Rock damage and failure smooth molecular dynamics analysis method
By discretizing particles using the Generalized Differential Material Point Method (GIMP) and assigning material parameters, combined with the Mohr Coulomb criterion and background mesh, the problems of computational accuracy and operational complexity in rock nonlinear mechanical simulation are solved, achieving efficient simulation of rock damage and failure.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-10-09
- Publication Date
- 2026-04-07
AI Technical Summary
Existing technologies are difficult to effectively simulate the changes in nonlinear mechanical properties of rocks and the crack propagation process. In particular, the finite element method has uncertainties in large deformation problems, the discrete element method has little advantage in simulating continuous media, and the traditional material point method has insufficient calculation results.
The Generalized Differential Material Point Method (GIMP) is used to discretize the rock region into material points, assign material mechanical parameters, use the Mohr Coulomb criterion as the failure criterion, draw an initial background mesh, simulate rock damage and failure through the failure process of material points, and use the GIMP algorithm to suppress numerical noise and simplify the operation process.
It achieves high-precision simulation of rock damage and failure, avoids the numerical solution difficulties caused by mesh distortion, simplifies the operation process, improves calculation accuracy and effect, and accurately simulates the progressive damage process of rocks.
Smart Images
Figure CN115602254B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a smooth molecular dynamics analysis method, specifically a smooth molecular dynamics analysis method for rock damage and destruction. Background Technology
[0002] Rock is a typical anisotropic material, containing various microstructural defects such as joints, cracks, pores, and faults. Under environmental influences or external loads, cracks initiate and propagate at these defects, resulting in typical heterogeneous and nonlinear characteristics of the rock structure and causing irreversible damage. Describing the variation laws of the nonlinear mechanical properties of rocks has been a research challenge in recent years.
[0003] Due to the diversity of cracks and the complexity of their propagation processes, not only is theoretical analysis difficult to advance, but experimental methods also face many challenges. With the rapid development of computer technology, numerical simulation methods have made significant progress in recent years, providing a good alternative for studying the nonlinear characteristics of rocks. Compared with experimental methods, numerical methods are less expensive, and as long as reasonable constitutive relations and computational parameters are provided, the entire process of dynamic rock fracturing can be predicted. Therefore, nonlinear numerical simulation of rocks is increasingly favored by scholars.
[0004] However, the commonly used finite element method (FEM) for simulating crack propagation direction has significant uncertainties. The extended finite element method (XFEM) also faces many difficulties in handling large deformation problems. The discrete element method (DEM) requires parameter calibration to establish the relationship between macroscopic and microscopic parameters, and it has limited advantages in simulating continuous media. Currently, the material point method (MPM) algorithm is continuously developing and has been successfully applied in research fields such as ultra-high-speed impact, explosion, fracturing, and multiphase flow, providing more accurate calculation results compared to traditional MPM algorithms. The advantages of Material Point Method (MPM) have led to its initial application in simulating rock damage and failure (such as fracture mechanics). For example, the paper "Material Point Method Calculations with Explicit Cracks, Computer Modeling" proposes using three velocity fields to simulate cracks. Although three velocity fields are defined, each particle can only have a maximum of two velocity fields, making the process relatively cumbersome. The paper "Two-dimensional mixed mode crack simulation using the material point method" proposes using irregular meshes to simulate two-dimensional cracks and using damaged particles to determine the approximate location of the crack, but this method does not introduce explicit cracks. Compared to MPM, GIMP has better computational accuracy and performance; therefore, the application of the GIMP algorithm in the field of rock damage and failure requires further in-depth research. Summary of the Invention
[0005] The purpose of this invention is to provide a simple and easy-to-use numerical simulation method for rock fracture.
[0006] The objective of this invention is achieved as follows:
[0007] This invention discloses a molecular dynamics analysis method for smooth rock damage and failure, comprising the following technical steps.
[0008] (1) The material region is discretized into particles using the material point method.
[0009] (2) Assign certain material mechanical parameters to discrete-domain particles;
[0010] (3) The Mohr Coulomb criterion, commonly used in rock mechanics, is adopted as the material failure criterion.
[0011] (4) Draw the initial background grid;
[0012] (5) The Generalized Differential Material Point Method (GIMP) is used as the calculation method;
[0013] (6) When a particle reaches the failure condition, the particle is subjected to failure treatment;
[0014] (7) The failure process of particles is used to simulate the progressive damage and failure process of rocks.
[0015] The present invention may also include:
[0016] The particle diagram is drawn based on the extent of the computational material domain, and the overall shape of the particles is the shape of the computational material domain. Each particle represents a region of material and carries all the material information of that region, such as stress, velocity, and mass. All particles carry all the information of the continuum. The more discrete particles there are, the higher the computational accuracy.
[0017] Based on the object of calculation, the particle is assigned corresponding mechanical parameters, such as tensile strength, cohesion, and internal friction angle in rock mechanics.
[0018] Tensile failure criterion: σ f =σ t .
[0019] Shear failure criterion:
[0020] Where: σ f and τ f The maximum tensile and shear stresses at the hypothetical failure surface, σ tσ is the tensile strength of the material; c is the cohesion of the material; and φ is the angle of internal friction of the material. It is worth noting that when the mass satisfies the tensile failure condition (σ... f＝ σ t ), prioritize tensile failure, when equation (σ f＝ σ t If the condition is not met, then the shear failure condition (τ) is determined. f＝ c+σ f* tanφ).
[0021] In each calculation step, a new background mesh is drawn. This background mesh is generally consistent with the initial background mesh, but it can also be changed in different calculation steps according to its own requirements. However, a new background mesh is drawn at the beginning of each calculation step. The background mesh needs to cover the entire material calculation domain. The mass points and the background mesh are fixed. The mass point information is mapped onto the background mesh nodes. The standard finite element method is used to solve the problem on the background mesh. Afterward, the background mesh node information is mapped back to the mass points. After each calculation step, the deformed background mesh is discarded, and a new background mesh is drawn again in the next calculation step. This avoids the numerical solution difficulties caused by mesh distortion in the Lagrange method.
[0022] Compared to the traditional material point method (MPM), the generalized difference material point method (GIMP) effectively suppresses numerical noise caused by particles crossing the background grid, and the calculation results obtained by the GIMP algorithm are more accurate than those of the MPM algorithm.
[0023] GIMP shape function S ip As shown in the following formula:
[0024]
[0025] Where: ξ=|(x p -x i ) / L|,x p Let x be the coordinate position of the particle. i L represents the coordinates of the background grid nodes, and L represents the length of the background grid.
[0026] In the case of a three-dimensional problem, S ip As shown in the following formula:
[0027] S ip (x)=S ip (ξ)S ip (η)S ip (ζ)
[0028] Where: ξ=|(x p -x i ) / L|,η=|(y p -y i) / L|,ζ=|(z p -z i ) / L|.
[0029] x p y p , z p These are the x, y, and z coordinates of the particle, respectively. i y i , z i These are the x, y, and z coordinates of the background grid node, respectively.
[0030] When a particle reaches the failure criterion, the deviatoric stress of the failed particle is set to zero, and the sound velocity and pressure of its artificial volumetric viscosity are no longer corrected. Currently, the following pressure handling methods are available:
[0031] (1) After a particle fails, it cannot withstand tensile force, but it can withstand compressive force.
[0032] (2) After a particle fails, it can neither withstand pressure nor tension.
[0033] (3) After the mass point fails, it can withstand a certain tensile force and a certain pressure. The pressure threshold range needs to be set.
[0034] (4) In rock mechanics, a particle can not withstand tensile force after it fails, but it can withstand compressive force.
[0035] Failed particles are permanently damaged. The progressive failure process of particles is used to simulate the damage and failure process of rocks. For example, in rock fracture, the crack represented by the failed particles is the visible crack.
[0036] The advantages of this invention are: compared to the finite element method, it avoids the numerical solution difficulties caused by mesh distortion in the Lagrange method. Compared to the initial application of MPM in rock damage and failure, this algorithm is simpler in form and operation, does not require setting multiple velocity fields, and simulates the explicit damage and failure process of rock using the failure process of mass points, thus obtaining the entire process of progressive damage and failure of rock. GIMP itself has better computational accuracy and better computational results than MPM. Attached Figure Description
[0037] Figure 1 This is a schematic diagram of the process of the present invention;
[0038] Figure 2 This is a schematic diagram of material domain discretization using the material point method.
[0039] Figure 3 This is a schematic diagram showing the dimensions and mass distribution of a uniaxial compression case model.
[0040] Figure 4A schematic diagram comparing the maximum principal stress in a uniaxial compression example with the Abaqus calculation results;
[0041] Figure 5 This is a schematic diagram of damage failure in a uniaxial compression example.
[0042] Figure 6 This is a schematic diagram comparing the calculation results of a uniaxial compression case with the experimental results and theoretical calculation results. Detailed Implementation
[0043] The invention will now be described in more detail with reference to the accompanying drawings:
[0044] Combined with appendix Figure 1-6 This invention provides a molecular dynamics analysis method for smooth rock damage and failure, the specific steps of which are as follows:
[0045] (1) The material region is discretized into particles using the material point method.
[0046] (2) Assign certain material mechanical parameters to discrete-domain particles;
[0047] (3) The Mohr Coulomb criterion, commonly used in rock mechanics, is adopted as the material failure criterion.
[0048] (4) Draw the initial background grid;
[0049] (5) The Generalized Differential Material Point Method (GIMP) is used as the calculation method;
[0050] (6) When a particle reaches the failure condition, the particle is subjected to failure treatment;
[0051] (7) The failure process of particles is used to simulate the progressive damage and failure process of rocks.
[0052] In step (1), the computational material domain is discretized into particles, as shown in the discretization diagram below. Figure 2 As shown. The overall shape of the particles is the shape of the computational material domain. This example uses a uniaxially compressed specimen of double-fractured rock, as shown. Figure 3 As shown in (a), the sample is 70 mm long and 140 mm high. Two 15 mm long cracks are pre-made in the center of the sample. The angle between the cracks and the horizontal direction is 30 degrees and the distance between the two cracks is 22 mm. Figure 3(b) The discrete particle representation of the double-fractured rock specimen. A higher number of discrete particles results in higher computational accuracy. Due to the high computational efficiency of GIMP, a large number of discrete particles were used in this example, resulting in 79,976 particles. Each particle represents a material region and carries all material information for that region. All particles carry information about the continuum. In this example, the material density carried by each particle is 2600 kg / m³. 3 All of them have an elastic modulus of 17 GPa and a Poisson's ratio of 0.14.
[0053] In step (2), certain material mechanical parameters are assigned to the discrete domain particles. In this example, the cohesion of the particles is 5.95 MPa, the internal friction angle is 40°, and the tensile strength is 2 MPa.
[0054] In step (3), the Mohr-Coulomb criterion, commonly used in rock mechanics, is adopted as the material failure criterion. When the mass point satisfies the tensile failure condition (σ f＝ σ t ), prioritize tensile failure, when equation (σ f＝ σ t If the condition is not met, then the shear failure condition (τ) is determined. f＝ c+σ f* tanφ). Where: σ f and τ f The maximum tensile and shear stresses at the hypothetical failure surface, σ t φ is the tensile strength of the material; c is the cohesive force of the material; φ is the internal friction angle of the material. The material parameter values have been given in step (2).
[0055] In step (4), a new background mesh is drawn at the beginning of each calculation step. The background mesh needs to cover the entire material calculation area. The mass points and the background mesh are fixedly connected, and the mass point information is mapped onto the background mesh nodes. The standard finite element method is used to solve the problem on the background mesh, and then the background mesh node information is mapped back to the material points. In this example, the length of the background mesh is 0.5 mm.
[0056] In step (5), the Generalized Differential Material Point Method (GIMP) is used as the calculation method. Compared with the traditional Material Point Method (MPM), the Generalized Differential Material Point Method (GIMP) effectively suppresses numerical noise caused by particles crossing the background grid. The calculation results obtained by the GIMP algorithm are more accurate than those obtained by the MPM algorithm.
[0057] By calculating the principal stresses and other mechanical parameters of the material, the failure of the mass point can be determined. The maximum principal stress contour map of the mass point before failure obtained in this example is shown below. Figure 4 As shown in (a). Figure 4(b) shows the calculation results from Abaqus software, and the two are highly consistent.
[0058] GIMP shape function S ip As shown in the following formula:
[0059]
[0060] Where: ξ=|(x p -x i ) / L|,x p Let x be the coordinate position of the particle. i L represents the coordinates of the background grid nodes, and L represents the length of the background grid.
[0061] In the case of a three-dimensional problem, S ip As shown in the following formula:
[0062] S ip (x)=S ip (ξ)S ip (η)S ip (ζ)
[0063] Where: ξ=|(x p -x i ) / L|,η=|(y p -y i ) / L|,ζ=|(z p -z i ) / L|.
[0064] x p y p , z p These are the x, y, and z coordinates of the particle, respectively. i y i , z i These are the x, y, and z coordinates of the background grid node, respectively.
[0065] Step (6) determines whether a particle has failed and then processes the failed particle. The particle is judged to be failed based on the calculation results of steps (3) and (5). When a particle fails, the deviatoric stress of the failed particle is set to zero, and its artificial volume viscosity velocity and pressure are no longer corrected. The failed particle cannot withstand tensile force, but can withstand compressive force.
[0066] Step (7) simulates the progressive damage and failure process of rock using the failure process of particles. Since particle failure is permanent, the progressive failure process of particles is used to simulate the damage and failure process of rock. The rock failure process in this example is as follows: Figure 5 As shown, Figure 6The experimental and theoretical calculation results for this example show that the numerical simulation results are in high agreement with the experimental and theoretical calculation results, verifying the accuracy of a smooth molecular dynamics analysis method for rock damage and failure in numerical simulation of rock fracture.
Claims
1. A molecular dynamics analysis method for smooth rock damage and failure, characterized in that, The technical steps include the following: (1) The material point method is used to discretize the calculation material region into particles; (2) Assign certain material mechanics parameters to discrete-domain particles; (3) The Mohr Coulomb criterion, which is commonly used in rock mechanics, is adopted as the material failure criterion; (4) Draw the initial background grid; (5) The generalized difference material point method is used as the calculation method; (6) When a particle reaches the failure condition, perform failure processing on the particle; (7) Simulate the progressive damage and failure process of rocks by using the failure process of particles; The calculation using the generalized difference material point calculation method described in step (5) is as follows: Compared to the traditional material point method, the generalized difference material point method effectively suppresses numerical noise caused by particles crossing the background grid, and the calculation results obtained by the generalized difference material point method are more accurate than those of the traditional material point method. GIMP shape function S ip As shown in the following formula: ； in: ξ = |( x p - x i ) / L |, x p The coordinates of the particle are... x i The coordinates of the background grid nodes. L The length of the background grid; In the case of a three-dimensional problem, S ip As shown in the following formula: ； in: ξ =|( x p - x i ) / L |, η =|( y p - y i ) / L |, ζ =|( z p - z i ) / L |; x p , y p , z p These are the x, y, and z coordinates of the particle, respectively. x i , y i , z i These are the x, y, and z coordinates of the background grid node, respectively.
2. The method for analyzing the smoothness of rock damage and failure according to claim 1, characterized in that, The material region discretization method described in step (1) is as follows: Particles are plotted based on the extent of the computational material domain, and the overall shape of the particles is the shape of the computational material domain. Each particle represents a material region and carries all the material information of that region. All particles carry all the information of the continuum. The more discrete particles there are, the higher the computational accuracy will be.
3. The method for analyzing the smoothness of rock damage and failure according to claim 1, characterized in that, The material mechanical parameters assigned to the discrete-domain particles in step (2) are as follows: Based on the object of calculation, the particle is assigned corresponding mechanical parameters, such as tensile strength, cohesion, and internal friction angle as rock mechanical parameters.
4. The method for analyzing the smoothness of rock damage and failure according to claim 1, characterized in that, The Mohr Coulomb criteria described in step (3) are as follows: Tensile failure criterion: ; Shear failure criterion: ; in: σ f and τ f These are the maximum tensile and shear stresses at the hypothetical failure surface. σ t It is the tensile strength of the material; c It is the cohesive force of the material. φ Let be the internal friction angle of the material; it is worth noting that when the mass satisfies the tensile failure condition... σ f = σ t Prioritize judging tensile failure, when formula σ f = σ t If the condition is not met, then a shear failure check is performed. τ f = c+σ f* tanφ .
5. The method for smooth molecular dynamics analysis of rock damage and failure according to claim 1, characterized in that, The initial background mesh drawn in step (4) is as follows: In each calculation step, a new background mesh is drawn. This background mesh is generally consistent with the initial background mesh, but it can also be changed in different calculation steps according to its own requirements. However, a new background mesh is drawn at the beginning of each calculation step. The background mesh needs to cover the entire material calculation domain. The mass points and the background mesh are fixed. The mass point information is mapped onto the background mesh nodes. The standard finite element method is used to solve the problem on the background mesh. Afterward, the background mesh node information is mapped back to the mass points. After each calculation step, the deformed background mesh is discarded, and a new background mesh is drawn again in the next calculation step. This avoids the numerical solution difficulties caused by mesh distortion in the Lagrange method.
6. The method for smooth molecular dynamics analysis of rock damage and failure according to claim 1, characterized in that, The particle failure handling described in step (6) is as follows: When a particle reaches the failure criterion, the deviatoric stress of the failed particle is set to zero, and the sound velocity and pressure of its artificial volume viscosity are no longer corrected. Currently, the following pressure handling methods are available: A particle cannot withstand tensile force after it fails, but it can withstand compressive force; After a particle fails, it can neither withstand pressure nor tension. After a particle fails, it can withstand a certain tensile force and a certain compressive force, so a pressure-bearing threshold range needs to be set. In rock mechanics, it is assumed that a point mass, after failure, cannot withstand tensile force but can withstand compressive force.
7. The method for smooth molecular dynamics analysis of rock damage and failure according to claim 1, characterized in that: The simulation of rock damage and failure process using the failure process of mass points described in step (7) is as follows: Failed particles are permanently damaged. The progressive failure process of particles is used to simulate the damage and failure process of rocks. For example, in rock fracture, the crack represented by the failed particles is the visible crack.