Point-surface contact modeling method and device based on near-field dynamic contact force

Abstract

The invention provides a point-surface contact modeling method and device based on near-field dynamic contact force, and the method comprises the steps: building a PD particle model based on a finite element mesh model of a target object; constructing a contact neighbor list of the particle set; generating a surface element contact list according to the contact neighbor list; identifying free surface particles, determining unit surfaces associated with the free surface particles, and obtaining a free surface and surface normal information; performing contact judgment on the target particles in the surface element contact list and the target element surface, and when contact is judged to occur, determining the penetration depth; according to the penetration depth and the surface normal information corresponding to the target unit surface, the contact force is calculated; and introducing the contact force into the near-field kinetic equation, updating the motion state of the particles, and returning to the step of constructing the dynamically updated contact neighbor list corresponding to the particle set until the preset calculation termination condition is met, so that the accuracy, stability and calculation efficiency of PD contact model modeling are improved.

Description

Technical Field

[0001] This invention relates to the fields of solid mechanics and numerical simulation technology, specifically to a point-to-surface contact modeling method and apparatus based on near-field dynamic contact forces. Background Technology

[0002] Peridynamics (PD) is a theory of nonlocal continuum mechanics based on spatial integrals, exhibiting unique advantages in studying the complex mechanical behavior of structures containing discontinuities or damage. In modern engineering applications, many key problems, such as structural impact, material extrusion, friction and wear, and re-contact of closed cracks, involve complex contact behaviors. These problems often exhibit triple nonlinearity in geometry, material constitutive properties, and boundary conditions. Given the extreme difficulty in experimentally capturing the dynamic deformation and failure processes within contact structures, high-precision numerical simulation has become a crucial means of solving contact problems.

[0003] However, for contact problems within the perifield dynamics framework, existing PD contact models are typically particle-to-particle direct contact models that do not rely on explicit surface identification. These models cannot accurately analyze and calculate normal contact forces, resulting in insufficient accuracy of the calculated contact forces when simulating complex collision problems. This reduces the accuracy, stability, and computational efficiency of perifield dynamics in simulating complex contact problems such as contact collisions and impact dynamics. Summary of the Invention

[0004] In view of this, it is necessary to provide a point-to-surface contact modeling method and apparatus based on peridynamic contact forces to solve the technical problems of low accuracy, stability and computational efficiency of existing peridynamic contact models.

[0005] To address the aforementioned technical problems, in a first aspect, the present invention provides a point-to-surface contact modeling method based on near-field dynamic contact forces, the method comprising: Based on the finite element mesh model of the target object, a corresponding particle model based on peri-field dynamics is established. The particle model includes a set of particles and a set of unit surfaces, as well as the point-to-surface mapping relationship between the unit surfaces and the particles. The set of unit surfaces includes multiple unit surfaces, and the set of particles includes multiple particles. Construct a dynamically updated contact nearest neighbor list corresponding to the particle set. The contact nearest neighbor list records the potential contact particles of each particle within a preset range and the contact relationship information of each potential contact particle. Based on the particle model and the contact nearest neighbor list, analyze the contact information between the unit surface and the particle, and generate a surface element contact list; Identify free surface particles located on the surface of the particle model, determine the unit surface associated with the free surface particles based on the point-to-surface mapping relationship, obtain the free surface, and determine the surface normal information of the free surface; Based on the surface normal information, contact determination is performed between the target particle and the target unit surface in the surface element contact list. When contact is determined, the penetration depth of the target particle into the target unit surface is determined. The target particle and the target unit surface are the free surface particle and the free surface in the surface element contact list corresponding to the surface normal information, respectively. Based on the penetration depth and the surface normal information corresponding to the target unit surface, the contact force acting on the target particle is calculated; The contact force is introduced into the near-field dynamics equation to update the motion state of the particle. Based on the updated particle, the process returns to the step of constructing a dynamically updated list of contact neighbors corresponding to the particle set, until a preset calculation termination condition is met.

[0006] In one possible implementation, the establishment of a corresponding particle model based on peri-field dynamics based on the finite element mesh model of the target object includes: Obtain the input file corresponding to the finite element mesh model. The input file includes element number, element-node topology, and node coordinates. Based on the node coordinates and the unit-node topology, each node is mapped to a particle based on near-field dynamics to obtain the particle set; Traverse the units corresponding to each unit number, identify the unit surfaces, and obtain the set of unit surfaces; The point-surface mapping relationship is constructed based on the particle set, the unit surface set, and the unit-node topological relationship.

[0007] In one possible implementation, identifying free surface particles located on the surface of the particle model includes: For each particle in the particle set, a renormalization matrix is ​​constructed based on the spatial distribution of near-field particles within a preset near-field range; Eigenvalue decomposition is performed on the renormalized matrix to obtain multiple eigenvalues ​​corresponding to the particle; If the smallest particle feature value is greater than a preset feature threshold, the particle corresponding to the particle feature value is determined to be a free surface particle.

[0008] In one possible implementation, determining the surface normal information of the free surface includes: For each free surface particle, calculate the corresponding unit normal vector; The surface normal information is determined based on the unit normal vector of each free surface particle in the free surface.

[0009] In one possible implementation, constructing the dynamically updated contact nearest neighbor list corresponding to the particle set includes: A spherical neighborhood with a radius of a first threshold is constructed with each particle as the center, and an update security layer with a thickness of a second threshold is added outside the spherical neighborhood; Based on the spherical neighborhood and the updated safety layer, an initial contact nearest neighbor list is generated for all particles. The cumulative displacement of each particle in the particle model at each time step is obtained. When the maximum cumulative displacement is greater than the second threshold, the contact nearest neighbor list is updated.

[0010] In one possible implementation, the step of analyzing the contact information between the unit surface and the particle based on the particle model and the contact nearest neighbor list, and generating a surface element contact list, includes: For each unit surface, obtain all vertex particles that constitute the unit surface; The union of the contact nearest neighbor lists of each vertex particle is used to obtain the candidate particle set corresponding to the unit face. Based on the candidate particle set and the point-to-surface mapping relationship, candidate surface-particle contact pairs corresponding to the unit surface are generated to obtain the surface-to-surface contact list.

[0011] In one possible implementation, the step of determining contact between target particles and target unit surfaces in the surface contact list based on the surface normal information, and determining the penetration depth of the target particle into the target unit surface when contact is determined, includes: Obtain the surface normal information of the target unit surface; Based on the surface normal information of the target unit surface, calculate the orthogonal projection point of the target particle onto the plane containing the target unit surface; Determine whether the orthogonal projection point is located within the boundary of the target unit surface; If the orthogonal projection point is located within the boundary, calculate the normal distance from the target particle to the plane containing the target unit surface; If the normal distance is less than the preset critical contact distance, then contact is determined to have occurred, and the normal distance is used as the penetration depth.

[0012] In one possible implementation, calculating the contact force acting on the target particle based on the penetration depth and the surface normal information corresponding to the target unit surface includes: Based on the penalty function method, the normal contact force between the target particle and the target unit surface is calculated according to the following formula:

[0013] in, The penetration depth is m, which is a nonlinear power exponent, and K is the penalty function stiffness coefficient, which is determined based on the material parameters of the target particle and the target unit surface. For each target particle, the normal contact forces corresponding to each target unit surface that comes into contact with the target particle are vector-accumulated to obtain the contact force.

[0014] In one possible implementation, the formula for calculating the penalty function stiffness coefficient K is:

[0015] in, It is the radius of the particle. and The contact stiffness control factor is related to the Poisson's ratio of the materials at both ends of the contact. and elastic modulus Related; among them, , ( l = i, j ).

[0016] Secondly, the present invention also provides a point-to-surface contact modeling device based on near-field dynamic contact force, the device comprising: A building unit is used to establish a corresponding particle model based on peri-field dynamics based on the finite element mesh model of the target object. The particle model includes a particle set and a set of unit surfaces, as well as the point-to-surface mapping relationship between the unit surfaces and the particles. The set of unit surfaces includes multiple unit surfaces, and the set of particles includes multiple particles. The update unit is used to construct a dynamically updated contact nearest neighbor list corresponding to the particle set. The contact nearest neighbor list records the potential contact particles of each particle within a preset range and the contact relationship information of each potential contact particle. An analysis unit is used to analyze the contact information between the unit surface and the particle based on the particle model and the contact nearest neighbor list, and generate a surface element contact list. The first determining unit is used to identify free surface particles located on the surface of the particle model, determine the unit surface associated with the free surface particles based on the point-to-surface mapping relationship, obtain the free surface, and determine the surface normal information of the free surface. The second determining unit is used to determine the contact between the target particle and the target unit surface in the surface element contact list based on the surface normal information. When contact is determined to occur, the unit determines the penetration depth of the target particle into the target unit surface. The target particle and the target unit surface are respectively the free surface particle and the free surface in the surface element contact list that correspond to the surface normal information. The calculation unit is used to calculate the contact force acting on the target particle based on the penetration depth and the surface normal information corresponding to the target unit surface; The loop calculation unit is used to introduce the contact force into the near-field dynamics equation, update the motion state of the particle, and based on the updated particle, return to the step of constructing the dynamically updated contact nearest neighbor list corresponding to the particle set, until the preset calculation termination condition is met.

[0017] The beneficial effects of this invention are: This invention provides a point-to-surface contact modeling method based on peri-field dynamics contact forces. It establishes a corresponding peri-field dynamics-based particle model using a finite element mesh model of the target object. The particle model includes a particle set and a set of element surfaces, as well as the point-to-surface mapping relationship between the element surfaces and particles. The set of element surfaces includes multiple element surfaces, and the particle set includes multiple particles. This achieves a precise conversion from a general finite element model to a PD particle computation model, introducing explicit geometric surface information into the PD model. This fundamentally overcomes the surface geometric ambiguity problem caused by pure particle representation in traditional PD methods, facilitating improved accuracy in subsequent point-to-surface contact determination. A dynamically updated contact nearest neighbor list corresponding to the particle set is constructed. This list records potential contact particles within a preset range for each particle and the contact relationship information of each potential contact particle. This reduces the global particle pair search, which was originally required at each time step, to a list query, optimizing the computational efficiency of subsequent contact search. Based on the particle model and the contact nearest neighbor list, the contact information between element surfaces and particles is analyzed to generate a surface element contact list, achieving efficient focusing of the contact search. Free surface particles located on the particle model surface are identified based on point... By mapping the surface relationship, the unit surface associated with the free surface particle is determined, thus obtaining the free surface and determining the surface normal information of the free surface. This enables accurate identification of free surface particles and calculation of surface normal information in the near-field dynamics discrete particle model, solving the problem of ambiguity in the contact force direction caused by the inability to determine the surface normal in traditional PD contact models, and effectively improving the physical accuracy of contact force calculation. Based on the surface normal information, contact determination is performed between the target particle and the target unit surface in the surface element contact list. When contact is determined, the penetration depth of the target particle into the target unit surface is determined. Here, the target particle and the target unit surface are the free surface particle and the free surface corresponding to the surface normal information in the surface element contact list, respectively. The contact determination is upgraded from a fuzzy criterion based on simple distance between particles to point-to-surface penetration geometry analysis, which greatly improves the accuracy and numerical stability of the simulation. Based on the penetration depth and the surface normal information corresponding to the target unit surface, the contact force acting on the target particle is calculated, so that the magnitude and direction of the calculated contact force have clear physical meaning, solving the problem of ambiguity in contact force calculation in traditional methods, and realizing the construction of a physically realistic and numerically stable contact force model.By incorporating contact forces into the peridynamic equations to update the particle's motion state, and then returning to the step of constructing a dynamically updated list of contact neighbors corresponding to the particle set, the calculation continues until a preset termination condition is met. This completes the point-to-surface contact modeling of the target object based on peridynamic contact forces, realizing the closure and evolution of the dynamic system. It integrates locally calculated contact forces into the nonlocal mechanics framework of PD (Problem-Solving Method), achieving a complete simulation capability from static geometry and contact detection to dynamic evolution. This enables the PD method to be reliably applied to complex transient dynamic analyses such as impacts and collisions, improving the accuracy, stability, and computational efficiency of peridynamics in simulating contact problems. It also enhances the accuracy, stability, and computational efficiency of point-to-surface contact modeling based on peridynamic contact forces, demonstrating significant engineering application value. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A schematic flowchart of an embodiment of the point-to-surface contact modeling method based on near-field dynamic contact force provided by the present invention; Figure 2 For the present invention Figure 1 A schematic diagram of an embodiment of S101; Figure 3 For the present invention Figure 1 A schematic diagram of an embodiment of S104; Figure 4 For the present invention Figure 1 A schematic diagram of an embodiment of S104; Figure 5 For the present invention Figure 1 A schematic diagram of an embodiment of S102; Figure 6 A schematic diagram illustrating the principle of constructing a contact nearest neighbor list based on the Verlet algorithm provided by this invention; Figure 7 For the present invention Figure 1 A schematic diagram of an embodiment of S103; Figure 8 For the present invention Figure 1 A schematic diagram of an embodiment of S105; Figure 9(a) is a three-dimensional contact diagram of the rigid indenter and the elastic half-space provided by the present invention, and Figure 9(b) is a two-dimensional contact diagram of the rigid indenter and the elastic half-space. Figure 10 A schematic diagram comparing the contact model provided by this invention with Hertz contact theory values; Figure 11 This is a schematic diagram of an embodiment of the point-to-surface contact modeling device based on near-field dynamic contact force provided by the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0021] In the description of the embodiments of the present invention, unless otherwise stated, "multiple" means two or more. "And / or" describes the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone.

[0022] The terms "first," "second," etc., used in the embodiments of this invention are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a technical feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature.

[0023] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0024] This invention provides a point-to-surface contact modeling method and apparatus based on near-field dynamic contact forces, which will be described below.

[0025] The execution entity of the point-to-surface contact modeling method based on near-field dynamic contact force in this application embodiment can be the point-to-surface contact modeling device based on near-field dynamic contact force provided in this application embodiment, or different types of electronic devices such as server equipment, physical host, or user equipment (UE) that integrate the point-to-surface contact modeling device based on near-field dynamic contact force. The point-to-surface contact modeling device based on near-field dynamic contact force can be implemented in hardware or software. The UE can specifically be a terminal device such as a smartphone, tablet computer, laptop computer, handheld computer, desktop computer, or personal digital assistant (PDA).

[0026] Figure 1 This is a schematic flowchart of an embodiment of the point-to-surface contact modeling method based on near-field dynamic contact force provided by the present invention. The point-to-surface contact modeling method based on near-field dynamic contact force includes: S101. Based on the finite element mesh model of the target object, establish a corresponding particle model based on near-field dynamics. The particle model includes a set of particles and a set of unit surfaces, as well as the point-to-surface mapping relationship between unit surfaces and particles. The set of unit surfaces includes multiple unit surfaces, and the set of particles includes multiple particles.

[0027] In this embodiment, the target object refers to a continuous solid structure or component that requires contact, collision, or impact dynamics simulation analysis and whose mechanical behavior may involve material damage and fracture.

[0028] In PD (Particle-Specific) models, particles refer to particles, while unit surfaces are auxiliary geometric entities inherited from the original finite element mesh model. These entities are used to accurately describe the geometric boundaries of the model, such as contact surfaces, providing a lacking, explicit, and high-precision surface geometric description for the pure particle peri-field dynamics model. Point-to-face mapping relationships refer to the geometric relationships between unit surfaces and their vertex particles.

[0029] Specifically, based on the finite element mesh model of the target object, a corresponding particle model based on near-field dynamics is established. The particle model includes a set of particles and a set of unit surfaces, as well as the point-to-surface mapping relationship between unit surfaces and particles. This achieves an accurate conversion from the general finite element model to the PD particle computation model, introduces clear geometric surface information into the PD model, and fundamentally overcomes the surface geometric ambiguity problem caused by pure particle representation in the traditional PD method, which facilitates the improvement of the accuracy of subsequent point-to-surface contact determination.

[0030] S102. Construct a dynamically updated contact nearest neighbor list corresponding to the particle set. The contact nearest neighbor list records the potential contact particles of each particle within a preset range and the contact relationship information of each potential contact particle.

[0031] Specifically, the Verlet list algorithm can be used to construct a dynamically updated list of contact nearest neighbors for the particle set. By constructing and reusing the contact nearest neighbor list, the global particle pair search that was originally required at each time step is reduced to a list query, thus optimizing the computational efficiency of subsequent contact searches.

[0032] S103. Based on the particle model and the contact nearest neighbor list, analyze the contact information between the unit surface and the particle, and generate a surface element contact list.

[0033] The surface contact list includes the set of candidate particles in the contact nearest neighbor list and the set of candidate unit surfaces that have a point-to-surface mapping relationship with the set of candidate particles.

[0034] Specifically, the contact information between particles and unit surfaces in the nearest neighbor list can be analyzed based on the particle set, the unit surface set, and the point-to-surface mapping relationship between unit surfaces and particles. The analysis process is as follows: For each unit surface in the unit surface set, obtain all its vertex particles. Take the union of the nearest neighbor lists of these vertex particles to obtain a candidate particle set. Any particle in this candidate particle set is adjacent to at least one vertex particle constituting the unit surface, and therefore may have contact with the unit surface. All pairs (unit surface, particles in the candidate particle set corresponding to the unit surface) are summarized to generate a surface contact list. By utilizing the nearest neighbor relationship between particles, all possible particle-surface combinations that may have contact are quickly and accurately screened, eliminating a large number of impossible combinations, such as internal particles far from the surface. This achieves efficient focusing of contact search, avoids redundant search calculations, and improves the efficiency of contact determination.

[0035] S104. Identify the free surface particles located on the surface of the particle model, determine the unit surface associated with the free surface particles based on the point-to-surface mapping relationship, obtain the free surface, and determine the surface normal information of the free surface.

[0036] In PD's particle model, a free surface particle refers to a particle located on the physical outer boundary of the target object, representing a potential location where the model comes into contact with external space (or another object). A free surface is a set of unit surfaces associated with free surface particles, which can be determined based on point-to-surface mapping relationships and free surface particles.

[0037] Surface normal information refers to the spatial vector information used to describe the orientation of each unit face on a free surface, such as the unit normal vector of a local surface.

[0038] Specifically, the Smooth Particle Hydrodynamics (SPH) method can be used to identify free surface particles located on the surface of the particle model. After identifying the free surface particles, the free surface can be determined, and then the surface normal information can be determined. This embodiment, based on the particle model, realizes the accurate identification of free surface particles and the calculation of surface normal information for a near-field dynamic discrete particle model, solving the problem of ambiguity in the direction of contact force caused by the inability to determine the surface normal in traditional PD contact models, and effectively improving the physical accuracy of contact force calculation.

[0039] S105. Based on the surface normal information, a contact determination is made between the target particle and the target unit surface in the surface element contact list. When a contact is determined, the penetration depth of the target particle into the target unit surface is determined. The target particle and the target unit surface are the free surface particle and the free surface in the surface element contact list that correspond to the surface normal information, respectively.

[0040] Here, target particles refer to free surface particles corresponding to the surface normal information in the list of surface elements that may come into contact and require contact determination. Target unit surfaces refer to free surfaces corresponding to the surface normal information in the list of surface elements that may come into contact and require contact determination.

[0041] Specifically, based on surface normal information, contact is determined between the target particle and the target unit surface. If contact is determined to have occurred, the penetration depth of the target particle into the target unit surface is calculated. This embodiment upgrades the contact determination from a fuzzy criterion based on simple distances between particles to point-to-surface penetration geometry analysis. This ensures that only particle-surface elements that actually undergo geometric interference are processed, and the depth of interference can be accurately quantified. This provides a reliable input for physics-based contact force calculations, greatly improving the accuracy and numerical stability of the simulation.

[0042] S106. Calculate the contact force acting on the target particle based on the penetration depth and the surface normal information corresponding to the target unit surface.

[0043] Specifically, based on the penetration depth and the surface normal information corresponding to the target unit surface, the contact force obtained by the particle penetrating the unit surface is calculated. Because it is based on the penetration depth and normal, the calculated contact force has clear physical meaning in both magnitude and direction, solving the problem of fuzzy contact force calculation in traditional methods. A physically realistic and numerically stable contact force model was constructed.

[0044] S107. Introduce the contact force into the near-field dynamics equation, update the motion state of the particle, and based on the updated particle, return to the step of constructing the dynamically updated contact nearest neighbor list corresponding to the particle set, until the preset calculation termination condition is met.

[0045] Here, motion state refers to particle displacement and velocity. Preset calculation termination conditions can be total simulation time, maximum number of steps, etc.

[0046] Specifically, the contact force is divided by the particle's mass density and added to the peridynamic equation (i.e., the integral equation) in the form of body force density. An explicit time integration algorithm, such as the velocity-Verlet algorithm, is used to solve this equation, updating the displacement and velocity of all particles. At the end of each time step, a preset calculation termination condition is checked. If not, the process returns to step S102, where the new particle position determines whether the nearest neighbor list needs updating, and the calculation loop for the next time step begins. This completes the point-to-surface contact modeling of the target object based on peridynamic contact forces, realizing the closure and evolution of the dynamic system. It integrates locally calculated contact forces into the nonlocal mechanics framework of PD, achieving a complete simulation capability from static geometry and contact detection to dynamic evolution. This allows the PD method to be reliably applied to complex transient dynamic analyses such as impacts and collisions, improving the accuracy, stability, and computational efficiency of peridynamics in simulating contact problems. This has significant engineering application value.

[0047] In summary, the point-to-surface contact modeling method based on peri-field dynamics contact force provided by this invention establishes a corresponding particle model based on peri-field dynamics through a finite element mesh model of the target object. The particle model includes a particle set and a set of unit surfaces, as well as the point-to-surface mapping relationship between unit surfaces and particles. The set of unit surfaces includes multiple unit surfaces, and the particle set includes multiple particles. This achieves a precise conversion from a general finite element model to a PD particle computation model, introducing explicit geometric surface information into the PD model. This fundamentally overcomes the surface geometric ambiguity problem caused by pure particle representation in traditional PD methods, facilitating improved accuracy in subsequent point-to-surface contact determination. A dynamically updated contact nearest neighbor list corresponding to the particle set is constructed. This list records potential contact particles within a preset range for each particle and the contact relationship information of each potential contact particle. This reduces the global particle pair search, which was originally required at each time step, to a list query, optimizing the computational efficiency of subsequent contact search. Based on the particle model and the contact nearest neighbor list, the contact information between unit surfaces and particles is analyzed to generate a surface element contact list, achieving efficient focusing of the contact search. Free surface particles located on the particle model surface are identified. Based on the point-to-surface mapping relationship, the unit surface associated with the free surface particle is determined, thus obtaining the free surface. The surface normal information of the free surface is also determined, enabling accurate identification of free surface particles and calculation of surface normal information in a near-field dynamics discrete particle model. This solves the problem of ambiguity in the contact force direction caused by the inability to determine the surface normal in traditional PD contact models, effectively improving the physical accuracy of contact force calculation. Based on the surface normal information, contact determination is performed between the target particle and the target unit surface in the surface element contact list. When contact is determined, the penetration depth of the target particle into the target unit surface is determined. Here, the target particle and the target unit surface are the free surface particle and the free surface corresponding to the surface normal information in the surface element contact list, respectively. This upgrades the contact determination from a fuzzy criterion based on simple distance between particles to point-to-surface penetration geometry analysis, greatly improving the accuracy and numerical stability of the simulation. Based on the penetration depth and the surface normal information corresponding to the target unit surface, the contact force acting on the target particle is calculated, making the magnitude and direction of the calculated contact force have clear physical meaning. This solves the problem of ambiguity in contact force calculation in traditional methods, realizing the construction of a physically realistic and numerically stable contact force model.By incorporating contact forces into the peridynamic equations to update the particle's motion state, and then returning to the step of constructing a dynamically updated list of contact neighbors corresponding to the particle set, the calculation continues until a preset termination condition is met. This completes the point-to-surface contact modeling of the target object based on peridynamic contact forces, realizing the closure and evolution of the dynamic system. It integrates locally calculated contact forces into the nonlocal mechanics framework of PD (Problem-Solving Method), achieving a complete simulation capability from static geometry and contact detection to dynamic evolution. This enables the PD method to be reliably applied to complex transient dynamic analyses such as impacts and collisions, improving the accuracy, stability, and computational efficiency of peridynamics in simulating contact problems. It also enhances the accuracy, stability, and computational efficiency of point-to-surface contact modeling based on peridynamic contact forces, demonstrating significant engineering application value.

[0048] In some embodiments of the present invention, such as Figure 2 As shown, step S101 includes: S201. Obtain the input file corresponding to the finite element mesh model. The input file includes element number, element-node topology relationship, and node coordinates. S202. Based on the node coordinates and the unit-node topology, each node is mapped to a particle based on near-field dynamics to obtain the particle set; S203. Traverse the units corresponding to each unit number, identify the unit surfaces, and obtain the set of unit surfaces; S204. Construct the point-surface mapping relationship based on the particle set, the unit surface set, and the unit-node topological relationship.

[0049] In this embodiment, the element surface can be a quadrilateral element. The element number corresponds to the mesh information of the finite element mesh model.

[0050] Specifically, the input file generated after modeling and meshing in the target object finite element (FE) software can be read, the element and node information of the finite element mesh model can be extracted, the nodes can be mapped to particles of peridynamics, and the element number, node-element topological relationship, node coordinates, material number and material property parameters can be obtained. Based on the mesh information, the geometric position and topological relationship of all element surfaces can be identified and stored, an element surface set can be constructed, and the PD particle set associated with each element surface can be recorded. At the same time, the mapping relationship between surface elements and corresponding peridynamic (PD) particles can be established, generating an enhanced PD model that simultaneously contains material points (particles), geometric surfaces (element surfaces), and a clear relationship between the two (point-surface mapping relationship). This solves the problems of surface missing, geometric roughness, and unclear association in traditional PD contact simulation.

[0051] In one specific implementation, the model file (.inp, .cae, etc.) exported from finite element software (such as ABAQUS, ANSYS) is read, and the node coordinates, element topology (e.g., the connection relationship of the eight nodes of a hexahedral element), and material properties in the file are parsed. Each finite element node is directly mapped to a near-field dynamic particle, which inherits the node's spatial coordinates, volume (calculated based on associated elements), and material properties (e.g., elastic modulus, Poisson's ratio, density). Simultaneously, all elements are traversed, and the number of times each element face is shared is calculated (a face shared by two elements is an internal face, and a face shared by only one element is an external surface). All unshared element faces, such as quadrilaterals, are extracted to form an element face set. Each element face records the indices of all its vertices in the particle set, thus establishing a point-face mapping relationship between element faces and vertex particles.

[0052] In some embodiments of the present invention, such as Figure 3 As shown, step S104 includes: S301. For each particle in the particle set, a renormalization matrix is ​​constructed based on the spatial distribution of near-field particles within a preset near-field range. S302. Perform eigenvalue decomposition on the renormalized matrix to obtain multiple eigenvalues ​​corresponding to the particle; S303. If the smallest particle feature value is greater than a preset feature threshold, the particle corresponding to the particle feature value is determined to be a free surface particle.

[0053] Specifically, for each particle, a renormalization matrix is ​​constructed based on the spatial distribution of particles within its preset near-field range, and eigenvalue decomposition is performed to obtain multiple eigenvalues ​​corresponding to the particle. If the smallest particle eigenvalue is greater than a preset eigenvalue threshold, the particle is determined to be a free surface particle, thus achieving accurate identification of free surface particles and improving the accuracy of free surface identification.

[0054] In one specific implementation, drawing on the SPH eigenvalue method, a renormalization matrix is ​​constructed. Perform eigenvalue decomposition on the particle neighborhood spatial distribution tensor, and the particle renormalization matrix Due to its near-field range Particles inside With particles relative position vector and normalized kernel function Its composition, its expression is:

[0055] After calculating the matrix, eigenvalue decomposition is performed on it. When the smallest particle eigenvalue exceeds a preset eigenvalue threshold, the particle is... Determined to be surface particles, among which, For the initial configuration, It is a displacement vector. For particles The volume.

[0056] In some embodiments of the present invention, such as Figure 4 As shown, step S104 includes: S401. For each free surface particle, calculate the corresponding unit normal vector; S402. Determine the surface normal information based on the unit normal vector of each free surface particle in the free surface.

[0057] Specifically, for a free surface particle, the approximate normal direction of its local surface is obtained by calculating the product of the renormalization matrix and the weighted sum of the kernel function gradient, and then normalized to a unit vector. Then, according to the point-to-surface mapping relationship, the normals of the multiple vertex particles constituting each unit surface are weighted and averaged to obtain the surface normal vector of that unit surface, which is the surface normal information.

[0058] In one specific implementation, surface normal information is calculated. The expression is:

[0059] in, v It is an unnormalized normal vector.

[0060] In some embodiments of the present invention, such as Figure 5 As shown, step S102 includes: S501. Construct a spherical neighborhood with a radius of a first threshold, centered on each particle, and add an update security layer with a thickness of a second threshold outside the spherical neighborhood. S502. Based on the spherical neighborhood and the updated safety layer, generate an initial contact nearest neighbor list for all particles, obtain the cumulative displacement of each particle in the particle model at each time step, and update the contact nearest neighbor list when the maximum cumulative displacement is greater than the second threshold.

[0061] Specifically, a search range is defined for each particle, which is defined by a truncated sphere (radius). (equal to the near-field radius of the PD) and a safety layer surrounding it (thickness) The system is constructed using a near-neighbor list (e.g., 0.3 times the near-field radius). During initialization, a global search is performed to record the indices and relative position vectors of all other particles within the truncated sphere + safety layer for each particle, forming an initial nearest-neighbor list. During the simulation, the maximum cumulative displacement of the particles is monitored. A global list update is triggered only when this displacement exceeds the safety layer thickness δ_l; otherwise, the current list is used. By constructing and reusing the nearest-neighbor list, the computational efficiency of the contact search is greatly optimized, and the frequency of list reconstruction is minimized using the safety layer mechanism.

[0062] In one specific implementation, such as Figure 6 The diagram illustrates the principle of constructing a contact nearest neighbor list based on the Verlet algorithm. Specifically, the Verlet method is used to generate a contact nearest neighbor list for all particles. A Verlet list is constructed for the PD particle discrete model, searching for all particles that may make contact. During construction, the current particle... Centered on, the construction radius is The truncated sphere, and an outer radius of is added around it. The skin area. Skin thickness. The initial Verlet list was generated by performing a pairwise search through nested loops of all particles in the system, and each Rebuild once per time step. The value satisfies ,in For particle velocity, The time step is set to 1. This method allows for preliminary contact detection of the model and effectively avoids a full search of all particles at every step, significantly reducing the computational cost and complexity of nearest neighbor search and improving the overall efficiency of the computational solution process.

[0063] In some embodiments of the present invention, such as Figure 7 As shown, step S103 includes: S601. For each unit surface, obtain all vertex particles that constitute the unit surface; S602. Take the union of the nearest neighbor lists of each vertex particle to obtain the candidate particle set corresponding to the unit surface. S603. Based on the candidate particle set and the point-surface mapping relationship, generate the surface element-particle contact candidate pairs corresponding to the unit surface to obtain the surface element contact list.

[0064] Specifically, for each unit face in the unit face set (e.g., a quadrilateral face composed of particles P1, P2, P3, and P4), by querying the point-face mapping relationship, all its constituent vertex particles, i.e., particles P1, P2, P3, and P4, are obtained. The contact nearest neighbor list of each vertex particle (P1, P2, P3, P4) constructed and maintained in step S102 is read sequentially. All particle identifiers (IDs) in these four lists are merged into a set, and duplicate particle IDs are removed, i.e., the union is taken. The final candidate particle set contains all particles that are at least adjacent to one vertex particle constituting the unit face. For example, particle Q may only appear in the nearest neighbor list of P1, but not in the lists of P2, P3, and P4, but it is still included in the candidate set. Based on the candidate particle set, for each candidate particle in the set (e.g., particle Q), it is combined with the currently processed unit face (e.g., face F) to form a particle-unit face (i.e., (Q, F)). By traversing all unit surfaces and their corresponding candidate particle sets, all generated (particle, unit surface) pairs are paired and summarized into a global surface contact list, which serves as the precise input for subsequent contact determination. This clearly lists all potential contact pairs that need to be examined by detailed geometric interference.

[0065] In one specific implementation, a surface-based contact list, or surface element contact list, is constructed based on the information of free surface particles and a contact nearest neighbor list, which can be represented as:

[0066] Among them, the contact nearest neighbor list of face A The contact can be represented by the union of the contact nearest neighbor lists of the nodes that make up surface A. Then, the particles in the contact list of the surface element are traversed to determine the spatial geometric relationship between the particle and the element surface in order to calculate the detailed contact.

[0067] In some embodiments of the present invention, such as Figure 8 As shown, step S105 includes: S701. Obtain the surface normal information of the target unit surface; S702. Based on the surface normal information of the target unit surface, calculate the orthogonal projection point of the target particle onto the plane where the target unit surface is located; S703. Determine whether the orthogonal projection point is located within the boundary of the target unit surface; S704. If the orthogonal projection point is located within the boundary, calculate the normal distance from the target particle to the plane containing the target unit surface; S705. If the normal distance is less than the preset critical contact distance, then contact is determined to have occurred, and the normal distance is used as the penetration depth.

[0068] Specifically, for each pair of combinations in the element contact list, the element surface normal... n and one of its vertex positions x 0, Calculate candidate particles x p Directed distance to the plane containing the element face d = (x p - x 0 )·n and the coordinates of the projection point x proj = x p - d · n By using the shape function method, that is, transforming the coordinates of the projected points to the parametric coordinate system of the element surface, we can determine... x proj Is it located inside the element surface boundary? If the projection point is inside, and 0 < |d| < δ critical ( δ critical If the preset critical contact distance is used, then contact is determined to have occurred, and |d| is used as the penetration depth. δ p .

[0069] In some embodiments of the present invention, step S106 includes: calculating the normal contact force between the target particle and the target unit surface based on the penalty function method according to the following formula:

[0070] in, The penetration depth is m, the nonlinear power exponent is K, and the penalty function stiffness coefficient is determined based on the material parameters of the target particle and the target unit surface. For each target particle, the normal contact forces corresponding to each target unit surface that comes into contact with the target particle are vector-accumulated to obtain the contact force.

[0071] Specifically, for each particle-plane pair determined to be in contact, the normal contact force is calculated using the penalty function method. The magnitude of the force has a non-linear relationship with the penetration depth, for example... The penalty function stiffness coefficient K is determined based on the material parameters of both contacting elements (such as elastic modulus and Poisson's ratio) and the particle radius, for example, using the derivation form of Hertz contact theory. The direction of the force is consistent with the normal n of the element surface (or opposite, depending on the notation convention, usually the direction that pushes the particle away from the surface). Finally, for the same particle, the vector summation of its normal contact force with the normal contact forces calculated from all contact surface elements yields the total normal contact force acting on that particle, i.e., the contact force.

[0072] Understandably, in this embodiment, by combining the penalty function method with precise penetration depth and normal, the magnitude and direction of the contact force have clear physical meaning, i.e., simulating elastic restoring force, thus solving the problem of fuzzy contact force calculation in traditional methods. The nonlinear characteristics of the force help improve numerical stability and prevent excessive force from being generated during deep penetration. Vector accumulation ensures the correctness of force composition for particles in complex contact scenarios.

[0073] In some embodiments of the present invention, the formula for calculating the penalty function stiffness coefficient K is as follows:

[0074] in, It is the radius of the particle. and The contact stiffness control factor is related to the Poisson's ratio of the materials at both ends of the contact. and elastic modulus Related; among them, , ( l = i, j ).

[0075] In one specific embodiment, as shown in Figure 9(a), a three-dimensional contact diagram of a rigid indenter and an elastic half-space is presented. The upper part is the rigid indenter (Rigid), and the lower part is the three-dimensional elastic half-space (Elastic). It should be noted that the arrows in the diagram represent the load direction, and the mesh represents a discretized particle model. Figure 9(b) shows a two-dimensional contact diagram of a rigid indenter and an elastic half-space; a numerical example demonstrates the performance of the improved point-to-surface contact model method in this application. Specifically, it simulates the contact between a rigid indenter and an elastic half-space, i.e., the contact problem between a rigid indenter and an elastic half-space under quasi-static loading. As shown in Figure 9(a), this is a contact problem between a rigid indenter and an elastic half-space with a density of... The size is The rigid indenter, under external force Under the influence of [something], it comes into contact with an elastic half-space, the density of which is [something]. The elastic modulus is 1 GPa and the Poisson's ratio is 0.25. During loading, when the indenter interacts with the elastic half-space and causes deformation, the two-dimensional deformation diagram is shown in Figure 9(b), where the contact force and the external load P reach equilibrium. Under this equilibrium state, the normal contact stress can be obtained through Hertz contact theory, and its formula is:

[0076] Where a is the half-bandwidth of the contact.

[0077] In another specific implementation, such as Figure 10The figure shows a comparison between the contact model and Hertz contact theory values, specifically the comparison between the simulated contact force obtained after reaching equilibrium and the results calculated using Hertz contact theory. As can be seen from the figure, the results of the improved point-to-surface contact model in this embodiment are in high agreement with the Hertz contact theory values, verifying the effectiveness and accuracy of the contact model in this embodiment.

[0078] To better implement the point-to-surface contact modeling method based on near-field dynamic contact force in the embodiments of the present invention, based on the point-to-surface contact modeling method based on near-field dynamic contact force, correspondingly, as follows: Figure 11 As shown, this embodiment of the invention also provides a point-to-surface contact modeling device based on near-field dynamic contact force. The point-to-surface contact modeling device 1100 based on near-field dynamic contact force includes: The construction unit 1101 is used to establish a corresponding particle model based on the finite element mesh model of the target object. The particle model includes a particle set and a set of element surfaces, as well as the point-to-surface mapping relationship between the element surfaces and the particles. The set of element surfaces includes multiple element surfaces, and the set of particles includes multiple particles. The update unit 1102 is used to construct a dynamically updated contact nearest neighbor list corresponding to the particle set. The contact nearest neighbor list records the potential contact particles of each particle within a preset range and the contact relationship information of each potential contact particle. Analysis unit 1103 is used to analyze the contact information between the unit surface and the particle based on the particle model and the contact nearest neighbor list, and generate a surface element contact list. The first determining unit 1104 is used to identify free surface particles located on the surface of the particle model, determine the unit surface associated with the free surface particles based on the point-to-surface mapping relationship, obtain the free surface, and determine the surface normal information of the free surface. The second determining unit 1105 is used to determine the contact between the target particle and the target unit surface in the surface element contact list based on the surface normal information. When contact is determined to occur, the penetration depth of the target particle into the target unit surface is determined. The target particle and the target unit surface are respectively the free surface particle and the free surface in the surface element contact list corresponding to the surface normal information. The calculation unit 1106 is used to calculate the contact force acting on the target particle based on the penetration depth and the surface normal information corresponding to the target unit surface; The loop calculation unit 1107 is used to introduce the contact force into the near-field dynamics equation, update the motion state of the particle, and based on the updated particle, return to the step of constructing the dynamically updated contact nearest neighbor list corresponding to the particle set, until the preset calculation termination condition is met.

[0079] The point-to-surface contact modeling device 800 based on near-field dynamic contact force provided in the above embodiments can realize the technical solutions described in the above embodiments of the point-to-surface contact modeling method based on near-field dynamic contact force. The specific implementation principles of each module or unit can be found in the corresponding content in the above embodiments of the point-to-surface contact modeling method based on near-field dynamic contact force, and will not be repeated here.

[0080] The point-to-surface contact modeling method and apparatus based on near-field dynamic contact force provided by the present invention have been described in detail above. Specific examples have been used to illustrate the principle and implementation of the present invention. The description of the above embodiments is only for the purpose of helping to understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A point-to-surface contact modeling method based on near-field dynamic contact forces, characterized in that, The method includes: Based on the finite element mesh model of the target object, a corresponding particle model based on peri-field dynamics is established. The particle model includes a set of particles and a set of unit surfaces, as well as the point-to-surface mapping relationship between the unit surfaces and the particles. The set of unit surfaces includes multiple unit surfaces, and the set of particles includes multiple particles. Construct a dynamically updated contact nearest neighbor list corresponding to the particle set. The contact nearest neighbor list records the potential contact particles of each particle within a preset range and the contact relationship information of each potential contact particle. Based on the particle model and the contact nearest neighbor list, analyze the contact information between the unit surface and the particle, and generate a surface element contact list; Identify free surface particles located on the surface of the particle model, determine the unit surface associated with the free surface particles based on the point-to-surface mapping relationship, obtain the free surface, and determine the surface normal information of the free surface; Based on the surface normal information, contact determination is performed between the target particle and the target unit surface in the surface element contact list. When contact is determined, the penetration depth of the target particle into the target unit surface is determined. The target particle and the target unit surface are the free surface particle and the free surface in the surface element contact list corresponding to the surface normal information, respectively. Based on the penetration depth and the surface normal information corresponding to the target unit surface, the contact force acting on the target particle is calculated; The contact force is introduced into the near-field dynamics equation to update the motion state of the particle. Based on the updated particle, the process returns to the step of constructing a dynamically updated list of contact neighbors corresponding to the particle set, until a preset calculation termination condition is met.

2. The point-to-surface contact modeling method based on near-field dynamic contact force according to claim 1, characterized in that, The finite element mesh model based on the target object is used to establish a corresponding particle model based on peri-field dynamics, including: Obtain the input file corresponding to the finite element mesh model. The input file includes element number, element-node topology, and node coordinates. Based on the node coordinates and the unit-node topology, each node is mapped to a particle based on near-field dynamics to obtain the particle set; Traverse the units corresponding to each unit number, identify the unit surfaces, and obtain the set of unit surfaces; The point-surface mapping relationship is constructed based on the particle set, the unit surface set, and the unit-node topological relationship.

3. The point-to-surface contact modeling method based on near-field dynamic contact force according to claim 1, characterized in that, The identification of free surface particles located on the surface of the particle model includes: For each particle in the particle set, a renormalization matrix is ​​constructed based on the spatial distribution of near-field particles within a preset near-field range; Eigenvalue decomposition is performed on the renormalized matrix to obtain multiple eigenvalues ​​corresponding to the particle; If the smallest particle feature value is greater than a preset feature threshold, the particle corresponding to the particle feature value is determined to be a free surface particle.

4. The point-to-surface contact modeling method based on near-field dynamic contact force according to claim 1, characterized in that, Determining the surface normal information of the free surface includes: For each free surface particle, calculate the corresponding unit normal vector; The surface normal information is determined based on the unit normal vector of each free surface particle in the free surface.

5. The point-to-surface contact modeling method based on near-field dynamic contact force according to claim 1, characterized in that, The construction of the dynamically updated contact nearest neighbor list corresponding to the particle set includes: A spherical neighborhood with a radius of a first threshold is constructed with each particle as the center, and an update security layer with a thickness of a second threshold is added outside the spherical neighborhood; Based on the spherical neighborhood and the updated safety layer, an initial contact nearest neighbor list is generated for all particles. The cumulative displacement of each particle in the particle model at each time step is obtained. When the maximum cumulative displacement is greater than the second threshold, the contact nearest neighbor list is updated.

6. The point-to-surface contact modeling method based on near-field dynamic contact force according to claim 1, characterized in that, The step of analyzing the contact information between the unit surface and the particles based on the particle model and the contact nearest neighbor list, and generating a surface element contact list, includes: For each unit surface, obtain all vertex particles that constitute the unit surface; The union of the contact nearest neighbor lists of each vertex particle is used to obtain the candidate particle set corresponding to the unit face. Based on the candidate particle set and the point-to-surface mapping relationship, candidate surface-particle contact pairs corresponding to the unit surface are generated to obtain the surface-to-surface contact list.

7. The point-to-surface contact modeling method based on near-field dynamic contact force according to claim 1, characterized in that, The step of determining contact between target particles and target unit surfaces in the surface contact list based on the surface normal information, and determining the penetration depth of the target particle into the target unit surface when contact is determined, includes: Obtain the surface normal information of the target unit surface; Based on the surface normal information of the target unit surface, calculate the orthogonal projection point of the target particle onto the plane containing the target unit surface; Determine whether the orthogonal projection point is located within the boundary of the target unit surface; If the orthogonal projection point is located within the boundary, calculate the normal distance from the target particle to the plane containing the target unit surface; If the normal distance is less than the preset critical contact distance, then contact is determined to have occurred, and the normal distance is used as the penetration depth.

8. The point-to-surface contact modeling method based on near-field dynamic contact force according to claim 1, characterized in that, The step of calculating the contact force acting on the target particle based on the penetration depth and the surface normal information corresponding to the target unit surface includes: Based on the penalty function method, the normal contact force between the target particle and the target unit surface is calculated according to the following formula: in The penetration depth is m, which is a nonlinear power exponent, and K is the penalty function stiffness coefficient, which is determined based on the material parameters of the target particle and the target unit surface. For each target particle, the normal contact forces corresponding to each target unit surface that comes into contact with the target particle are vector-accumulated to obtain the contact force.

9. The point-to-surface contact modeling method based on near-field dynamic contact force according to claim 8, characterized in that, The formula for calculating the penalty function stiffness coefficient K is as follows: in, It is the radius of the particle. and The contact stiffness control factor is related to the Poisson's ratio of the materials at both ends of the contact. and elastic modulus Related; among them, , ( l = i, j ).

10. A point-to-surface contact modeling device based on near-field dynamic contact force, characterized in that, The device includes: A building unit is used to establish a corresponding particle model based on peri-field dynamics based on the finite element mesh model of the target object. The particle model includes a particle set and a set of unit surfaces, as well as the point-to-surface mapping relationship between the unit surfaces and the particles. The set of unit surfaces includes multiple unit surfaces, and the set of particles includes multiple particles. The update unit is used to construct a dynamically updated contact nearest neighbor list corresponding to the particle set. The contact nearest neighbor list records the potential contact particles of each particle within a preset range and the contact relationship information of each potential contact particle. An analysis unit is used to analyze the contact information between the unit surface and the particle based on the particle model and the contact nearest neighbor list, and generate a surface element contact list. The first determining unit is used to identify free surface particles located on the surface of the particle model, determine the unit surface associated with the free surface particles based on the point-to-surface mapping relationship, obtain the free surface, and determine the surface normal information of the free surface. The second determining unit is used to determine the contact between the target particle and the target unit surface in the surface element contact list based on the surface normal information. When contact is determined to occur, the unit determines the penetration depth of the target particle into the target unit surface. The target particle and the target unit surface are respectively the free surface particle and the free surface in the surface element contact list that correspond to the surface normal information. The calculation unit is used to calculate the contact force acting on the target particle based on the penetration depth and the surface normal information corresponding to the target unit surface; The loop calculation unit is used to introduce the contact force into the near-field dynamics equation, update the motion state of the particle, and based on the updated particle, return to the step of constructing the dynamically updated contact nearest neighbor list corresponding to the particle set, until the preset calculation termination condition is met.

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