A numerical calculation method and related device for simulating crack growth in two-dimensional space

Abstract

This application discloses a numerical calculation method and related device for simulating two-dimensional crack propagation, relating to the field of computational mechanics. The method comprises: obtaining a cantilever beam's overall crack solution region and a crack tip region; establishing a transition region based on the overall crack region and the crack tip region; constructing a transition region basis function based on the transition region; solving the transition region, overall region, and crack tip region based on the transition region basis function, overall region basis function, and crack tip region basis function to obtain a two-dimensional crack propagation result; the overall region basis function is a finite element basis function obtained by discretizing linear quadrilateral or triangular elements; the crack tip region basis function is a B-spline basis function; and the two-dimensional crack propagation result includes an overall displacement solution, a crack tip region displacement solution, and a transition region displacement solution. This application can accurately and stably simulate the numerical value of two-dimensional crack propagation.

Description

Technical Field

[0001] The present application relates to the field of computational mechanics technology, and in particular to a numerical calculation method and related device for simulating two-dimensional crack propagation. Background Art

[0002] Numerical simulation of crack problems has always been a research hotspot in the field of computational mechanics. Crack propagation simulation requires very high numerical simulation accuracy and stability. However, the stress field distribution at the crack tip is complex and the calculation of the crack propagation process generally requires mesh re-division, which makes it difficult to simultaneously meet the high accuracy and high stability of the simulation process. Therefore, most numerical methods are not very effective in simulating crack propagation. Summary of the Invention

[0003] The purpose of this application is to provide a numerical calculation method and related device for simulating two-dimensional space crack propagation, which can accurately and stably simulate the numerical value of two-dimensional crack propagation.

[0004] To achieve the above objectives, this application provides the following solutions.

[0005] In a first aspect, the present application provides a numerical calculation method for simulating crack propagation in two-dimensional space, and the numerical calculation method for simulating crack propagation in two-dimensional space includes the following steps.

[0006] Obtain the overall crack solution region and crack tip region of the cantilever beam.

[0007] A transition region is established based on the crack overall region and the crack tip region.

[0008] A transition region basis function is constructed based on the transition region.

[0009] The transition region, the overall region and the crack tip region are solved based on the transition region basis function, the overall region basis function and the crack tip region basis function to obtain a two-dimensional crack propagation result; the overall region basis function is a finite element basis function obtained after discretization using linear quadrilateral or triangular elements; the crack tip region basis function is a B-spline basis function; the two-dimensional crack propagation result includes: an overall displacement solution, a crack tip region displacement solution and a transition region displacement solution.

[0010] In a second aspect, the present application provides a computer device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-mentioned numerical calculation method for simulating crack propagation in two-dimensional space.

[0011] In a third aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned numerical calculation method for simulating two-dimensional space crack propagation.

[0012] According to the specific embodiments provided in this application, this application discloses the following technical effects.

[0013] This application provides a numerical calculation method and related device for simulating crack propagation in two-dimensional space. First, the overall crack solution region and crack tip region of a cantilever beam are obtained, which can accurately define the spatial range required for numerical calculation. The overall solution region covers most of the cantilever beam area except the crack tip, while the crack tip region focuses on the area with the most dramatic stress and strain changes. This division enables subsequent numerical calculations to adopt different calculation strategies for different regions, avoiding the use of a unified and overly complex calculation model for the entire cantilever beam, thereby improving computational efficiency. Second, a transition region is established based on the overall crack region and the crack tip region, which can effectively alleviate the numerical solution differences between the overall region and the crack tip region. By establishing the transition region, the overall region, the crack tip region, and the subsequently constructed transition region basis functions are organically linked. This makes the crack solution model of the entire cantilever beam more complete in terms of mathematics and physics, and the various regions are coordinated with each other, which can more realistically reflect the crack propagation in the cantilever beam, rather than simply piecing together the solutions of each region independently. Then, a transition region basis function is constructed based on the transition region. This ensures a continuous and smooth transition between the basis functions of different regions, avoiding numerical oscillations or error accumulation caused by sudden changes in the basis functions. This makes the entire solution process more stable and the results more reliable. Finally, based on the transition region basis function, the overall region basis function, and the crack tip region basis function, the transition region, the overall region, and the crack tip region are solved to obtain two-dimensional crack propagation results. These detailed solution results provide comprehensive and accurate data support for subsequent structural safety assessments, fatigue life predictions, and other analyses, helping engineers better evaluate the performance and remaining service life of the cantilever beam. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0015] Figure 1 This is a diagram of the application environment of a numerical calculation method for simulating two-dimensional crack propagation in one embodiment of the present application.

[0016] Figure 2 A schematic flow chart of a numerical calculation method for simulating crack propagation in two-dimensional space provided in one embodiment of the present application.

[0017] Figure 3 A schematic diagram of a circular area at the crack tip provided in one embodiment of the present application.

[0018] Figure 4 A schematic diagram of the transition area between the whole area and the circular area provided in one embodiment of the present application.

[0019] Figure 5 Schematic diagram of a calculation model for a cracked cantilever beam provided in one embodiment of the present application.

[0020] Figure 6a Schematic diagram of the mesh model 1 of the entire cracked cantilever beam and the crack tip area provided in one embodiment of the present application.

[0021] Figure 6b Schematic diagram of the mesh model 2 of the entire cracked cantilever beam and the crack tip area provided in one embodiment of the present application.

[0022] Figure 7 A schematic diagram of a crack propagation path provided in one embodiment of the present application.

[0023] Figure 8 A schematic diagram of the structure of a computer device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0024] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0025] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0026] The numerical calculation method for simulating two-dimensional space crack propagation provided in the embodiment of the present application can be applied to Figure 1In the application environment shown, the terminal 102 communicates with the server 104 via a network. The data storage system can store data that the server 104 needs to process. The data storage system can be set up separately, integrated on the server 104, or placed on the cloud or other servers. The terminal 102 can send the obtained overall crack solution region and crack tip region of the cantilever beam to the server 104. After receiving the overall crack solution region and crack tip region of the cantilever beam, the server 104 establishes a transition region based on the overall crack solution region and the crack tip region; constructs a transition region basis function based on the transition region; and solves the transition region, the overall region, and the crack tip region based on the transition region basis function, the overall region basis function, and the crack tip region basis function to obtain a two-dimensional crack propagation result. The overall region basis function is a finite element basis function obtained by discretizing linear quadrilateral or triangular elements; the crack tip region basis function is a B-spline basis function; and the two-dimensional crack propagation result includes: an overall displacement solution, a crack tip region displacement solution, and a transition region displacement solution. The server 104 can provide feedback of the obtained two-dimensional crack propagation result to the terminal 102. In addition, in some embodiments, the numerical calculation method for simulating two-dimensional space crack extension can also be implemented independently by the server 104 or the terminal 102. For example, the terminal 102 can directly perform numerical calculations to simulate two-dimensional space crack extension for the overall crack solution area and crack tip area of ​​the cantilever beam, or the server 104 can obtain the overall crack solution area and crack tip area of ​​the cantilever beam from the data storage system, and perform numerical calculations to simulate two-dimensional space crack extension for the overall crack solution area and crack tip area of ​​the cantilever beam.

[0027] The terminal 102 may be, but is not limited to, various desktop computers, laptop computers, smart phones, and tablet computers. The server 104 may be implemented as an independent server or a server cluster consisting of multiple servers, or a cloud server.

[0028] In an exemplary embodiment, Figure 2 As shown, a numerical calculation method for simulating crack propagation in two-dimensional space is provided. The method is executed by a computer device, specifically, it can be executed by a computer device such as a terminal or a server alone, or it can be executed by a terminal and a server together. In the embodiment of the present application, the method is applied to Figure 1 The server 104 in the example is used for explanation, and the steps include the following steps S1 to S4.

[0029] S1: Obtain the overall crack solution area and crack tip area of ​​the cantilever beam.

[0030] S2: establishing a transition region based on the entire crack region and the crack tip region.

[0031] S3: Constructing a transition region basis function based on the transition region.

[0032] S4: Based on the transition region basis function, the overall region basis function and the crack tip region basis function, the transition region, the overall region and the crack tip region are solved to obtain a two-dimensional crack propagation result; the overall region basis function is a finite element basis function obtained after discretization using linear quadrilateral or triangular units; the crack tip region basis function is a B-spline basis function; the two-dimensional crack propagation result includes: an overall displacement solution, a crack tip region displacement solution and a transition region displacement solution.

[0033] Implement the above steps S1 to S4, first consider using finite element mesh for discretization in the overall solution area, and establish local coordinates in the circular area centered on the crack tip in the crack tip area, and use parameterization to describe the regional geometry and the cracks in the area. Establish a transition area based on the boundary of the circular area, and construct related basis functions. Use B-spline basis functions to approximate the corresponding circular curve and transition area. In the transition area, introduce related weight functions to transform the finite element basis functions and circular area basis functions in the transition area. The transformed related basis functions can at least reconstruct linear polynomials to ensure the numerical accuracy of the transition area and the stability of the overall solution. Compared with the existing methods, the present application can establish a local coordinate system at the crack tip to simulate the stress field in the crack tip area, accurately grasp the singular characteristics of the crack solution, and the numerical solution stability is very good; at the same time, a new coupling technology is used to seamlessly connect the crack tip area basis function and the overall finite element basis function, so that the calculation during the crack propagation process maintains high efficiency and stability.

[0034] The overall finite element mesh is discretized.

[0035] If the overall solution area is discretized using linear quadrilateral or triangular elements, the overall displacement solution can be expressed as follows.

[0036] (1).

[0037] in, is the overall displacement solution; is the finite element basis function of the entire region, is the number of finite element basis functions in the entire region; is the first variable to be determined.

[0038] The expression of the overall displacement solution in two-dimensional space can be expressed by the following formula.

[0039] (2).

[0040] (3).

[0041] in, is the overall displacement solution in the x direction of two-dimensional space; is the overall displacement solution in the y direction of two-dimensional space; is the finite element basis function in two-dimensional space; is the first variable to be determined in the x direction of the two-dimensional space; is the first variable to be determined in the y direction of the two-dimensional space.

[0042] B-spline approximation of the crack tip region.

[0043] The displacement solution in the crack tip region is approximated using B-spline basis functions.

[0044] (4).

[0045] in, is the displacement solution in the crack tip area; is the B-spline basis function in the crack tip region, is the number of B-spline basis functions in the crack tip region; is the second variable to be determined; is a parameter space variable.

[0046] The expression of the displacement solution of the crack tip region in the two-dimensional parameter space can be expressed by the following formula.

[0047] (5).

[0048] (6).

[0049] (7).

[0050] in, is the displacement solution of the crack tip region in the x-direction of the two-dimensional parameter space; is the displacement solution of the crack tip region in the y direction in the two-dimensional parameter space; is the B-spline basis function of the crack tip region in the two-dimensional parameter space; is the second variable to be determined in the x direction of the two-dimensional parameter space; is the second variable to be determined in the y direction of the two-dimensional parameter space; is the circumferential one-dimensional B-spline basis function; is the radial one-dimensional B-spline basis function; are the coordinates in the two-dimensional parameter space.

[0051] Transition region coupling technology.

[0052] like Figure 3 and Figure 4 As shown, the radius of the circular area centered on the crack tip is , then the crack tip is the center and the radius is The circle with radius is The circle forms a transition area , the outer and inner circular boundaries of the transition region are approximated by B-spline curves.

[0053] (8).

[0054] (9).

[0055] in, is the outer circular boundary curve of the transition area; is the circular boundary curve inside the transition area; The control points of the B-spline basis function corresponding to the outer circular boundary curve; are the control points of the B-spline basis function corresponding to the inner circular boundary curve; is the B-spline basis function; is the number of B-spline basis functions in the transition region.

[0056] In two-dimensional space, the physical coordinates of a curve can be expressed as follows.

[0057] (10).

[0058] (11).

[0059] (12).

[0060] (13).

[0061] (14).

[0062] in, For control points Coordinates in two-dimensional space; For control points Coordinates in two-dimensional space; ( , ) are the physical coordinates of the control points of the circular boundary curve outside the transition area corresponding to the B-spline basis function; ( , ) are the physical coordinates of the control points of the circular boundary curve inside the transition region corresponding to the B-spline basis function.

[0063] Then the expression of the transition region in the two-dimensional parameter space is as follows.

[0064] (15).

[0065] (16).

[0066] (17).

[0067] in,( , ) is the representation of the transition region in two-dimensional parameter space.

[0068] The expression of the transition region basis function is as follows.

[0069] (18).

[0070] (19).

[0071] (20).

[0072] in, is the B-spline basis function of the transition region in the two-dimensional parameter space; is the finite element basis function of the transition region in the two-dimensional parameter space; is the B-spline basis function of the crack tip region in the two-dimensional parameter space; Finite element basis functions for the overall solution region in two-dimensional parameter space; is the basic weight function; are the coordinates in the two-dimensional parameter space.

[0073] The present application also provides an application scenario, which applies the above-mentioned numerical calculation method for simulating crack extension in two-dimensional space. Specifically: the numerical calculation method for simulating crack extension in two-dimensional space provided in this embodiment can be applied in a crack extension simulation scenario. The crack extension simulation scenario includes: a data acquisition link, a transition region establishment link, a transition region basis function construction link and a two-dimensional crack extension link; first, the overall crack solution area and the crack tip area of ​​the cantilever beam are obtained; secondly, based on the overall crack area and the crack tip area, a transition area is established; then, a transition area basis function is constructed based on the transition area; finally, based on the transition area basis function, the overall area basis function and the crack tip area basis function, the transition area, the overall area and the crack tip area are solved to obtain a two-dimensional crack extension result; the overall area basis function is a finite element basis function obtained after discretization using linear quadrilateral or triangular units; the crack tip area basis function is a B-spline basis function; the two-dimensional crack extension result includes: an overall displacement solution, a crack tip area displacement solution and a transition area displacement solution.

[0074] The following is a practical example to verify the effectiveness of this application. Figure 5 As shown in the figure, there is a pre-set crack in the two-dimensional cantilever beam. The left end of the beam is subjected to a concentrated force in the opposite direction. The overall finite element analysis uses a structural grid. The crack tip area used for local singular geometric analysis is set as a circular area with the crack tip as the center, as shown in the figure. Figure 6a and Figure 6b As shown in Figure 2, two mesh models with different sizes are used to simulate the crack growth.

[0075] exist Figure 6a In the finite element mesh , the radius of the circular area , the B-spline nodes used for analysis in the crack tip region are .

[0076] exist Figure 6b In the finite element mesh , the radius of the circular area , the B-spline nodes used for analysis in the crack tip region are .

[0077] The calculation of the crack propagation direction is based on the maximum circumferential stress criterion. Two propagation step sizes of 1 and 0.5 are adopted, and the stress intensity factor is calculated using the interactive integration method. Figure 7 The crack propagation path is displayed. It can be seen that the crack propagation paths calculated based on the two mesh models using the same expansion step are almost the same. The difference in crack propagation paths under different expansion step sizes is obvious. The simulated crack propagation of this application has good stability.

[0078] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Figure 8 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O) and a communication interface. The processor, memory and input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store the overall solution area and crack tip area of ​​the cantilever beam. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a numerical calculation method for simulating crack propagation in two-dimensional space is implemented.

[0079] Those skilled in the art will understand that Figure 8 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0080] In an exemplary embodiment, a computer device is further provided, including a memory and a processor. The memory stores a computer program, and the processor implements the above method embodiments when executing the computer program.

[0081] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, which implements the above-mentioned method embodiments when executed by a processor.

[0082] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0083] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the above-mentioned embodiments. In particular, any reference to memory, database, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0084] The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may include, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic units, data processing logic units based on quantum computing, and the like.

[0085] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0086] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A numerical calculation method for simulating crack propagation in two-dimensional space, characterized in that: The numerical calculation method for simulating two-dimensional space crack growth includes: Obtain the overall crack solution area and crack tip area of ​​the cantilever beam; Establishing a transition region based on the overall crack region and the crack tip region; constructing a transition region basis function based on the transition region; Solving the transition region, the overall region, and the crack tip region based on the transition region basis function, the overall region basis function, and the crack tip region basis function to obtain a two-dimensional crack growth result; the overall region basis function is a finite element basis function obtained by discretizing linear quadrilateral or triangular elements; the crack tip region basis function is a B-spline basis function; the two-dimensional crack growth result includes: an overall displacement solution, a crack tip region displacement solution, and a transition region displacement solution; The expression of the transition region basis function is: ； ； ； in, is the B-spline basis function of the transition region in the two-dimensional parameter space; is the finite element basis function of the transition region in the two-dimensional parameter space; is the B-spline basis function of the crack tip region in the two-dimensional parameter space; Finite element basis functions for the overall solution region in two-dimensional parameter space; is the basic weight function; are the coordinates in the two-dimensional parameter space.

2. The numerical calculation method for simulating two-dimensional crack growth according to claim 1, characterized in that: The expression of the overall displacement solution is: ； in, is the overall displacement solution; is the finite element basis function of the entire region, is the number of finite element basis functions in the entire region; is the first variable to be determined.

3. The numerical calculation method for simulating two-dimensional crack growth according to claim 1, characterized in that: The expression of the overall displacement solution in two-dimensional space is: ； ； in, is the overall displacement solution in the x direction of two-dimensional space; is the overall displacement solution in the y direction of two-dimensional space; is the finite element basis function in two-dimensional space; is the first variable to be determined in the x direction of the two-dimensional space; is the first variable to be determined in the y direction of the two-dimensional space.

4. The numerical calculation method for simulating two-dimensional crack growth according to claim 1, characterized in that: The expression of the displacement solution in the crack tip area is: ； in, is the displacement solution in the crack tip area; is the B-spline basis function in the crack tip region, is the number of B-spline basis functions in the crack tip region; is the second variable to be determined.

5. The numerical calculation method for simulating two-dimensional crack growth according to claim 1, characterized in that: The expression of the crack tip regional displacement solution in the two-dimensional parameter space is: ； ； ； in, is the displacement solution of the crack tip region in the x-direction of the two-dimensional parameter space; is the displacement solution of the crack tip region in the y direction in the two-dimensional parameter space; is the B-spline basis function of the crack tip region in the two-dimensional parameter space; is the second variable to be determined in the x direction of the two-dimensional parameter space; is the second variable to be determined in the y direction of the two-dimensional parameter space; is the circumferential one-dimensional B-spline basis function; is the radial one-dimensional B-spline basis function; are the coordinates in the two-dimensional parameter space.

6. The numerical calculation method for simulating two-dimensional crack growth according to claim 1, characterized in that: The boundary curve of the transition region is expressed as: ； ； ； ； ； ； ； in, is the outer circular boundary curve of the transition area; is the circular boundary curve inside the transition area; The control points of the B-spline basis function corresponding to the outer circular boundary curve; are the control points of the B-spline basis function corresponding to the inner circular boundary curve; is the B-spline basis function; is the number of B-spline basis functions in the transition region; For control points Coordinates in two-dimensional space; For control points Coordinates in two-dimensional space; ( , ) are the physical coordinates of the control points of the circular boundary curve outside the transition area corresponding to the B-spline basis function; ( , ) are the physical coordinates of the control points of the circular boundary curve inside the transition region corresponding to the B-spline basis function.

7. The numerical calculation method for simulating two-dimensional crack growth according to claim 1, characterized in that: The expression of the transition region in the two-dimensional parameter space is: ； ； ； in,( , ) are the physical coordinates of the control points of the circular boundary curve outside the transition area corresponding to the B-spline basis function; ( , ) are the physical coordinates of the control points of the circular boundary curve inside the transition region corresponding to the B-spline basis function; is the coordinate in the two-dimensional parameter space; ( , ) is the representation of the transition region in two-dimensional parameter space.

8. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the numerical calculation method for simulating two-dimensional space crack propagation according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the numerical calculation method for simulating two-dimensional crack growth according to any one of claims 1 to 7 is implemented.

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