Multi-resolution PD-FEM structure fracture analysis method based on companion virtual particle coupling

Abstract

The invention discloses a multi-resolution PD-FEM structure fracture analysis method based on companion virtual particle coupling. The method comprises the steps that S1, a fracture simulation analysis model is established and initialized; s2, carrying out regional discretization on the fracture simulation analysis model by adopting an FEM grid and PD particles, and obtaining material parameters and initial field variable information of grid units and particles; s3, dividing a transition region in the FEM region, and obtaining partner virtual particles of each grid unit of the transition region and field variables and related parameter information of the partner virtual particles; s4, carrying out adjacent particle search, determining adjacent particles in a near field range of partner virtual particles and PD particles, and establishing a coupling'key 'relation between the two types of particles; s5, transmitting interface boundary information and calculating a coupling force through a coupling'key '; s6, after the coupling force is transmitted to PD particles and unit nodes, field variable information is updated based on PD and FEM motion equations; and S7, judging whether to return to the step S5 or stop calculation.

Description

Technical Field

[0001] The invention belongs to the field of engineering structure damage and fracture analysis, and specifically relates to a multi-resolution PD-FEM structural fracture analysis method based on companion virtual particle coupling. Background Art

[0002] Structural fracture analysis plays a vital role in civil engineering, hydraulic engineering, aerospace and other fields. When dealing with discontinuous problems, traditional continuum mechanics causes stress singularities at the crack tip due to the non-existence of displacement derivatives. Peridynamics (PD) uses nonlocal integral equations to successfully avoid this problem and can naturally simulate the initiation and propagation of cracks, so it has been widely used. However, as a nonlocal method, PD has inherent defects of large computational complexity and low computational efficiency.

[0003] In order to take into account both the accuracy and computational efficiency of crack simulation, combining PD with the finite element method (FEM) becomes an effective approach. There are two main types of current PD-FEM (peri-field dynamics-finite element) coupling schemes: shared node coupling scheme and interface unit coupling scheme. The shared node coupling scheme transmits interaction information through nodes or particles in the coupling area, which is suitable for different grid types, but requires the grid size in the coupling area to match the PD particle size, which limits its flexibility. The interface unit coupling scheme uses dynamic virtual PD particles in the unit to transmit interaction information, without the need for size matching requirements, but requires a large number of dynamic virtual particles to be arranged in the interface unit, which increases the computational complexity, and the applicable unit types are limited. In view of the shortcomings of the prior art, the present invention proposes a multi-resolution PD-FEM structural fracture analysis method based on companion virtual particle coupling. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention proposes a multi-resolution PD-FEM structural fracture analysis method based on companion virtual particle coupling. This method uses FEM discretization in the solid continuous region and PD discretization in the vulnerable region, taking into account both the solution of discontinuous problems and the computational efficiency. At the same time, by proposing a companion virtual particle coupling scheme, the problems of strict grid size requirements and complex virtual particle arrangement in the prior art are overcome, and the flexibility of the method is improved while ensuring accuracy and efficiency.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A multi-resolution PD-FEM structural fracture analysis method based on companion virtual particle coupling includes the following steps:

[0007] S1. Establish and initialize the fracture simulation analysis model in the field of engineering structure damage and fracture analysis;

[0008] S2, using FEM grid and PD particles to discretize the initialized fracture simulation analysis model into regions, and obtain the material parameters and initial field variable information of the grid unit and particles;

[0009] S3, dividing the transition region in the FEM region, obtaining the companion virtual particles and corresponding field variables and related parameter information of each grid unit in the transition region;

[0010] S4. Conduct neighboring particle search to determine the neighboring particles within the near field of the companion virtual particles and PD particles, and establish a coupling "bond" connection between the two types of particles;

[0011] S5. Transmit interface boundary information and calculate coupling force F through coupling "key" connection PD-FEM and F FEM-PD ;

[0012] S6, the coupling force F PD-FEM and F FEM-PD After being transmitted to the PD particles and unit nodes, the field variable information is updated based on the PD and FEM motion equations, and the PD damage field is calculated based on the field variables;

[0013] S7, determine whether the simulation time t reaches the total simulation time t max If not, return to S5 to perform the calculation of the next time step. If so, stop the calculation.

[0014] Preferably, before establishing the fracture simulation analysis model in the field of engineering structure damage and fracture analysis in S1, the steps include: determining the overall size of the calculation domain, the size of the PD region, the size of the FEM region and the total simulation time.

[0015] Preferably, in S1, the method of establishing and initializing a fracture simulation analysis model in the field of engineering structure damage and fracture analysis includes: setting boundary conditions, wherein the boundary conditions include force boundary conditions, displacement boundary conditions and contact boundary conditions in the FEM area and the PD area.

[0016] Preferably, in S2, the method of using FEM grids and PD particles to discretize the initialized fracture simulation analysis model by regions, and obtaining material parameters of grid units and particles and initial field variable information includes:

[0017] Determine the size of the FEM grid and the PD particles, and discretize the continuous FEM area and the damaged PD area and PD boundary in the fracture simulation analysis model into units, real PD particles and virtual PD particles respectively;

[0018] The units, the real PD particles and the virtual PD particles are assigned mass, density, elastic modulus, Poisson's ratio, displacement and velocity field variable values.

[0019] Preferably, in S3, the method of dividing the transition region in the FEM region and obtaining the companion virtual particles and corresponding field variables and related parameter information of each grid unit in the transition region includes:

[0020] The FEM area within a preset range from the PD-FEM interface is divided into a transition area, wherein the preset range is calculated by:

[0021] L PD-FEM =2.0×m PD l e

[0022] Among them, m PD is a non-local factor, l e is the unit characteristic length;

[0023] Each unit in the transition region is matched with a unique companion virtual particle located at the centroid to obtain a relationship between the unit and the companion virtual particle, wherein the relationship between the unit and the companion virtual particle is:

[0024]

[0025] Wherein, subscripts a and b represent the unit number and companion virtual particle number, respectively;

[0026] Based on the relationship between the unit and the companion virtual particle, the unit field variable information is assigned to the companion virtual particle, and the calculation method is:

[0027]

[0028] Among them, N I is the shape function of node I, X b and Pos I ini denote the position tensors of the companion virtual particles and nodes in the initial configuration, u b 、v b 、V b and ρ b They represent the displacement, velocity, volume and density of the companion virtual particle respectively.

[0029] Preferably, in S4, the method of conducting a neighboring particle search, determining neighboring particles within the near field of the companion virtual particles and the PD particles, and establishing a coupling "bond" connection between the two types of particles includes:

[0030] The near-field range of the companion virtual particle and the PD particle is determined by:

[0031]

[0032] Wherein, the subscript i represents the PD particle number, b represents the companion virtual particle number, and are the near field radii of the companion virtual particle b and PD particle i, dx PD is the PD particle size, ndim represents the spatial dimension;

[0033] The companion virtual particle b with the neighboring particle relationship is coupled with the PD particle i by a “bond” connection, which can be expressed as:

[0034] ξ′=X b -X i .

[0035] Among them, ξ′ represents the “coupling bond” composed of PD particle i and virtual particle b.

[0036] Preferably, in S5, the interface boundary information is transmitted and the coupling force F is calculated by coupling the "key" PD-FEM and F FEM-PD include:

[0037] Based on the velocity and displacement information of the companion virtual particle and the PD particle, the relative deformation of the coupling "key" is determined, and the calculation method is:

[0038] Y=ξ′+η

[0039] in, Y is the “key” deformation tensor, η is the relative displacement tensor;

[0040] The coupling force is calculated based on the relative deformation of the coupling "key" and the local external force compensation technology. The calculation method is:

[0041]

[0042] in, and denote the near field range of PD particle i and virtual particle b respectively, t i (Y) and t b (Y) represents the force scalar state of PD particle i and virtual particle b, M(Y) is the unit direction vector state of the “bond” after deformation, V i is the volume of PD particle i.

[0043] Preferably, in S6, the coupling force F PD-FEM and F FEM-PD After being transmitted to the PD particles and unit nodes, the field variable information is updated based on the PD and FEM motion equations. The method for calculating the PD damage field based on the field variables includes: PD-FEM and FFEM-PD Transform and solve the equation of motion according to the boundary conditions. The calculation method is:

[0044]

[0045] Among them, f(X i ,Y,t) represents the coupling force F FEM-PD The force density of the transformation, represents the coupling force F assigned to node I PD-FEM The component of force, ρ i represents the density of PD particle i, represents the acceleration of PD particle i, J represents the number of other nodes in the same unit as node I, represents the acceleration of node J, L u (X i ,t) represents the combined force density of PD particle i on other PD particles in the neighborhood, b(Xi,t) is the external force density acting on PD particle i, M IJ is the mass matrix of the FEM system, which is independent of time; is the external force at node I, is the internal force at node I.

[0046] Preferably, in S7, it is determined whether the simulation time t reaches the total simulation time t max If not, then return to S5 to perform the calculation of the next time step. If so, the method of stopping the calculation includes:

[0047] The explicit time integration scheme of the central difference format is used to solve the PD and FEM motion equations. The method for selecting a reasonable time step is:

[0048]

[0049] Among them, Δt PD-FEM , Δt PD and Δt FEM They represent the time step increments for PD-FEM coupling calculation, PD calculation and FEM calculation respectively, and the constant C CFL Must satisfy 0≤C CFL ≤1, δ is the near-field radius, E is the elastic modulus, v is the Poisson's ratio, ρ is the density, and c' represents the expansion wave velocity in the solid material.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] The present invention discretizes the solid structure in different regions based on the PD-FEM coupling method. In terms of the interface processing of PD-FEM, a companion virtual particle coupling scheme is proposed. The scheme presets a coupling transition region in the FEM region, and generates a unique companion virtual particle at the centroid position of the unit in the transition region, which greatly simplifies the complexity of the virtual particle arrangement. At the same time, the coupling scheme introduces the local external force compensation (LEFC) technology to calculate the coupling force between companion virtual particles and PD particles of different sizes, which not only overcomes the requirement of unit-particle size matching, but also ensures the momentum conservation of the system. The simulation results are compared with the results of a single method, and it is found that the results of the two are in good agreement, and the method of the present invention is less time-consuming. The present invention can quickly and effectively perform structural fracture analysis in engineering problems, and has the characteristics of high precision, high efficiency and high flexibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0053] Figure 1 It is a schematic flow chart of a multi-resolution PD-FEM structural fracture analysis method based on companion virtual particle coupling according to an embodiment of the present invention;

[0054] Figure 2 It is a schematic diagram of the geometric model and PD-FEM modeling of an embodiment of the present invention;

[0055] Figure 3 This is a schematic diagram of a companion virtual particle coupling scheme according to an embodiment of the present invention;

[0056] Figure 4 A schematic diagram of coupling force calculation according to an embodiment of the present invention;

[0057] Figure 5 Schematic diagram of crack opening displacement at t=16.7 μs when damage is not allowed in an embodiment of the present invention;

[0058] Figure 6 Schematic diagram of the change in crack length during crack propagation and the final damage condition when λ=5.0 according to an embodiment of the present invention. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0060] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0061] Embodiment 1

[0062] Figure 1 This is a flow chart of a multi-resolution PD-FEM structural fracture analysis method based on companion virtual particle coupling according to an embodiment of the present invention, which is described in detail below in conjunction with an example of rapid stretching of a cracked square plate.

[0063] The embodiment is mainly to evaluate the calculation accuracy and efficiency of the companion virtual particle PD-FEM multi-resolution coupling scheme. Before establishing the fracture simulation model in the field of engineering structure damage and fracture analysis in step 1, the overall size of the calculation domain, the PD area size, the FEM area size and the total simulation time are determined according to the problem to be solved. Plates are the most commonly used structures in ships and marine structures. Under the action of wave loads and internal loads, flat plates will produce small cracks. When encountering harsh environments, the cracks will expand rapidly and cause the structure to break, thus seriously threatening the safety of the hull structure. Figure 2 As shown in (a), the side length of the square plate is L = 50 mm, and the length of the horizontal initial crack in the center of the square plate is a = 10 mm. Figure 2 As shown in (b), the area with a height of H = 20 mm in the middle of the square plate is selected as the PD area, and the rest is the FEM area. During the simulation, the time step increment is set to Δt PD-FEM =1.3367×10 -8 s, and the total simulation time is 16.7 μs.

[0064] Step 1: Establish and initialize the engineering structure fracture simulation analysis model. Specifically, boundary conditions are set according to the requirements of the problem to be solved. The boundary conditions include force boundary conditions, displacement boundary conditions and contact boundary conditions in the FEM area and the PD area. Figure 2 As shown in (a), the upper and lower edges of the square plate are selected as the boundaries of the FEM region and are subjected to a velocity v y = 20m / s tensile load. PD-FEM modeling diagram is shown in Figure 2 (b).

[0065] Step 2, determine the FEM grid and PD particle size and material type, discretize the fracture simulation analysis model into regions based on the units and particles, and assign material parameters and initial field variable information to the units and particles. Specifically, determine the grid and particle size, discretize the continuous FEM area and the PD area where damage may occur and the PD boundary in the fracture simulation analysis model into units, solid PD particles and virtual PD particles respectively. Assign mass, density, elastic modulus, Poisson's ratio, displacement and velocity field variable values ​​to the units, solid PD particles and virtual PD particles. According to the problem to be solved, the PD particle size is fixed to dx PD =0.1mm, and the grid unit size dx FEM The PD and PD-FEM discretization schemes for this problem are listed in Table 1. The relevant material parameters include: density ρ s =8000kg / m 3 , elastic modulus E = 192 GPa, Poisson's ratio ν = 0.333.

[0066] Table 1 Layout of the tensile simulation of cracked square plate

[0067]

[0068] Step 3: Divide the transition region in the FEM region and obtain the companion virtual particles and their field variables and related parameter information of each grid unit in the transition region. Figure 3 Specifically, the FEM area within a preset range from the PD-FEM interface is divided into a transition area, wherein the preset range is calculated by:

[0069] L PD-FEM =2.0×m PD l e

[0070] Among them, m PD is a non-local factor, l e is the element characteristic length.

[0071] Each unit in the transition region is matched with a unique companion virtual particle located at its centroid, and the relationship between the unit and the companion virtual particle is:

[0072]

[0073] The subscripts a and b represent the unit number and the companion virtual particle number, respectively.

[0074] The unit field variable information is assigned to the companion virtual particle, and the calculation method is:

[0075]

[0076] Among them, N I is the shape function of node I, X b and Pos I ini denote the position tensors of the companion virtual particles and nodes in the initial configuration, u b 、v b 、V b and ρ b They represent the displacement, velocity, volume and density of the companion virtual particle respectively.

[0077] Step 4: Conduct a neighboring particle search to determine the neighboring particles within the near field of the companion virtual particles and the PD particles, and establish a coupling "bond" connection between the two types of particles. Figure 3 , specifically to determine the near field range of the companion virtual particles and PD particles (including real PD particles and virtual PD particles), the calculation method is:

[0078]

[0079] Wherein, the subscript i represents the PD particle number, b represents the companion virtual particle number, and are the near field radii of the companion virtual particle b and PD particle i, dx PD is the PD particle size, and ndim represents the spatial dimension.

[0080] The companion virtual particle b having a neighboring particle relationship is coupled with the PD particle i by a “bond” connection, which is expressed as:

[0081] ξ′=X b -X i .

[0082] Among them, ξ′ represents the “coupling bond” composed of PD particle i and virtual particle b.

[0083] Step 5: Transfer interface boundary information and calculate coupling force F through coupling "keys" PD-FEM and F FEM-PD .according to Figure 4 , based on the velocity and displacement information of the companion virtual particle and the PD particle, the relative deformation of the coupling “key” is determined by the calculation method:

[0084] Y=ξ′+η

[0085] Among them, Y is the "key" deformation tensor and η is the relative displacement tensor.

[0086] The coupling force is calculated based on the relative deformation of the coupling "key" and the local external force compensation (LEFC) technique, as follows:

[0087]

[0088] in, and denote the near field range of PD particle i and virtual particle b respectively, t i ( Y ) and t b (Y) represents the force scalar state of PD particle i and virtual particle b, M(Y) is the unit direction vector state of the “bond” after deformation, V i is the volume of PD particle i.

[0089] The interface velocity and displacement boundary conditions are indirectly applied to the PD particles through the relative deformation of the coupling "bond". The coupling force caused by the relative deformation of the coupling "bond" is calculated using the LEFC technology, which is applicable to the conditions where the companion virtual particle and the PD particle are neighboring particles of each other and only one particle is a neighboring particle of the other particle, ensuring the interaction symmetry and momentum conservation.

[0090] Step 6: After the coupling force is transmitted to the PD particles and unit nodes, the field variable information is updated based on the PD and FEM motion equations, and the PD damage field is calculated based on the field variables. Specifically, the coupling force F PD-FEM and F FEM-PD The transformation is performed and the motion equation is solved according to the boundary conditions. The calculation method is:

[0091]

[0092] Among them, f(X i ,Y,t) represents the coupling force F FEM-PD The force density of the transformation, represents the coupling force F assigned to node I PD-FEM The component of force, ρ i represents the density of PD particle i, represents the acceleration of PD particle i, J represents the number of other nodes in the same unit as node I, represents the acceleration of node J, L u (X i ,t) represents the combined force density of PD particle i on other PD particles in the neighborhood, b(Xi,t) is the external force density acting on PD particle i, M IJ is the mass matrix of the FEM system, which is independent of time; is the external force at node I, is the internal force at node I.

[0093] According to the statistics of the number of broken "bonds" on each PD particle, the concept of PD local damage is defined, and the calculation method is:

[0094]

[0095] Among them, D i Indicates local damage, V j is the volume of PD particle j, μ ij is a discontinuous function, which characterizes the breaking state of the “bond” between PD particles i and j. The calculation method is:

[0096]

[0097] Among them, s 0 is the critical elongation, which can be defined as Among them G 0 is the energy release rate, K is the bulk modulus, δ is the near field radius; s ij is the elongation of the “bond” between PD particles i and j, calculated as:

[0098]

[0099] Where ξ represents the relative position vector of PD particles i and j in the initial configuration; η is the relative displacement vector between PD particles i and j. Local damage D i The value range is 0≤D i ≤1. When the fracture damage of the "bond" accumulates into a surface, a macro crack is formed. i =0.38 is used as the crack formation criterion.

[0100] Step 7: Determine whether the simulation time t reaches the total simulation time t max If not, then return to step S5 to perform the calculation of the next time step. If yes, then stop the calculation. Specifically, both PD and FEM motion equations are solved using an explicit time integration scheme in a central difference format. The method for selecting a reasonable time step is:

[0101]

[0102] Among them, Δt PD-FEM , Δt PD and Δt FEM They represent the time step increments for PD-FEM coupling calculation, PD calculation and FEM calculation respectively, and the constant C CFL Must satisfy 0≤C CFL ≤1, δ is the near-field radius, E is the elastic modulus, v is the Poisson's ratio, ρ is the density, and c' represents the expansion wave velocity in the solid material.

[0103] Determine whether the simulation time t reaches the total simulation time t max =16.7μs;

[0104] If not reached, return to step S5 to perform calculation of the next time step;

[0105] Reached, end calculation.

[0106] This example simulation first obtains the crack opening displacement at t = 16.7 μs when damage is not allowed, such as Figure 5 As shown in the figure, the crack opening displacement curves obtained using the PD-FEM method are basically consistent with the results of the PD method alone, and these results are not affected by the mesh-particle size ratio. At the same time, unlike the elliptical crack opening displacement in classical continuum mechanics, the crack tip displacement obtained based on the PD method is sharp, showing the physical significance of the PD method in describing the crack opening shape. The crack opening shapes of PD-FEM and PD are consistent, indicating that the PD-FEM coupling method successfully inherits the advantages of the PD method. When damage is allowed to occur, the square plate exhibits crack extension under tensile load. Figure 6 (a) shows the crack length change process under different discrete schemes. The figure shows that with the application of velocity load, the opening displacement of the initial crack gradually increases, and the damage of the PD particles continues to accumulate. Using the local damage value of PD particles D = 0.38 as the cracking criterion, the crack initiation time of all discrete schemes is about 6.55μs. Subsequently, the crack continues to expand until t = 16.7μs to form the following Figure 6 (b) shows a typical mode I crack. The crack length variation curves obtained by the PD-FEM method under different unit-particle size ratios are basically consistent and are in good agreement with the results of the PD method alone. At the same time, according to the obtained curve, the crack growth rate is calculated to be about 1610m / s, which is lower than the upper limit of the mode I crack growth rate of 2800m / s (Rayleigh wave speed), indicating that the simulation results are reasonable.

[0107] To further evaluate the computational efficiency of the coupling method, the computational costs required by the PD calculation model and the PD-FEM calculation model for the rapid tensile problem of the square plate are given in Table 2. The results show that the computational efficiency of the PD model is low, and the full simulation time reaches 2207.25s. However, when the PD-FEM model is adopted and only the unit-particle size ratio is set to λ=1.0, the time required for the full simulation is reduced to 63.2% of the PD model; as the mesh-particle size ratio increases to λ=5.0, the number of meshes is further reduced (fixed PD particle size), and the computational time of the PD-FEM model is reduced to 37.4% of the PD model. These results show that the PD-FEM coupling method not only inherits the ability of the PD method to deal with discontinuous problems, but also gives full play to the advantages of FEM in computational efficiency.

[0108] Table 2 Total calculation time for simulation of cracked square plate

[0109]

[0110] The present invention can realize efficient simulation of structural fracture problems using a multi-resolution PD-FEM coupling method. In the multi-resolution PD-FEM coupling modeling and analysis of the rapid tensile problem of a cracked square plate, it was found that the PD-FEM coupling method based on the PGP scheme proposed in the present invention not only successfully simulated complex structural fracture problems, but also proved its ability to accurately capture structural fracture details without the need for precise grid-particle matching, and the simulation results were consistent. By comparing the calculation time of PD-FEM under different conditions with the calculation time of using PD alone, it was proved that the PD-FEM coupling method not only ensures the calculation accuracy, but also improves the calculation efficiency.

[0111] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A multi-resolution PD-FEM structural fracture analysis method based on companion virtual particle coupling, characterized in that: The following steps are involved: S1. Establish and initialize the fracture simulation analysis model in the field of engineering structure damage and fracture analysis; S2, using FEM grid and PD particles to discretize the initialized fracture simulation analysis model into regions, and obtain the material parameters and initial field variable information of the grid unit and particles; S3, dividing the transition region in the FEM region, obtaining the companion virtual particles and corresponding field variables and related parameter information of each grid unit in the transition region; S4. Conduct neighboring particle search to determine the neighboring particles within the near field of the companion virtual particles and PD particles, and establish a coupling "bond" connection between the two types of particles; S5. Transmit interface boundary information and calculate coupling force F through coupling "key" connection PD-FEM and F FEM-PD ; S6, the coupling force F PD-FEM and F FEM-PD After being transmitted to the PD particles and unit nodes, the field variable information is updated based on the PD and FEM motion equations, and the PD damage field is calculated based on the field variables; S7, determine whether the simulation time t reaches the total simulation time t max If not, return to S5 to perform the calculation of the next time step. If so, stop the calculation.

2. The multi-resolution PD-FEM structural fracture analysis method based on companion virtual particle coupling according to claim 1 is characterized in that: Before establishing the fracture simulation analysis model in the field of engineering structure damage and fracture analysis in S1, it includes: determining the overall size of the calculation domain, the PD area size, the FEM area size and the total simulation time.

3. The multi-resolution PD-FEM structural fracture analysis method based on companion virtual particle coupling according to claim 1 is characterized in that: In S1, the method of establishing and initializing a fracture simulation analysis model in the field of engineering structure damage and fracture analysis includes: setting boundary conditions, wherein the boundary conditions include force boundary conditions, displacement boundary conditions and contact boundary conditions in the FEM area and the PD area.

4. The multi-resolution PD-FEM structural fracture analysis method based on companion virtual particle coupling according to claim 3 is characterized in that: In S2, the method of using FEM grids and PD particles to discretize the initialized fracture simulation analysis model by regions and obtaining material parameters of grid units and particles and initial field variable information includes: Determine the size of the FEM grid and the PD particles, and discretize the continuous FEM area and the damaged PD area and PD boundary in the fracture simulation analysis model into units, real PD particles and virtual PD particles respectively; The units, the real PD particles and the virtual PD particles are assigned mass, density, elastic modulus, Poisson's ratio, displacement and velocity field variable values.

5. The multi-resolution PD-FEM structural fracture analysis method based on companion virtual particle coupling according to claim 1, characterized in that: In S3, the method of dividing the transition region in the FEM region and obtaining the companion virtual particles and corresponding field variables and related parameter information of each grid unit in the transition region includes: The FEM area within a preset range from the PD-FEM interface is divided into a transition area, wherein the preset range is calculated by: L PD-FEM =2.0×m PD L e Among them, m PD is a non-local factor, l e is the unit characteristic length; Each unit in the transition region is matched with a unique companion virtual particle located at the centroid to obtain a relationship between the unit and the companion virtual particle, wherein the relationship between the unit and the companion virtual particle is: Wherein, subscripts a and b represent the unit number and companion virtual particle number, respectively; Based on the relationship between the unit and the companion virtual particle, the unit field variable information is assigned to the companion virtual particle, and the calculation method is: Among them, N I is the shape function of node I, X b and denote the position tensors of the companion virtual particles and nodes in the initial configuration, u b 、v b 、V b and ρ b They represent the displacement, velocity, volume and density of the companion virtual particle respectively.

6. The multi-resolution PD-FEM structural fracture analysis method based on companion virtual particle coupling according to claim 5 is characterized in that: In S4, the method of conducting a neighboring particle search, determining neighboring particles within the near field of the companion virtual particles and the PD particles, and establishing a coupling "key" connection between the two types of particles includes: The near-field range of the companion virtual particle and the PD particle is determined by: Wherein, the subscript i represents the PD particle number, b represents the companion virtual particle number, and are the near field radii of the companion virtual particle b and PD particle i, dx PD is the PD particle size, ndim represents the spatial dimension; The companion virtual particle b with the neighboring particle relationship is coupled with the PD particle i by a "bond" connection, which is expressed as: ξ′=X b -X i 。 Among them, ξ′ represents the "coupling bond" composed of PD particle i and virtual particle b.

7. The multi-resolution PD-FEM structural fracture analysis method based on companion virtual particle coupling according to claim 6 is characterized in that: In S5, the interface boundary information is transmitted and the coupling force F is calculated through the coupling "key". PD-FEM and F FEM-PD include: Based on the velocity and displacement information of the companion virtual particle and the PD particle, the relative deformation of the coupling "key" is determined, and the calculation method is: Y=ξ′+η Among them, Y is the "key" deformation tensor, η is the relative displacement tensor; The coupling force is calculated based on the relative deformation of the coupling "key" and the local external force compensation technology. The calculation method is: in, and denote the near field range of PD particle i and virtual particle b respectively, t i (Y) and t b (Y) represents the force scalar state of PD particle i and virtual particle b, M ( Y ) is the unit direction vector state of the "key" after deformation, V i is the volume of PD particle i.

8. The multi-resolution PD-FEM structural fracture analysis method based on companion virtual particle coupling according to claim 7 is characterized in that: In S6, the coupling force F PD-FEM and F FEM-PD After being transmitted to the PD particles and unit nodes, the field variable information is updated based on the PD and FEM motion equations. The method for calculating the PD damage field based on the field variables includes: PD-FEM and F FEM-PD Transform and solve the equation of motion according to the boundary conditions. The calculation method is: Among them, f(X i ,Y,t) represents the coupling force F FEM-PD The force density of the transformation, represents the coupling force F assigned to node I PD-FEM The component of force, ρ i represents the density of PD particle i, represents the acceleration of PD particle i, J represents the number of other nodes in the same unit as node I, represents the acceleration of node J, L u (X i ,t) represents the combined force density of PD particle i on other PD particles in the neighborhood, b(Xi,t) is the external force density acting on PD particle i, M IJ is the mass matrix of the FEM system, which is independent of time; is the external force at node I, is the internal force at node I.

9. The multi-resolution PD-FEM structural fracture analysis method based on companion virtual particle coupling according to claim 1, characterized in that: In S7, it is determined whether the simulation time t reaches the total simulation time t max If not, then return to S5 to perform the calculation of the next time step. If so, the method of stopping the calculation includes: The explicit time integration scheme of the central difference format is used to solve the PD and FEM motion equations. The method for selecting a reasonable time step is: Among them, Δt PD-FEM , Δt PD and Δt FEM They represent the time step increments for PD-FEM coupling calculation, PD calculation and FEM calculation respectively, and the constant C CFL Must satisfy 0≤C CFL ≤1, δ is the near-field radius, E is the elastic modulus, v is the Poisson's ratio, ρ is the density, and c' represents the expansion wave velocity in the solid material.

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