Unit-based near-field dynamic contact modeling method

Abstract

The invention relates to the technical field of numerical modeling and material damage, and provides a unit-based near-field dynamic contact modeling method, which is characterized in that contact elements, surfaces and judgment criteria are finely defined, and contact force is calculated. According to the method, the problems of abnormal tangential force and unstable contact force are effectively solved by constructing a contact unit and introducing a distance influence function. The accuracy of the method is verified by comparing numerical simulation of impact, friction and rolling contact with methods such as finite element analysis. Researches prove that the method can reliably simulate the complex contact problem including material damage.

Description

Technical Field

[0001] The invention relates to the technical field of numerical modeling and material damage, and in particular to a unit-based peridynamic contact modeling method. Background Art

[0002] Contact damage is a common engineering problem that can lead to fracture and failure of engineering structures, such as rolling contact fatigue and impact fracture. The finite element method based on classical continuum mechanics is a common tool for contact modeling. However, classical continuum mechanics uses partial differential equations to describe mechanical problems, and faces the problem of failure of mathematical tools in discontinuous areas such as damage. Therefore, it is difficult for the finite element method to simulate contact problems involving material damage and fracture.

[0003] Nonlocal peridynamics is an emerging mechanical theory that uses integral equations instead of partial differential equations to describe mechanical problems. It does not have the problem of failure of mathematical tools at discontinuities such as material damage. Peridynamics directly characterizes material damage through bond breaking and can spontaneously simulate damage extension without the need for additional criteria. Therefore, peridynamic theory has great advantages in the study of damage problems.

[0004] Compared with the classical finite element analysis method, peridynamic contact modeling has not received much attention and is still an open research field. Existing peridynamic contact models at home and abroad generally have the following problems in application: abnormal tangential contact force, unstable contact force, and these models are usually only applicable to a single impact or sliding friction contact scenario. Therefore, it is urgent to develop a new peridynamic contact algorithm for studying contact problems involving material damage and fracture. Summary of the invention

[0005] The present invention provides a unit-based peridynamic contact modeling method for contact damage research, which overcomes the defects of the existing peridynamic contact modeling methods, such as false tangential force, unstable contact force and only applicable to a single contact scenario.

[0006] A unit-based peridynamic contact modeling method according to the present invention comprises the following steps:

[0007] S1. Set and initialize material, geometry, simulation and other parameters and variables;

[0008] S2, dividing the two objects involved in the contact into a slave object and a master object;

[0009] S3. Using the meshless method, the slave object and the master object are discretized into peridynamic particles, the particles that may participate in the contact interaction are defined as contact particles, the contact particles on the slave object and the master object are called slave particles and master particles, and the set R of slave particles and master particles is constructed.s and R m ;

[0010] S4, for each contact particle on the main object, that is, the main particle y i Building contact elements

[0011] S5, the main particle y i and from particle y j Total normal contact force and the total tangential contact force , The value of is initialized to 0;

[0012] S6. Visit all particles y in the collection j , and traverse each particle y from the object j ;

[0013] S7, by each particle y j Access all main particles y in the collection i , and traverse each main particle y in the main object i ;

[0014] S8. Determine the main particle y i Contact elements constructed The contact plane;

[0015] S9: Determine whether the contact condition is met. If it is met, continue the subsequent operation. Otherwise, terminate the particle y i and j Contact calculation between

[0016] S10, calculate the material normal overlap depth after contact occurs Contact stiffness And the distance influence function ω ij ;

[0017] S11, calculate the particle y j With the main particle y i Normal contact force

[0018] S12, calculate the particle y j With the main particle y i Normal contact force Add to Get y i ,y j The total normal contact force is:

[0019] S13, if y j and i First contact, record the current moment from particle yj With the main particle y i , for subsequent analysis; otherwise, recalculate and normal contact force And add it to the total normal contact force to update the contact status;

[0020] S14. Define the test tangential contact force;

[0021] S15. Calculate relative slip distance

[0022] S16. Define the tangential contact boundary according to the Coulomb friction criterion

[0023] S17, determining a tangential contact force according to a tangential contact boundary;

[0024] S18. Sum the tangential contact forces generated by all slave particles and the master particle and obtain the force acting on y j ,y i The total tangential contact force of

[0025] S19, applying the calculated total tangential contact force to the contact particles in the form of body force density, and updating the particle displacement by the numerical scheme of PD;

[0026] S20. If the termination condition is met, the calculation is terminated; otherwise, the process returns to S6.

[0027] Preferably, in S4, each contact unit includes the current contact particle and its two adjacent contact particles, that is, any contact particle y on the main object. i , contact element Defined as y i Its two adjacent contact particles y i1 and i2 A collection of:

[0028]

[0029] Based on the spatial position relationship, the contact particles on the main object are divided into three categories: non-boundary particles, boundary particles and particles adjacent to defects; for non-boundary particles, the adjacent particles of the contact unit are the two closest contact particles to it; for particles at the left and right boundaries, the adjacent particles of the contact unit are the two closest contact particles to it. b , its neighboring particle y in the main object b2 It is determined by searching for the nearest contact particle, but the neighboring particles outside the main object do not exist. Therefore, a virtual neighboring particle y is introduced. bv , whose position is determined by linear extrapolation of internal neighboring particles:

[0030] y bv =2y b -yb2

[0031] For the contact particle y near the defect d , is y d Introducing virtual neighboring particle y dv ,y dv The spatial position of is determined by linear extrapolation from another neighboring particle;

[0032] All contact particles should have at least one neighboring particle that does not require additional processing, that is, there is at least one neighboring particle with y i Distance Δx i adjacent particles to avoid the problem of not being able to find adjacent particles.

[0033] Preferably, in S8, the contact unit The two adjacent particles in are used to determine the contact surface direction, while the contact surface position is determined by three particles together;

[0034] First, the contact surface direction is defined by two adjacent particles, where the vector y i2 -y i1 The direction is the tangent direction of the contact surface, and the main particle y i Construct parallel to y i2 -y i1 The plane χ i , which is the contact unit Defined contact plane, adjacent particles y i1 and i2 In χ i Projection point and For plane χ i the boundaries of;

[0035] Contact surface unit tangent vector Written as:

[0036]

[0037] Determined by the following formula and Spatial location:

[0038] k = 1 or 2

[0039] Where k represents any adjacent particle;

[0040] χ i For contact elements The contact plane is defined as:

[0041]

[0042] definition is i The unit normal vector of Pointing outward from the contact surface, the unit normal vector and the unit tangent vector Vertical, that is, the following relationship:

[0043]

[0044] From particle y j In χ i The projection point is Its position is determined by the following formula:

[0045]

[0046] Preferably, in S9, from the contact particle y j In χ i The projection point is When the contact particle y j About contact surface χ i Projection point In χ i Projection distance When it is less than the critical value, the contact event is determined to have occurred:

[0047]

[0048] Δx i represents the interparticle distance of the primary particles, Δx j represents the interparticle distance from the particle; yes Located in i Projection distance of internal projection; Yes j and χ i The critical contact distance between .

[0049] Preferably, in S10, the material normal overlap depth Contact stiffness And the distance influence function ω ij The calculation formula is as follows:

[0050]

[0051] Where p si is the control coefficient of contact stiffness, K ij represents the bulk modulus, δ ij is the neighborhood radius, ΔV i and ΔV j is the bulk modulus of the material.

[0052] As a preference, in S11, the normal contact force The calculation formula is as follows:

[0053]

[0054] f cn (y i ,y j ) represents y j and i Normal contact force between .

[0055] Preferably, in S12, y i The total normal contact force is given by:

[0056]

[0057] f cn (y i ,t) represents the main particle y i The total normal force on ;

[0058] According to Newton's third law, from particle y j The contact force and y i The opposite direction is equal, so the expression is:

[0059]

[0060] is the contact force received by the particle, is the contact force on the main particle;

[0061] From particle y j With all the main particles y i Sum the reaction forces and get the force acting on y j The total normal contact force is:

[0062]

[0063] Where R m is the collection of main particles.

[0064] As a preferred embodiment, in S14, the test tangential contact force is as follows:

[0065]

[0066] is the test tangential contact force.

[0067] As a preferred embodiment, in S15, the relative sliding distance is the initial contact time t c The difference in the tangential distance between the two contacting particles at the current time t is expressed as follows:

[0068]

[0069] In S16, the tangential contact boundary The expression is as follows:

[0070]

[0071] μ represents the friction coefficient;

[0072] In S17, the tangential contact force expression is as follows:

[0073]

[0074] As a preferred embodiment, in S18, acting on y i The expression of the total tangential contact force is as follows:

[0075]

[0076] Similarly, Newton's third law acts on y j The total tangential contact force expression is as follows:

[0077]

[0078] The present invention provides a unit-based peridynamic contact modeling method for contact damage research, which can solve the defects of false tangential force, unstable contact force and only applicable to a single contact scenario in the existing peridynamic contact modeling method; the present invention is very suitable for contact damage problems and various contact scenario research. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 A flowchart of an element-based peridynamic contact modeling approach;

[0080] Figure 2 It is a schematic diagram of contact area discretization and contact unit;

[0081] Figure 3 Schematic diagram of the Kalthoff-Winkler experiment;

[0082] Figure 4(a) is a schematic diagram showing the comparison of contact forces over time calculated by the EBCM and EMU program methods;

[0083] Figure 4(b) is a schematic diagram showing the comparison of projectile velocity over time calculated by the EBCM and EMU program methods;

[0084] Figure 5 Schematic diagram of damage distribution at the termination time calculated by EBCM method and EMU program;

[0085] Figure 6Schematic diagram of the friction contact test between two flexible plates;

[0086] Figure 7(a) is a schematic diagram showing the comparison of contact stress distribution calculated by the PD model and the FE model;

[0087] Figure 7(b) is a schematic diagram showing the comparison of contact stress distribution calculated by the PD model and the FE model. DETAILED DESCRIPTION

[0088] In order to further understand the content of the present invention, the present invention is described in detail in conjunction with the accompanying drawings and embodiments. It should be understood that the embodiments are only for explaining the present invention and are not intended to limit it.

[0089] Example

[0090] like Figure 1 As shown, this embodiment provides a unit-based peridynamic contact modeling method (EBCM method), which includes the following steps:

[0091] S1. Set and initialize material, geometry, simulation and other parameters and variables.

[0092] S2. Divide the two objects involved in the contact into a slave object and a master object.

[0093] S3. Using the meshless method, the slave object and the master object are discretized into peridynamic particles, the particles that may participate in the contact interaction are defined as contact particles, the contact particles on the slave object and the master object are called slave particles and master particles, and the set R of slave particles and master particles is constructed. s and R m .

[0094] S4, for each contact particle on the main object, that is, the main particle y i Building contact elements

[0095] In S4, each contact unit includes the current contact particle and its two adjacent contact particles, that is, any contact particle y on the main object i , contact element Defined as y i Its two adjacent contact particles y i1 and i2 A collection of:

[0096]

[0097] Based on the spatial position relationship, the contact particles on the main object are divided into three categories: non-boundary particles, boundary particles and particles adjacent to defects; for non-boundary particles, the adjacent particles of the contact unit are the two closest contact particles to it; for particles at the left and right boundaries, the adjacent particles of the contact unit are the two closest contact particles to it. b, its neighboring particle y in the main object b2 It is determined by searching for the nearest contact particle, but the neighboring particles outside the main object do not exist. Therefore, a virtual neighboring particle y is introduced. bv , whose position is determined by linear extrapolation of internal neighboring particles:

[0098] y bv =2y b -y b2

[0099] For the contact particle y near the defect d , where the neighboring particle y on the left d1 On the other side of the defect, resulting in y d With y d1 There is a long distance between Figure 2 As shown, y d With y d1 The distance is 3Δx. The defect causes the contact surface to be discontinuous. If y is selected d If the particles on the left and right sides construct contact units, the contact surface will be forced to be continuous, which will also lead to inaccurate representation of the contact surface. d -y da ‖>1.5Δx d When da No longer selected as an adjacent particle. Similar to the particles at the boundary, d Introducing virtual neighboring particle y dv ,y dv The spatial position of is determined by linear extrapolation from another neighboring particle;

[0100] To ensure the accuracy and precision of contact calculation, all contact particles should have at least one neighboring particle that does not require additional processing, that is, there should be at least one particle that is connected to y i Distance Δx i adjacent particles to avoid the problem of not being able to find adjacent particles.

[0101] S5, the main particle y i and from particle y j Total normal contact force and the total tangential contact force , The value of is initialized to 0.

[0102] S6. Visit all particles y in the collection j , and traverse each particle y from the object j .

[0103] S7, by each particle y j Access all main particles y in the collection i, and traverse each main particle y in the main object i .

[0104] S8. Determine the main particle y i Contact elements constructed contact plane.

[0105] In S8, contact unit The two adjacent particles in are used to determine the contact surface direction, while the contact surface position is determined by three particles together;

[0106] First, the contact surface direction is defined by two adjacent particles, where the vector y i2 -y i1 The direction is the tangent direction of the contact surface, and the main particle y i Construct parallel to y i2 -y i1 The plane χ i , which is the contact unit Defined contact plane, adjacent particles y i1 and i2 In χ i Projection point and For plane χ i the boundaries of;

[0107] Contact surface unit tangent vector Written as:

[0108]

[0109] Determined by the following formula and Spatial location:

[0110] k = 1 or 2

[0111] Where k represents any adjacent particle;

[0112] χ i For contact elements The contact plane is defined as:

[0113]

[0114] definition is i The unit normal vector of Pointing outward from the contact surface, the unit normal vector and the unit tangent vector Vertical, that is, the following relationship:

[0115]

[0116] From particle y j In χ i The projection point is Its position is determined by the following formula:

[0117]

[0118] S9: Determine whether the contact condition is met. If it is met, continue the subsequent operation. Otherwise, terminate the particle y i and j Contact calculation between .

[0119] In S9, from the contact particle y j In χ i The projection point is When the contact particle y j About contact surface χ i Projection point In χ i Inside and projection distance When it is less than the critical value, the contact event is determined to have occurred:

[0120]

[0121] Δx i represents the interparticle distance of the primary particles, Δx j represents the interparticle distance from the particle; yes Located in i Projection distance of internal projection; Yes j and χ i The critical contact distance between .

[0122] S10, calculate the material normal overlap depth after contact occurs Contact stiffness And the distance influence function ω ij .

[0123] In S10, the material normal overlap depth Contact stiffness And the distance influence function ω ij The calculation formula is as follows:

[0124]

[0125] Where p si is the control coefficient of contact stiffness, K ij represents the bulk modulus, δ ij is the neighborhood radius, ΔV i and ΔV j is the bulk modulus of the material.

[0126] S11, calculate the particle y j With the main particle y i Normal contact force

[0127] In S11, the normal contact force The calculation formula is as follows:

[0128]

[0129] f cn (y i ,y j ) represents y j and i Normal contact force between .

[0130] S12, calculate the particle y j With the main particle y i Normal contact force Add to Get y i ,y j The total normal contact force.

[0131] In S12, y i The total normal contact force is given by:

[0132]

[0133] f cn (y i ,t) represents the main particle y i The total normal force on ;

[0134] According to Newton's third law, from particle y j The contact force and y i The magnitude and opposite direction are equal, so the expression is:

[0135]

[0136] is the contact force received by the particle, is the contact force on the main particle;

[0137] From particle y j With all the main particles y i The sum of the reaction forces on y is obtained. j The total normal contact force is:

[0138]

[0139] Where R m is the collection of main particles.

[0140] S13, if y j and i First contact, record the current moment from particle y j With the main particle y i , for subsequent analysis; otherwise, recalculate and normal contact force It is added to the total normal contact force to update the contact status.

[0141] S14. Define the test tangential contact force.

[0142] The tangential contact force is proportional to the relative sliding distance between particles. The tangential contact force is constrained by the Coulomb friction criterion. Therefore, a trial tangential contact force is defined as follows:

[0143]

[0144] is the test tangential contact force.

[0145] S15. Calculate relative slip distance

[0146] In S15, the relative sliding distance is the initial contact time t c The difference in the tangential distance between the two contacting particles at the current time t is expressed as follows:

[0147]

[0148] S16. Define the tangential contact boundary according to the Coulomb friction criterion

[0149] In S16, the tangential contact boundary The expression is as follows:

[0150]

[0151] μ represents the friction coefficient.

[0152] S17. Determine the tangential contact force according to the tangential contact boundary.

[0153] In S17, the tangential contact force expression is as follows:

[0154]

[0155] S18. Sum the tangential contact forces generated by all slave particles and the master particle and obtain the force acting on y j ,y i The total tangential contact force.

[0156] In S18, acting on yi The expression of the total tangential contact force is as follows:

[0157]

[0158] Similarly, Newton's third law acts on y j The total tangential contact force expression is as follows:

[0159]

[0160] S19. The calculated total tangential contact force is applied to the contact particles in the form of body force density, and the particle displacement is updated by the PD numerical scheme.

[0161] S20. If the termination condition (iteration time or number of iterations) is met, the calculation is terminated; otherwise, the process returns to S6.

[0162] This embodiment demonstrates the performance of the proposed EBCM (Element-based contact modeling, EBCM) method through two numerical examples.

[0163] The first example is the Kalthoff-Winkler experiment, which studies the fracture behavior of materials under dynamic loading, involving impact contact between a rigid body and a flexible body. Figure 3 As shown in the figure, a 1.57kg rigid object vertically impacts a flexible steel plate with two cracks. The steel plate is not constrained by displacement, and the two cracks are symmetrically distributed on the central axis. The material parameters of the steel plate include: Young's modulus 191GPa, Poisson's ratio 0.25, density 8000kg / m 3 and critical bond elongation 0.01, the geometry of the impactor and the steel plate is shown in Figure 3 .

[0164] Figures 4(a) and 4(b) show the variation of total contact force and impactor velocity over time. The results show that at all impact velocities, the contact results calculated by EBCM and other EMU methods are highly consistent, verifying the effectiveness and accuracy of EBCM in the impact contact between rigid and flexible bodies. In the first half of the simulation, the contact force and compression wave increased significantly due to the impact. In the second half, the contact force and compression wave separated the impactor from the steel plate, the contact force dropped to zero, and the impactor velocity basically stopped changing.

[0165] Figure 5The crack propagation results under different impact velocities are shown. Consistent with the contact force results, the damage mode and crack propagation rate calculated by the EBCM and EMU methods are highly consistent. Under all conditions, the two propagation cracks are also symmetrically distributed due to the symmetry of the loading conditions and the initial cracks about the central axis. In addition, the degree of damage to the steel plate and the average crack propagation rate increase with the increase of the impact velocity. When the crack length reaches a certain value, it stops propagating; as the impact velocity increases, the crack length also increases accordingly, and eventually extends to the left and right boundaries of the steel plate. When the velocity increases further, additional damage appears at the bottom of the steel plate.

[0166] The second example is a friction contact test of two flexible plates, which studies the friction contact of two elastic plates and the influence of material strength on the contact behavior under fixed compression displacement conditions. Figure 6 As shown in the figure, displacement loading is applied to the top of the upper plate, while full constraint is applied to the bottom of the lower plate. The two elastic plates have exactly the same geometry, density and Poisson's ratio, but different Young's modulus: the density and Poisson's ratio of the two plates are 1 / 3 and 7850 kg / m respectively. 3 , the Young's modulus of the upper plate is set to 200 GPa, while the lower plate considers two working conditions of 100 GPa and 200 GPa. The friction coefficient between the two plates is set to 0.2. This embodiment does not involve material damage and can be verified by the FE (finite element) model. Due to the commercialization and standardization of the software used, when damage and discontinuity are not involved, you can choose to compare with the FE model to verify the accuracy and effectiveness of the peridynamic model. Therefore, an FE model with completely consistent parameters with the peridynamic model is also established for comparative analysis.

[0167] Figure 7(a) and Figure 7(b) show the normal and tangential contact stress distributions calculated by the PD (the peridynamics) model and the FE model, and Table 1 records the contact force solutions under the two working conditions. The results show that the contact stress distributions calculated by the PD model and the FE model are highly consistent, and the error of the total contact force is less than 1.4%. As the material strength increases, the contact force also increases. When the strength increases from to, the normal contact force increases from 667.6N to 1000.6N, with a significant increase. Due to the application of fixed displacement loading conditions, the deformation of the plate remains relatively unchanged under changes in material strength. Under similar deformation conditions, it is reasonable for stronger materials to produce greater contact forces.

[0168] Table 1 PD model solutions and FE model solutions for the total contact force components

[0169]

[0170] In summary, the unit-based peridynamic contact modeling method proposed in this embodiment is suitable for contact damage problems and various contact scenario studies.

[0171] The present invention and its embodiments are described schematically above, and the description is not restrictive. The drawings show only one embodiment of the present invention, and the actual structure is not limited thereto. Therefore, if a person skilled in the art is inspired by it and designs a structural method and an embodiment similar to the technical solution without creativity without departing from the purpose of the invention, they shall all fall within the protection scope of the present invention.

Claims

1. A unit-based peridynamic contact modeling method, characterized by: The following steps are involved: S1, set and initialize materials, geometry, simulation parameters and variables; S2, dividing the two objects involved in the contact into a slave object and a master object; S3. Using the meshless method, the slave object and the master object are discretized into peridynamic particles, the particles that may participate in the contact interaction are defined as contact particles, the contact particles on the slave object and the master object are called slave particles and master particles, and the set R of slave particles and master particles is constructed. s and R m ; S4, for each contact particle on the main object, that is, the main particle y i Building contact elements S5, the main particle y i and from particle y j Total normal contact force and the total tangential contact force The value of is initialized to 0; S6. Visit all particles y in the collection j , and traverse each particle y from the object j ; S7, by each particle y j Access all main particles y in the collection i , and traverse each main particle y in the main object i ; S8. Determine the main particle y i Contact elements constructed The contact plane; S9: Determine whether the contact condition is met. If it is met, continue the subsequent operation. Otherwise, terminate the particle y i and j Contact calculation between S10, calculate the material normal overlap depth after contact occurs Contact stiffness And the distance influence function ω ij ; S11, calculate the particle y j With the main particle y i Normal contact force S12, calculate the particle y j With the main particle y i Normal contact force Add to Get y i ,y j The total normal contact force is: S13, if y j and i First contact, record the current moment from particle y j With the main particle y i , for subsequent analysis; otherwise, recalculate and normal contact force And add it to the total normal contact force to update the contact status; S14. Define the test tangential contact force; S15. Calculate relative slip distance S16. Define the tangential contact boundary according to the Coulomb friction criterion S17, determining a tangential contact force according to a tangential contact boundary; S18. Sum the tangential contact forces generated by all slave particles and the master particle and obtain the force acting on y j ,y i The total tangential contact force of S19, applying the calculated total tangential contact force to the contact particles in the form of body force density, and updating the particle displacement by the numerical scheme of PD; S20. If the termination condition is met, the calculation is terminated; otherwise, the process returns to S6.

2. A cell-based peridynamic contact modeling method according to claim 1, characterized in that: In S4, each contact unit includes the current contact particle and its two adjacent contact particles, that is, any contact particle y on the main object i , contact element Defined as y i Its two adjacent contact particles y i1 and i2 A collection of: Based on the spatial position relationship, the contact particles on the main object are divided into three categories: non-boundary particles, boundary particles and particles adjacent to defects; for non-boundary particles, the adjacent particles of the contact unit are the two closest contact particles to it; for particles at the left and right boundaries, the adjacent particles of the contact unit are the two closest contact particles to it. b , its neighboring particle y in the main object b2 It is determined by searching for the nearest contact particle, but the neighboring particles outside the main object do not exist. Therefore, a virtual neighboring particle y is introduced. bv , whose position is determined by linear extrapolation of internal neighboring particles: and bv =2y b -and b2 For the contact particle y near the defect d , is y d Introducing virtual neighboring particle y dv ,y dv The spatial position of is determined by linear extrapolation from another neighboring particle; All contact particles should have at least one neighboring particle that does not require additional processing, that is, there is at least one neighboring particle with y i Distance Δx i adjacent particles to avoid the problem of not being able to find adjacent particles.

3. A unit-based peridynamic contact modeling method according to claim 2, characterized in that: In S8, contact unit The two adjacent particles in are used to determine the contact surface direction, while the contact surface position is determined by three particles together; First, the contact surface direction is defined by two adjacent particles, where the vector y i2 -y i1 The direction is the tangent direction of the contact surface, and the main particle y i Construct parallel to y i2 -y i1 The plane χ i , which is the contact unit Defined contact plane, adjacent particles y i1 and i2 In χ i The projection point and For plane χ i the boundaries of; Contact surface unit tangent vector Written as: Determined by the following formula and Spatial location: Where k represents any adjacent particle; χ i For contact elements The contact plane is defined as: definition is i The unit normal vector of Pointing outward from the contact surface, the unit normal vector and the unit tangent vector Vertical, that is, the following relationship: From particle y j In χ i The projection point is Its position is determined by the following formula:

4. A unit-based peridynamic contact modeling method according to claim 3, characterized in that: In S9, from the contact particle y j In χ i The projection point is When the contact particle y j About contact surface χ i The projection point In χ i Inside and projection distance When it is less than the critical value, the contact event is determined to have occurred: Δx i represents the interparticle distance of the primary particles, Δx j represents the interparticle distance from the particle; yes Located in i Projection distance of internal projection; Yes j and χ i The critical contact distance between .

5. A cell-based peridynamic contact modeling method according to claim 4, characterized in that: In S10, the material normal overlap depth Contact stiffness And the distance influence function ω ij The calculation formula is as follows: Where p si is the control coefficient of contact stiffness, K ij represents the bulk modulus, δ ij is the neighborhood radius, ΔV i and ΔV j is the bulk modulus of the material.

6. A cell-based peridynamic contact modeling method according to claim 5, characterized in that: In S11, the normal contact force The calculation formula is as follows: f cn (y i ,y j ) represents y j and i Normal contact force between .

7. A cell-based peridynamic contact modeling method according to claim 6, characterized in that: In S12, y i The total normal contact force is given by: f cn (y i ,t) represents the main particle y i The total normal force on ; According to Newton's third law, from particle y j The contact force and y i The opposite direction is equal, so the expression is: is the contact force received by the particle, is the contact force on the main particle; From particle y j With all the main particles y i The sum of the reaction forces on y is obtained. j The total normal contact force is: Where R m is the collection of main particles.

8. A cell-based peridynamic contact modeling method according to claim 7, characterized in that: In S14, the test tangential contact force is as follows: is the test tangential contact force.

9. A cell-based peridynamic contact modeling method according to claim 8, characterized in that: In S15, the relative sliding distance is the initial contact time t c The difference in the tangential distance between the two contacting particles at the current time t is expressed as follows: In S16, the tangential contact boundary The expression is as follows: μ represents the friction coefficient; In S17, the tangential contact force expression is as follows:

10. A cell-based peridynamic contact modeling method according to claim 9, characterized in that: In S18, acting on y i The expression of the total tangential contact force is as follows: Similarly, Newton's third law acts on y j The total tangential contact force expression is as follows:

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