Numerical Simulation Method and System for Progressive Failure Process of Elastic-Brittle Materials Based on DDDA

Abstract

This invention discloses a numerical simulation method and system for the progressive failure process of elastobrittle materials based on DDDA (Differentiated Optimal-Displacement Amplitude) simulation. The method includes the following steps: S1. Constructing a two-dimensional DDDA numerical model with the same geometric dimensions as the actual elastobrittle material sample, using the geometric parameters as a reference; S2. Grouping the circular elements in the constructed numerical model based on the compression-tension ratio of the actual elastobrittle material; S3. Bonding the circular elements and adding bonding elements based on the proposed three-spring bonded circular element model; S4. Calibrating the input parameters of the numerical model based on the mechanical parameters of the actual elastobrittle material sample; S5. Adding boundary conditions to the numerical model based on the calibration results to simulate the progressive failure process of the elastobrittle material. This invention achieves accurate prediction of the progressive failure process of elastobrittle materials, featuring high simulation accuracy and strong practicality.

Description

Technical Field

[0001] This invention belongs to the field of computational mechanics and simulation of elastobrittle materials, specifically relating to a numerical simulation method and system for the progressive failure process of elastobrittle materials based on DDDA. Background Technology

[0002] Brittle-elastic materials, such as rock, concrete, ceramics, and glass, are found in almost all common engineering projects. Failure in these materials, including the initiation and propagation of cracks in intact or fractured materials, is very common in engineering. This failure accumulates to form a penetrating sliding surface, creating conditions for large displacements of the sliding mass and easily triggering disasters. Taking rock engineering as an example, the initiation and propagation of cracks in intact or fractured rock masses, after forming a penetrating sliding surface, often leads to geological disasters such as rockfalls, collapses, landslides, and tunnel collapses. Revealing the failure mechanism of brittle-elastic materials helps predict crack initiation locations and crack propagation paths, thereby enabling more effective reinforcement measures to prevent the formation of sliding surfaces and avoid potential disasters.

[0003] Among the many research methods for material failure, numerical simulation has gradually become one of the most promising methods in terms of development and application. Traditional continuous numerical methods, such as the finite element method (FEM) and the effective difference method (FDM), cannot accurately simulate discontinuous phenomena such as multiple crack propagation in materials. On the other hand, discontinuous numerical methods, such as the discrete element method (DEM) and the discontinuous deformation analysis method (DDA), play an irreplaceable role in the numerical simulation of the entire material failure process. Both methods use discrete blocks as their basic computational unit, requiring the establishment of a bonding model to bind these discrete blocks into a whole. When the failure condition is met, crack propagation is simulated by breaking the bond between two bonded blocks. Compared with DEM, DDA has the following advantages: 1. Higher solution accuracy; 2. No need for very small time steps or artificial damping to ensure computational stability.

[0004] Currently, most DDA bonding models are based on traditional DDA, which uses polygonal / polyhedral blocks as basic units. The contact problem of basic units in traditional DDA is complex and computationally inefficient. Summary of the Invention

[0005] To address the shortcomings of existing technologies, one of the objectives of this invention is to provide a numerical simulation method and system for the progressive failure process of elastobrittle materials based on the circular element discontinuous deformation analysis (DDDA) method. This method can accurately predict the progressive failure process of elastobrittle materials and has the characteristics of high simulation accuracy and strong practicality.

[0006] The second objective of this invention is to provide a system for realizing the numerical simulation method and system for the progressive failure process of elastobrittle materials based on DDDA.

[0007] This invention provides a numerical simulation method and system for the progressive failure process of brittle-elastic materials based on DDDA, comprising the following steps:

[0008] S1. Based on the geometric parameters of real brittle-elastic material specimens, construct an initial two-dimensional DDDA numerical model;

[0009] S2. Based on the compression-tension ratio of real elastic-brittle materials, the circular elements in the two-dimensional DDDA numerical model obtained in step S1 are grouped to obtain the two-dimensional DDDA numerical model.

[0010] S3. Bond the circular elements in the two-dimensional DDDA numerical model, add bonded elements, and obtain a three-spring bonded circular element DDA numerical model;

[0011] S4. Using the mechanical parameters of real brittle-elastic material specimens as a reference, calibrate the input parameters of the three-spring bonded circular element DDA numerical model;

[0012] S5. Based on the actual working conditions of the target brittle-elastic material in actual engineering or experiments, add boundary conditions to the three-spring bonded circular element DDA numerical model to simulate the progressive failure process of the brittle-elastic material.

[0013] Step S1 is as follows:

[0014] An initial two-dimensional DDDA numerical model is constructed based on the geometric parameters of real elastobrittle materials;

[0015] The initial two-dimensional DDDA numerical model uses rigid circular elements as the basic computational units. Each circular element has three degrees of freedom, denoted as:

[0016]

[0017] in For the displacement of the circular element; This represents the translation of the center of the circular element in the x-direction; This represents the translation of the center of the circular element in the y-direction. Let be the angle of rotation of a circular element around its center.

[0018] The discontinuous deformation analysis of the circular element adopts an implicit solution method. In each time step of the stepwise time integration, the overall equilibrium equation is constructed based on the principle of minimum potential energy.

[0019] The overall equilibrium equation is expressed by the following formula:

[0020]

[0021] Among them, when hour, Let be the interaction stiffness submatrix between circular element i and circular element j, and the interaction stiffness submatrix be... matrix; Let i be the radius correlation matrix of the circular element i, and the radius correlation matrix is: matrix; Let be the unknown quantum matrix of the displacement of circular element i, denoted as ,in Let i be the circular element i with displacement in the x-direction. Let i be the circular element i with displacement in the y direction. Let i be the angle of rotation of the circular element i around its center; Let i be a generalized force quantum array of circular element i, denoted as ,in Let i be the generalized force in the x-direction of the circular element i. Let i be the generalized force in the y-direction of the circular element i. The generalized force is the force around the center of the circular element i;

[0022] In each calculation step, the discontinuous deformation analysis of the circular element assembles a set of simultaneous equilibrium equations based on the information of the contact pairs and various external loads acting on the circular element system; solves the set of equations to obtain the displacement increment of the circular element; and updates the calculation model data, including the velocity and coordinates of the circular element and the interaction forces between the circular elements.

[0023] Step S2 is as follows: Based on the compression-tension ratio of the real elastic-brittle material, the outer contour of the initial two-dimensional DDDA numerical model is used as the boundary. Circular elements are grouped based on spatial position or other criteria related to the compression-tension ratio. The discrete particles in the initial two-dimensional DDDA numerical model are divided into multiple particle groups. Particles in the same particle group are configured to cooperate in responding to mechanical behaviors related to the compression-tension ratio in subsequent simulations, and finally, a two-dimensional DDDA numerical model is obtained.

[0024] Specifically, the criteria based on spatial location or other factors related to the compressibility-to-pull ratio include grouping based on the Thiessen polygon mesh.

[0025] Step S3 specifically involves bonding the circular elements in the two-dimensional DDDA numerical model, adding bonding elements, and obtaining a three-spring bonded circular element DDA numerical model.

[0026] The three-spring bonded circular element DDA numerical model is a bonding contact model between circular elements, using three springs as load-bearing elements to bond discrete circular elements into a whole; the three springs include one tangential spring and two normal springs.

[0027] Based on the principle of minimum potential energy, the tangential spring sub-matrix is ​​superimposed into the simultaneous equilibrium equations, and expressed by the following formula:

[0028]

[0029] in, This refers to the tangential spring stiffness; This is the cumulative relative displacement of the tangential spring connection endpoints in the tangential direction at the start of the time step; It is the first intermediate matrix, and ; This is the second intermediate matrix, and ; Let x be the x-direction component of the tangential direction vector between circular element i and circular element j; Let y be the tangential direction vector of circular element i and circular element j; Let be the radius of the circular element i;

[0030] Based on the principle of minimum potential energy, the normal spring submatrix is ​​superimposed into the simultaneous equilibrium equations, and expressed by the following formula:

[0031]

[0032] in, Normal spring stiffness; It is the third intermediate matrix, and ; The distance between the normal spring and the center line of the bonding unit. The width of the bonding unit is , ; Let be the radius of the circular element i; Let be the radius of the circular element j; This is the cumulative relative displacement of the connection endpoint of the normal spring 1 in the normal direction;

[0033] The elastic-brittle constitutive model is used as the bond failure criterion, and the following three sub-criteria are used sequentially to determine whether the bonded elements have failed:

[0034]

[0035] in, This is the input value for the tensile strength of the bonded unit; This is the input value for the internal friction angle; This is the input value for cohesion; The normal spring compression; when hour, ,otherwise .

[0036] When the judgment criteria determine that at least one spring has broken, the bonding unit is considered to have failed. After the bond between the two bonded circular units fails, these two circular units will be regarded as ordinary circular unit-circle unit contact pairs, and their normal contact sub-matrix is:

[0037]

[0038] in, It is the normal spring stiffness between circular element i and circular element j; It is the fourth intermediate matrix, and ; It is the fifth intermediate matrix, and ; The x-coordinate of the connection point between the normal spring and circular element i; Let x be the x-coordinate of the connection point between the normal spring and the circular element j; The y-coordinate of the connection point between the normal spring and circular element i; The y-coordinate of the connection point between the normal spring and the circular element j;

[0039] For a typical circular element-to-circular element contact pair, the tangential contact submatrix is:

[0040]

[0041] in, Let be the tangential spring stiffness between circular element i and circular element j; Let i be the displacement transformation matrix of the circular element i; , Let i be the center coordinates of the circular element i; , Let be the center coordinates of circular element i.

[0042] Step S4 is as follows:

[0043] The input parameters of the three-spring bonded circular element DDA numerical model are calibrated based on the mechanical parameters of real brittle-elastic material specimens.

[0044] The input parameter calibration includes the calibration of elastic parameters and the calibration of strength parameters;

[0045] The elasticity parameter includes the Poisson's ratio input value. With elastic modulus input value The correspondence between the elastic parameters and the normal spring stiffness and tangential spring stiffness in the DDA numerical model of the three-spring bonded circular element is as follows:

[0046]

[0047] in, It is half the width of the bonding unit; H represents the initial length of the bonding unit; H represents the thickness of the entire model.

[0048] The calibration of the elastic parameter includes the following steps:

[0049] (1) Establish a numerical sample with an aspect ratio of 2, with a particle number of 6000~10000, and the radius range and distribution of the circular elements in the sample are consistent with the calculation model;

[0050] (2) Let Equivalent to the elastic modulus of real brittle and elastic materials Using several different Poisson ratios Numerical experiments were conducted to obtain several sets of results. and Data, including Poisson's ratio for real brittle-elastic materials;

[0051] (3) Based on the Logistic function, fit the result. Relationships and The Logistic function of the relation, the expression of which is:

[0052]

[0053] Where x is the independent variable and y is the dependent variable; The first coefficient to be determined; The second undetermined coefficient; p is the third undetermined coefficient; p is the fourth undetermined coefficient;

[0054] (4) Obtained through fitting Relational Logistic Function and The relational Logistic function calculates the specified... corresponding and the corresponding Thus, the specified calculation is obtained. corresponding ;

[0055] (5) Using the calculated and Conduct a numerical experiment to verify the results. and Check if the value is the specified value; if it meets the requirements, end the elastic parameter calibration. Otherwise, use the values ​​obtained from this numerical experiment. and Add the data to the dataset and fit it again. Relationships and The relation is represented by the Logistic function, and the result is returned to step (4).

[0056] The strength parameter includes the input value of the tensile strength of the bonding unit. Input value of internal friction angle Input values ​​for cohesion ;

[0057] The calibration of the strength parameters is specifically as follows:

[0058] Keep the Poisson ratio input value and elastic modulus input value Keep it unchanged, by adjusting the tensile strength input value and cohesion input values This makes the compressive strength of the numerical model... With tensile strength The compressive and tensile strengths corresponding to real brittle and elastic materials.

[0059] The calibration of the strength parameters includes the following steps:

[0060] The circular unit groups in step S2 are bonded together, and the circular unit groups are bonded to each other again. The units within each circular unit group are also bonded together. Increase 10 times;

[0061] Take the input value of the internal friction angle The value is between 30° and 50°, and the input value is the tensile strength of the bonded unit. To obtain 1.54 times the specified tensile strength, a single direct tensile test was performed on the numerical specimen, yielding... ,Sure Given a linear function expression, calculate the specified... corresponding ;

[0062] Take the input value of the internal friction angle For numerical samples with values ​​of 5, 20, 35, 50, 65, and 80, six uniaxial compression tests were conducted, resulting in six groups. The data is fitted using the Logistic function. Curve expression, calculate the specified curve. corresponding .

[0063] Step S5 is as follows:

[0064] Determine the input parameters of the numerical model;

[0065] Based on the actual working conditions of the target elastic-brittle material in actual engineering or experiments, the corresponding boundary conditions are applied to the numerical model.

[0066] Under the stated boundary conditions, the numerical model is driven to perform mechanical calculations, dynamically simulating the entire progressive failure process of the brittle-elastic material from initial deformation, microcrack initiation, propagation to macroscopic fracture, and acquiring dynamic change data such as displacement field, stress field and energy loss inside the model, thus completing the numerical simulation of the progressive failure process of the brittle-elastic material.

[0067] The boundary conditions include displacement boundary conditions, force / load boundary conditions, and velocity boundary conditions.

[0068] The present invention also provides a system for realizing the numerical simulation method and system for the progressive failure process of elastic-brittle materials based on DDDA, including a numerical model construction module, a model circular element grouping module, a three-spring bonding module, a model parameter calibration module, and a progressive failure simulation module for elastic-brittle materials;

[0069] The numerical model building module uses the geometric parameters of real elastobrittle material specimens as a reference to build an initial two-dimensional DDDA numerical model and uploads the data to the model circular element grouping module.

[0070] The model circular element grouping module, based on the received data and using the compression-tension ratio of real elastic-brittle materials as a benchmark, groups the circular elements in the two-dimensional DDDA numerical model to obtain the two-dimensional DDDA numerical model, and uploads the data to the three-spring bonding module.

[0071] The three-spring bonding module bonds the circular elements in the two-dimensional DDDA numerical model according to the received data, adds bonding elements, obtains the three-spring bonded circular element DDA numerical model, and uploads the data to the model parameter calibration module.

[0072] The model parameter calibration module calibrates the input parameters of the three-spring bonded circular element DDA numerical model based on the received data and the mechanical parameters of the real brittle-elastic material sample, and uploads the data to the brittle-elastic material progressive failure simulation module.

[0073] The progressive failure simulation module for brittle-elastic materials adds boundary conditions to the three-spring bonded circular element DDA numerical model based on the actual working conditions of the target brittle-elastic material in actual engineering or experiments, and simulates the progressive failure process of the brittle-elastic material.

[0074] This invention discloses a numerical simulation method and system for the progressive failure process of elastobrittle materials based on DDDA. The method of this invention provides an effective principle, algorithm, process and program running equipment for exploring the fracture failure mechanism of elastobrittle materials, and realizes accurate prediction of the progressive failure process of elastobrittle materials. It has the characteristics of high simulation accuracy and strong practicality. Attached Figure Description

[0075] Figure 1This is a flowchart illustrating the method of the present invention;

[0076] Figure 2 This is a schematic diagram of the three-spring bonded particle model proposed by the method of this invention;

[0077] Figure 3 This is a schematic diagram of a typical circular unit-circular unit contact pair proposed by the method of this invention;

[0078] Figure 4 This is a diagram of the computational model in an embodiment of the method of the present invention; wherein, Figure 4 (a) is a diagram of the initial two-dimensional DDDA numerical model constructed in the embodiment; Figure 4 (b) is the two-dimensional DDDA numerical model constructed in the embodiment; Figure 4 (c) is the numerical model of the three-spring bonded circular element DDA constructed in the embodiment;

[0079] Figure 5 This is a schematic diagram of the parameter calibration process in the embodiment of the method of the present invention;

[0080] Figure 6 This is a comparison diagram of the numerical test results and physical test results of the single-crack Brazilian circular unit splitting in the embodiment of the method of the present invention;

[0081] Figure 7 This is a comparison chart of numerical test results and physical test results of uniaxial compression progressive failure of square specimens with cross-cracks in the embodiments of the present invention;

[0082] Figure 8 These are numerical results of the progressive failure process of brittle-elastic materials in the engineering field in the embodiments of the method of the present invention. Detailed Implementation

[0083] This invention provides a numerical simulation method and system for the progressive failure process of elastobrittle materials based on DDDA, the flowchart of which is shown below. Figure 1 As shown, it includes the following steps:

[0084] S1. Based on the geometric parameters of real brittle-elastic material specimens, construct an initial two-dimensional DDDA numerical model;

[0085] Step S1 is as follows:

[0086] An initial two-dimensional DDDA numerical model is constructed based on the geometric parameters of real elastobrittle materials;

[0087] The initial two-dimensional DDDA numerical model uses rigid circular elements as the basic computational units. Each circular element has three degrees of freedom, denoted as:

[0088]

[0089] in For the displacement of the circular element; This represents the translation of the center of the circular element in the x-direction; This represents the translation of the center of the circular element in the y-direction. The angle of rotation of a circular element around its center;

[0090] The discontinuous deformation analysis of the circular element adopts an implicit solution method. In each time step of the stepwise time integration, the overall equilibrium equation is constructed based on the principle of minimum potential energy.

[0091] The overall equilibrium equation is expressed by the following formula:

[0092]

[0093] Among them, when hour, Let be the interaction stiffness submatrix between circular element i and circular element j, and the interaction stiffness submatrix be... matrix; Let i be the radius correlation matrix of the circular element i, and the radius correlation matrix is: matrix; Let be the unknown quantum matrix of the displacement of circular element i, denoted as ,in Let i be the circular element i with displacement in the x-direction. Let i be the circular element i with displacement in the y direction. Let i be the angle of rotation of the circular element i around its center; Let i be a generalized force quantum array of circular element i, denoted as ,in Let i be the generalized force in the x-direction of the circular element i. Let i be the generalized force in the y-direction of the circular element i. The generalized force is the force around the center of the circular element i;

[0094] In each calculation step, the discontinuous deformation analysis of the circular element assembles a set of simultaneous equilibrium equations based on the information of the contact pairs and various external loads acting on the circular element system; solves the set of equations to obtain the displacement increment of the circular element; and updates the calculation model data, including the velocity and coordinates of the circular element and the interaction forces between the circular elements.

[0095] S2. Based on the compression-tension ratio of real elastic-brittle materials, the circular elements in the two-dimensional DDDA numerical model obtained in step S1 are grouped to obtain the two-dimensional DDDA numerical model.

[0096] Step S2 is as follows: Based on the compression-tension ratio of the real elastic-brittle material, the outer contour of the initial two-dimensional DDDA numerical model is used as the boundary. Circular elements are grouped based on spatial position or other criteria related to the compression-tension ratio. The discrete particles in the initial two-dimensional DDDA numerical model are divided into multiple particle groups. Particles in the same particle group are configured to cooperate in responding to mechanical behaviors related to the compression-tension ratio in subsequent simulations, and finally, a two-dimensional DDDA numerical model is obtained.

[0097] Specifically, the criteria based on spatial location or other factors related to the compressibility-to-pull ratio include grouping based on the Thiessen polygon mesh.

[0098] S3. Bond the circular elements in the two-dimensional DDDA numerical model, add bonded elements, and obtain a three-spring bonded circular element DDA numerical model;

[0099] Step S3 specifically involves bonding the circular elements in the two-dimensional DDDA numerical model, adding bonding elements, and obtaining a three-spring bonded circular element DDA numerical model.

[0100] The three-spring bonded circular element DDA numerical model is a bonding contact model between circular elements. It uses three springs as load-bearing elements to bond discrete circular elements into a whole. Figure 2 As shown; the three springs include one tangential spring and two normal springs;

[0101] Based on the principle of minimum potential energy, the tangential spring sub-matrix is ​​superimposed into the simultaneous equilibrium equations, and expressed by the following formula:

[0102]

[0103] in, This refers to the tangential spring stiffness; This is the cumulative relative displacement of the tangential spring connection endpoints in the tangential direction at the start of the time step; It is the first intermediate matrix, and ; This is the second intermediate matrix, and ; Let x be the x-direction component of the tangential direction vector between circular element i and circular element j; Let y be the tangential direction vector of circular element i and circular element j; Let be the radius of the circular element i;

[0104] Based on the principle of minimum potential energy, the normal spring submatrix is ​​superimposed into the simultaneous equilibrium equations, and expressed by the following formula:

[0105]

[0106] in, Normal spring stiffness; It is the third intermediate matrix, and ; The distance between the normal spring and the center line of the bonding unit. The width of the bonding unit is , ; Let be the radius of the circular element i; Let be the radius of the circular element j; This is the cumulative relative displacement of the connection endpoint of the normal spring 1 in the normal direction;

[0107] The elastic-brittle constitutive model is used as the bond failure criterion, and the following three sub-criteria are used sequentially to determine whether the bonded elements have failed:

[0108]

[0109] in, This is the input value for the tensile strength of the bonded unit; This is the input value for the internal friction angle; This is the input value for cohesion; The normal spring compression; when hour, ,otherwise .

[0110] When the criteria determine that at least one spring has broken, the bonding unit is considered to have failed. After the bond between two bonded circular units fails, these two circular units will be considered a normal circular unit-circle unit contact pair, such as... Figure 3 As shown, its normal contact submatrix is:

[0111]

[0112] in, It is the normal spring stiffness between circular element i and circular element j; It is the fourth intermediate matrix, and ; It is the fifth intermediate matrix, and ; The x-coordinate of the connection point between the normal spring and circular element i; Let x be the x-coordinate of the connection point between the normal spring and the circular element j; The y-coordinate of the connection point between the normal spring and circular element i; The y-coordinate of the connection point between the normal spring and the circular element j;

[0113] For a typical circular element-to-circular element contact pair, the tangential contact submatrix is:

[0114]

[0115] in, Let be the tangential spring stiffness between circular element i and circular element j; Let i be the displacement transformation matrix of the circular element i; , Let i be the center coordinates of the circular element i; , Let be the center coordinates of circular element i.

[0116] S4. Using the mechanical parameters of real brittle-elastic material specimens as a reference, calibrate the input parameters of the three-spring bonded circular element DDA numerical model;

[0117] Step S4 is as follows:

[0118] The input parameters of the three-spring bonded circular element DDA numerical model are calibrated based on the mechanical parameters of real brittle-elastic material specimens.

[0119] The input parameter calibration includes the calibration of elastic parameters and the calibration of strength parameters;

[0120] The elasticity parameter includes the Poisson's ratio input value. With elastic modulus input value The correspondence between the elastic parameters and the normal spring stiffness and tangential spring stiffness in the DDA numerical model of the three-spring bonded circular element is as follows:

[0121]

[0122] in, It is half the width of the bonding unit; H represents the initial length of the bonding unit; H represents the thickness of the entire model.

[0123] The calibration of the elastic parameter includes the following steps:

[0124] (1) Establish a numerical sample with an aspect ratio of 2, with a particle number of 6000~10000, and the radius range and distribution of the circular elements in the sample are consistent with the calculation model;

[0125] (2) Let Equivalent to the elastic modulus of real brittle and elastic materials Using several different Poisson ratios Numerical experiments were conducted to obtain several sets of results. and Data, including Poisson's ratio for real brittle-elastic materials;

[0126] (3) Based on the Logistic function, fit the result. Relationships and The Logistic function of the relation, the expression of which is:

[0127]

[0128] Where x is the independent variable and y is the dependent variable; The first coefficient to be determined; The second undetermined coefficient; p is the third undetermined coefficient; p is the fourth undetermined coefficient;

[0129] (4) Obtained through fitting Relational Logistic Function and The relational Logistic function calculates the specified... corresponding and the corresponding Thus, the specified calculation is obtained. corresponding ;

[0130] (5) Using the calculated and Conduct a numerical experiment to verify the results. and Check if the value is the specified value; if it meets the requirements, end the elastic parameter calibration. Otherwise, use the values ​​obtained from this numerical experiment. and Add the data to the dataset and fit it again. Relationships and The relation is represented by the Logistic function, and the result is returned to step (4).

[0131] The strength parameter includes the input value of the tensile strength of the bonding unit. Input value of internal friction angle Input values ​​for cohesion ;

[0132] The calibration of the strength parameters is specifically as follows:

[0133] Keep the Poisson ratio input value and elastic modulus input value Keep it unchanged, by adjusting the tensile strength input value and cohesion input values This makes the compressive strength of the numerical model... With tensile strength The compressive and tensile strengths correspond to those of real brittle and elastic materials.

[0134] The calibration of the strength parameters includes the following steps:

[0135] The circular unit groups in step S2 are bonded together, and the circular unit groups are bonded to each other again. The units within each circular unit group are also bonded together. Increase 10 times;

[0136] Take the input value of the internal friction angle The value is between 30° and 50°, and the input value is the tensile strength of the bonded unit. To obtain 1.54 times the specified tensile strength, a single direct tensile test was performed on the numerical specimen, yielding... ,Sure Given a linear function expression, calculate the specified... corresponding ;

[0137] Take the input value of the internal friction angle For numerical samples with values ​​of 5, 20, 35, 50, 65, and 80, six uniaxial compression tests were conducted, resulting in six groups. The data is fitted using the Logistic function. Curve expression, calculate the specified curve. corresponding .

[0138] S5. Based on the actual working conditions of the target brittle-elastic material in actual engineering or experiments, add boundary conditions to the DDA numerical model of the three-spring bonded circular element to simulate the progressive failure process of the brittle-elastic material.

[0139] Step S5 is as follows:

[0140] Determine the input parameters of the numerical model;

[0141] Based on the actual working conditions of the target elastic-brittle material in actual engineering or experiments, the corresponding boundary conditions are applied to the numerical model.

[0142] Under the stated boundary conditions, the numerical model is driven to perform mechanical calculations, dynamically simulating the entire progressive failure process of the brittle-elastic material from initial deformation, microcrack initiation, propagation to macroscopic fracture, and acquiring dynamic change data such as displacement field, stress field and energy loss inside the model, thus completing the numerical simulation of the progressive failure process of the brittle-elastic material.

[0143] The boundary conditions include displacement boundary conditions, force / load boundary conditions, and velocity boundary conditions.

[0144] The present invention also provides a system for realizing the numerical simulation method and system for the progressive failure process of elastic-brittle materials based on DDDA, including a numerical model construction module, a model circular element grouping module, a three-spring bonding module, a model parameter calibration module, and a progressive failure simulation module for elastic-brittle materials;

[0145] The numerical model building module uses the geometric parameters of real elastobrittle material specimens as a reference to build an initial two-dimensional DDDA numerical model and uploads the data to the model circular element grouping module.

[0146] The model circular element grouping module, based on the received data and using the compression-tension ratio of real elastic-brittle materials as a benchmark, groups the circular elements in the two-dimensional DDDA numerical model to obtain the two-dimensional DDDA numerical model, and uploads the data to the three-spring bonding module.

[0147] The three-spring bonding module bonds the circular elements in the two-dimensional DDDA numerical model according to the received data, adds bonding elements, obtains the three-spring bonded circular element DDA numerical model, and uploads the data to the model parameter calibration module.

[0148] The model parameter calibration module calibrates the input parameters of the three-spring bonded circular element DDA numerical model based on the received data and the mechanical parameters of the real brittle-elastic material sample, and uploads the data to the brittle-elastic material progressive failure simulation module.

[0149] The progressive failure simulation module for brittle-elastic materials adds boundary conditions to the three-spring bonded circular element DDA numerical model based on the actual working conditions of the target brittle-elastic material in actual engineering or experiments, and simulates the progressive failure process of the brittle-elastic material.

[0150] The method of the present invention will be further described below with reference to an embodiment:

[0151] Based on the geometric parameters of the brittle-elastic material, a two-dimensional DDDA numerical model is constructed. Its basic computational unit is the rigid circular element, containing 17022 circular elements, such as... Figure 4 As shown in (a);

[0152] Based on the compressive-tensile ratio of 6.6 for this brittle-elastic material, it is divided into groups according to a Thiessen polygon mesh, with each group containing 6 to 12 circular elements. Figure 4 As shown in (b);

[0153] The particles are bonded together by adding bonding units, thus binding the discrete circular units into a whole, such as... Figure 4 As shown in (c);

[0154] According to the appendix Figure 3 The parameter calibration process in the document calibrates the input parameters. A flowchart is shown below. Figure 5 As shown;

[0155] After the input parameters are calibrated, a Brazilian splitting test is performed, and the results are compared with experimental phenomena, such as... Figure 6 As shown;

[0156] Furthermore, based on the above process, the initiation, propagation, and failure of uniaxial compression cracks in cross-cracked cement mortar specimens were also simulated, such as... Figure 7 As shown. Besides simulating the progressive failure of elastobrittle materials at the experimental scale, this invention can also be applied to engineering fields, such as simulating the progressive failure process of discontinuous jointed rock slopes during excavation and unloading. Figure 8 As shown.

[0157] While the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Any person skilled in the art can make many possible variations and modifications to the technical solutions of the present invention, or modify them into equivalent embodiments, without departing from the scope of the present invention. Therefore, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention, without departing from the scope of the present invention, should fall within the protection scope of the present invention.

Claims

1. A numerical simulation method for the progressive failure process of elastobrittle materials based on DDDA, characterized in that, Includes the following steps: S1. Based on the geometric parameters of real brittle-elastic material specimens, construct an initial two-dimensional DDDA numerical model; S2. Based on the compression-tension ratio of real elastic-brittle materials, the circular elements in the two-dimensional DDDA numerical model obtained in step S1 are grouped to obtain the two-dimensional DDDA numerical model. S3. Bond the circular elements in the two-dimensional DDDA numerical model, add bonded elements, and obtain a three-spring bonded circular element DDA numerical model; S4. Using the mechanical parameters of real brittle-elastic material specimens as a reference, calibrate the input parameters of the three-spring bonded circular element DDA numerical model; S5. Based on the actual working conditions of the target brittle-elastic material in actual engineering or experiments, add boundary conditions to the three-spring bonded circular element DDA numerical model to simulate the progressive failure process of the brittle-elastic material. Step S1 is as follows: Based on the geometric parameters of real elastobrittle materials, an initial two-dimensional DDDA numerical model is constructed; The initial two-dimensional DDDA numerical model uses rigid circular elements as the basic computational units. Each circular element has three degrees of freedom, denoted as: in For the displacement of the circular element; This represents the translation of the center of the circular element in the x-direction; This represents the translation of the center of the circular element in the y-direction; The angle of rotation of a circular element around its center; The initial two-dimensional DDDA numerical model adopts an implicit solution method, and in each time step of the stepwise time integration, the overall equilibrium equation is constructed based on the principle of minimum potential energy. The overall equilibrium equation is expressed by the following formula: Among them, when hour, Let be the interaction stiffness submatrix between circular element i and circular element j, and the interaction stiffness submatrix be... matrix; Let i be the radius correlation matrix of the circular element i, and the radius correlation matrix is: matrix; Let be the unknown quantum matrix of the displacement of circular element i, denoted as ,in Let i be the circular element i with displacement in the x-direction. Let i be the circular element i with displacement in the y direction. Let i be the angle of rotation of the circular element i around its center; Let i be a generalized force quantum array of circular element i, denoted as ,in Let i be the generalized force in the x-direction of the circular element i. Let i be the generalized force in the y-direction of the circular element i. The generalized force is the force around the center of the circular element i; In each calculation step, the discontinuous deformation analysis of the circular element assembles a set of simultaneous equilibrium equations based on the information of the contact pairs and various external loads acting on the circular element system; solves the set of equations to obtain the displacement increment of the circular element; Update the computational model data, including the velocity and coordinates of the circular elements and the interaction forces between the circular elements.

2. The numerical simulation method for the progressive failure process of elastobrittle materials based on DDDA according to claim 1, characterized in that, Step S2 is as follows: Based on the compression-tension ratio of the real elastic-brittle material, the outer contour of the initial two-dimensional DDDA numerical model is used as the boundary. Circular elements are grouped based on spatial position or other criteria related to the compression-tension ratio. The discrete particles in the initial two-dimensional DDDA numerical model are divided into multiple particle groups. Particles in the same particle group are configured to cooperate in responding to mechanical behaviors related to the compression-tension ratio in subsequent simulations, and finally, a two-dimensional DDDA numerical model is obtained.

3. The numerical simulation method for the progressive failure process of elastobrittle materials based on DDDA according to claim 1, characterized in that, Step S3 specifically involves bonding the circular elements in the two-dimensional DDDA numerical model, adding bonding elements, and obtaining a three-spring bonded circular element DDA numerical model. The three-spring bonded circular element DDA numerical model is a bonding contact model between circular elements, using three springs as load-bearing elements to bond discrete circular elements into a whole; the three springs include one tangential spring and two normal springs. Based on the principle of minimum potential energy, the tangential spring sub-matrix is ​​superimposed into the simultaneous equilibrium equations, and expressed by the following formula: in, This refers to the tangential spring stiffness; This is the cumulative relative displacement of the tangential spring connection endpoints in the tangential direction at the start of the time step; This is the first intermediate matrix, and ; It is the second intermediate matrix, and ; Let x be the x-direction component of the tangential direction vector between circular element i and circular element j; Let y be the tangential direction vector of circular element i and circular element j; Let be the radius of the circular element i; Based on the principle of minimum potential energy, the normal spring submatrix is ​​superimposed into the simultaneous equilibrium equations, and expressed by the following formula: in, Normal spring stiffness; It is the third intermediate matrix, and ; The distance between the normal spring and the center line of the bonding unit. The width of the bonding unit is , ; Let be the radius of the circular element j; This is the cumulative relative displacement of the connection endpoint of the normal spring 1 in the normal direction at the start of the time step; The elastic-brittle constitutive model is used as the criterion for bonded failure, and the following three sub-criteria are used sequentially to determine whether the bonded elements have failed: in, This is the input value for the tensile strength of the bonded unit; This is the input value for the internal friction angle; This is the input value for cohesion; The normal spring compression; when hour, ,otherwise .

4. The numerical simulation method for the progressive failure process of elastobrittle materials based on DDDA according to claim 3, characterized in that, When the judgment criteria determine that at least one spring has broken, the bonding unit is considered to have failed. After the bond between the two bonded circular units fails, these two circular units will be regarded as ordinary circular unit-circle unit contact pairs, and their normal contact sub-matrix is: in, It is the normal spring stiffness between circular element i and circular element j; It is the fourth intermediate matrix, and ; It is the fifth intermediate matrix, and ; The x-coordinate of the connection point between the normal spring and circular element i; Let x be the x-coordinate of the connection point between the normal spring and the circular element j; The y-coordinate of the connection point between the normal spring and circular element i; The y-coordinate of the connection point between the normal spring and the circular element j; For a typical circular element-to-circular element contact pair, the tangential contact submatrix is: in, Let be the tangential spring stiffness between circular element i and circular element j; Let i be the displacement transformation matrix of the circular element i; , Let i be the center coordinates of the circular element i; , Let be the center coordinates of the circular element j.

5. The numerical simulation method for the progressive failure process of elastobrittle materials based on DDDA according to claim 1, characterized in that, Step S4 is as follows: The input parameters of the three-spring bonded circular element DDA numerical model are calibrated based on the mechanical parameters of real brittle-elastic material specimens. The input parameter calibration includes the calibration of elastic parameters and the calibration of strength parameters; The elasticity parameter includes the Poisson's ratio input value. With elastic modulus input value The correspondence between the elastic parameters and the normal spring stiffness and tangential spring stiffness in the DDA numerical model of the three-spring bonded circular element is as follows: in, It is half the width of the bonding unit; H represents the initial length of the bonding unit; H represents the thickness of the entire model. The calibration of the elastic parameter includes the following steps: (1) Establish a numerical sample with an aspect ratio of 2, with a particle number of 6000~10000, and the radius range and distribution of the circular elements in the sample are consistent with the calculation model; (2) Let Equivalent to the elastic modulus of real brittle and elastic materials Using several different Poisson ratios Numerical experiments were conducted to obtain several sets of results. and Data, including Poisson's ratio for real brittle-elastic materials; (3) Based on the Logistic function, fit the result. Relationships and The Logistic function of the relation, the expression of which is: Where x is the independent variable and y is the dependent variable; The first coefficient to be determined; The second undetermined coefficient; p is the third undetermined coefficient; p is the fourth undetermined coefficient; (4) Obtained through fitting Relational Logistic Function and The relational Logistic function calculates the specified... corresponding and the corresponding Thus, the specified calculation is obtained. corresponding ; (5) Using the calculated and Conduct a numerical experiment to verify the results. and Is it a specified value? If it meets the requirements, then end the elastic parameter calibration; otherwise, use the values ​​obtained from this numerical experiment. and Add the data to the dataset and fit it again. Relationships and The relation is represented by the Logistic function, and the result is returned to step (4).

6. The numerical simulation method for the progressive failure process of elastobrittle materials based on DDDA according to claim 5, characterized in that, The strength parameter includes the input value of the tensile strength of the bonding unit. Input value of internal friction angle Input values ​​for cohesion ; The calibration of the strength parameters is specifically as follows: Keep the Poisson ratio input value and elastic modulus input value Keep it unchanged, by adjusting the tensile strength input value and cohesion input values This makes the compressive strength of the numerical model... With tensile strength Corresponding to the compressive and tensile strengths of real brittle and elastic materials; The calibration of the strength parameters includes the following steps: The circular unit groups in step S2 are bonded together, and the circular unit groups are bonded to each other again. The units within each circular unit group are also bonded together. Increase 10 times; Take the input value of the internal friction angle The value is between 30° and 50°, and the input value is the tensile strength of the bonded unit. To obtain 1.54 times the specified tensile strength, a single direct tensile test was performed on the numerical specimen, yielding... ,Sure Given a linear function expression, calculate the specified... corresponding ; Take the input value of the internal friction angle For numerical samples with values ​​of 5, 20, 35, 50, 65, and 80, six uniaxial compression tests were conducted, resulting in six groups. The data is fitted using the Logistic function. Curve expression, calculate the specified curve. corresponding .

7. The numerical simulation method for the progressive failure process of elastobrittle materials based on DDDA according to claim 1, characterized in that, Step S5 is as follows: Determine the input parameters of the numerical model; Based on the actual working conditions of the target elastic-brittle material in actual engineering or experiments, the corresponding boundary conditions are applied to the numerical model. Under the boundary conditions, the numerical model is driven to perform mechanical calculations, dynamically simulating the entire process of progressive failure of the elastic-brittle material from initial deformation, microcrack initiation, propagation to macroscopic fracture, and acquiring dynamic change data such as displacement field, stress field and energy loss inside the model, thus completing the numerical simulation of the progressive failure process of the elastic-brittle material. The boundary conditions include displacement boundary conditions, force / load boundary conditions, and velocity boundary conditions.

8. A system for implementing the numerical simulation method for the progressive failure process of elastobrittle materials based on DDDA as described in any one of claims 1 to 7, characterized in that, It includes a numerical model construction module, a model circular element grouping module, a three-spring bonding module, a model parameter calibration module, and a progressive failure simulation module for elastobrittle materials; The numerical model building module uses the geometric parameters of real elastobrittle material specimens as a reference to build an initial two-dimensional DDDA numerical model and uploads the data to the model circular element grouping module. The model circular element grouping module, based on the received data and using the compression-tension ratio of real elastic-brittle materials as a benchmark, groups the circular elements in the two-dimensional DDDA numerical model to obtain the two-dimensional DDDA numerical model, and uploads the data to the three-spring bonding module. The three-spring bonding module bonds the circular elements in the two-dimensional DDDA numerical model according to the received data, adds bonding elements, obtains the three-spring bonded circular element DDA numerical model, and uploads the data to the model parameter calibration module. The model parameter calibration module calibrates the input parameters of the three-spring bonded circular element DDA numerical model based on the received data and the mechanical parameters of the real brittle-elastic material sample, and uploads the data to the brittle-elastic material progressive failure simulation module. The progressive failure simulation module for brittle-elastic materials adds boundary conditions to the three-spring bonded circular element DDA numerical model based on the actual working conditions of the target brittle-elastic material in actual engineering or experiments, and simulates the progressive failure process of the brittle-elastic material.

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