

[0097] Figures 6a and 6b show the stress inheritance effect of the original mesh and the mesh after treatment by this method, respectively; Figures 7a and 7b show the aperture and relative slip of the bonded elements in the original mesh and the mesh after treatment by this method, respectively; Figures 8a and 8b show the damage values ​​of the bonded elements in the original mesh and the mesh after treatment by this method, respectively. All of these figures demonstrate the consistency between the old and new bonded elements before and after treatment.

[0098] Figures 9a-9d illustrate the results using this method, with a global 4mm mesh (i.e., all meshes are divided to a 4mm scale), a global 2mm mesh, and a global 0.5mm mesh, respectively. It can be seen that compared to the global coarse-scale (e.g., 4mm) meshing method, this method better guarantees the mesh quality of critical areas (near the crack tip); compared to the global fine-scale (e.g., 0.5mm) meshing method, while ensuring the mesh quality of critical areas, this method improves the computational efficiency of the continuous-discontinuous method because it eliminates the need for global fine-scale meshing.

[0099] As can be seen, the basic idea of ​​this invention is to degrade the current model to an initial state without inserted bonding elements before mesh re-partitioning through a mesh degradation operation; then, local re-partitioning is performed on the degraded mesh, and bonding elements are re-inserted after the re-partitioning is completed. During the mesh re-partitioning process, the triangular mesh edge midpoint connection method (first method) and vertex-to-edge partitioning method (second method) from finite element local refinement techniques are introduced. This achieves multi-level local refinement while ensuring that the original mesh node and boundary topology remain unchanged, avoiding the generation of dangling nodes and ensuring that the mesh quality does not deteriorate under any refinement level. Furthermore, to address the problem of bonding element variables being re-initialized during the re-partitioning process, a matching method based on adjacent entity parent element information is proposed to identify and match the old and new bonding elements before and after re-partitioning, thereby achieving the inheritance of internal variables within the bonding elements. Simultaneously, based on the edge midpoint insertion point linked list, the position of the copied interface edge of the newly generated bonding element is interpolated and inherited, thus ensuring the consistency of key physical quantities such as the normal opening and tangential slip of the bonding elements before and after re-partitioning. By matching new and old bonding elements and inheriting variables, this invention effectively avoids the problem of direct re-partitioning of bonding elements and realizes local mesh reconstruction of regions containing bonding elements.

[0100] In summary, the local dynamic adaptive mesh refinement method for continuous and discontinuous methods provided by the invention achieves local dynamic reconstruction of the mesh including the bonded element region while eliminating dangling nodes and ensuring mesh quality. This effectively maintains the consistency of crack geometry and mechanical state before and after re-meshing, and improves the computational efficiency of continuous and discontinuous methods.

[0101] Finally, it should be noted that the above description is only an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A local dynamic adaptive mesh refinement method applicable to continuous and discontinuous methods, characterized in that, The steps include: S1. Extract the mesh of the current continuous and discontinuous model and degenerate it to the state before inserting the bonding element. The mesh is a triangular mesh, which includes multiple triangular solid elements, referred to as triangular elements. S2. Perform mesh refinement. The mesh refinement process specifically includes: S2.

1. Search for the crack tip position in the current mesh and mark the triangular elements that need to be re-divided according to the preset re-division range radius; S2.

2. Perform mesh re-division processing on the marked triangular elements; S2.

3. Perform dangling node elimination processing on all elements to be processed. The meaning of elements to be processed and dangling nodes is: if there is a node in any triangular element that does not belong to the vertex of the triangular element, then the triangular element is called the element to be processed, and such nodes are called dangling nodes; S3. Re-insert bonding elements into the mesh after the processing in step S2, and perform variable inheritance and node position correction on the bonding elements.

2. The mesh local dynamic adaptive encryption method applicable to continuous and discontinuous methods according to claim 1, characterized in that, In step S2.1, after marking the triangular elements that need to be re-divided, the target subdivision level is determined by the following formula. ： in, It is a function that rounds up. The average mesh size for all currently labeled triangular cells. The value of the current partitioning level is the average size of the desired target mesh. The initial value is 0; after step S2.3, the following step is also included: S2.4, the value of the current partitioning level. Add 1, then check if the condition is met. If yes, proceed to step S3; otherwise, re-mark the triangular units that need to be re-divided according to the preset re-division radius, and then return to step S2.

2.

3. The mesh local dynamic adaptive encryption method applicable to continuous and discontinuous methods according to claim 1, characterized in that, In step S2, during the grid encryption process, a combination of the first method and the second method is used. The first method is to connect the midpoints of each side of the original triangular unit to subdivide the original triangular unit into four sub-triangular units. The second method is to connect a vertex of the original triangular unit with the midpoint of its opposite side to divide the original triangular unit into two sub-triangular units. The unprocessed original triangular unit or the triangular unit generated after processing by the first method is called the first unit, and the triangular unit generated after processing by the second method is called the second unit.

4. The local dynamic adaptive mesh refinement method applicable to continuous and discontinuous methods according to claim 3, characterized in that, In step S2.2, the following steps are specifically included: during the mesh re-division process, if the marked triangular unit is the first unit, it is subdivided into four new first units by the first method; if the marked triangular unit is the second unit, it is first degenerated to the form before the second method, and then subdivided into four new first units by the first method.

5. The mesh local dynamic adaptive encryption method applicable to continuous and discontinuous methods according to claim 4, characterized in that, Step S2.3 specifically includes the following steps: During the dangling node elimination process, all current triangular units are traversed to find all units to be processed; if the unit to be processed is a first unit and has one dangling node, the second method is used to connect the dangling node of the unit to be processed and the vertex opposite to the dangling node, thereby generating two second units and eliminating the dangling node; if the unit to be processed is a first unit and has two or three dangling nodes, the first method is used to subdivide the unit to be processed into four new first units; if the unit to be processed is a second unit, it is first degenerated to the form before the second method, and then subdivided into four new first units using the first method; after processing all current units to be processed, all current triangular units are traversed again to determine whether there are still units to be processed and dangling nodes. If there are, the above steps are repeated until there are no units to be processed and dangling nodes, indicating that all dangling nodes have been eliminated, and step S2.3 ends.

6. The mesh local dynamic adaptive encryption method applicable to continuous and discontinuous methods according to claim 5, characterized in that, In step S1, each triangle unit and each node are also numbered; in step S2, for each newly generated triangle unit, the number of the corresponding parent unit is also recorded, the parent unit refers to the original triangle unit before the processing in step S2; and for each newly generated edge, an edge midpoint information linked list is constructed, the edge midpoint information linked list contains the numbers of the two endpoints and the midpoint of each edge.

7. The mesh local dynamic adaptive encryption method applicable to continuous and discontinuous methods according to claim 6, characterized in that, After step S2 and before step S3, the stress and strain variables of the corresponding parent element are inherited according to the number of the parent element corresponding to the newly generated triangular element recorded in step S2.

8. The mesh local dynamic adaptive encryption method applicable to continuous and discontinuous methods according to claim 7, characterized in that, In step S3, when inheriting variables for the bonding unit, specifically: the new and old bonding units are matched using the parent unit number corresponding to the adjacent triangular unit of the newly generated bonding unit; for categorical variables, the newly generated bonding unit directly inherits the variable values ​​of the corresponding old bonding unit, the categorical variables including failure state and failure type; for continuous numerical variables, the corresponding variables are inherited by interpolation based on the local coordinate system of the newly generated bonding unit, the continuous numerical variables including energy and damage value.

9. The mesh local dynamic adaptive encryption method applicable to continuous and discontinuous methods according to claim 8, characterized in that, In step S3, when correcting the node positions of the bonding unit, specifically: the node coordinates of the corresponding old bonding unit are directly inherited by using the node number of the edge adjacent to the newly generated bonding unit; for the newly generated node, the coordinates of each newly generated node are gradually corrected to the average of the coordinates of its two corresponding endpoint nodes according to the order of the edge midpoint information linked list.

10. The mesh local dynamic adaptive encryption method applicable to continuous and discontinuous methods according to claim 1, characterized in that, During the dynamic change of the mesh in the continuous and discontinuous model, after a preset time, steps S1-S3 are executed once to process the mesh at the current moment, thereby achieving local dynamic adaptive densification of the mesh.

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