DDDA-based elastic and brittle material progressive failure process numerical simulation method and system

Abstract

The invention discloses a DDDA-based numerical simulation method and a DDDA-based numerical simulation system for a progressive failure process of an elastic and brittle material. The method comprises the following steps: S1, constructing a two-dimensional DDDA numerical model consistent with a real elastic and brittle material sample in geometric size by taking the geometric parameters of the real elastic and brittle material sample as a reference; s2, grouping the circle units in the established numerical model by taking the compression-draw ratio of the real elastic and brittle material as a reference; s3, based on the proposed three-spring bonding circle unit model, bonding the circle units, and adding bonding units; s4, calibrating input parameters of the numerical model by taking the mechanical parameters of the real elastic and brittle material sample as a reference; and S5, according to a calibration result, adding boundary conditions to the numerical model, and simulating a progressive failure process of the elastic and brittle material. According to the method, the progressive failure process of the elastic and brittle material is accurately predicted, and the method has the characteristics of high simulation precision and high practicability.

Description

Technical Field

[0001] The present invention belongs to the field of computational mechanics and elastic-brittle material simulation, and particularly relates to a DDDA-based numerical simulation method and system for the progressive failure process of elastic-brittle materials. Background Art

[0002] Brittle materials, such as rock, concrete, ceramics, and glass, are found in almost all common engineering projects. The destruction of brittle materials, including the initiation and propagation of cracks in intact or fractured materials, is very common in engineering projects. This type of destruction can accumulate to form a through-sliding surface, creating conditions for large displacements of the sliding body and easily causing disasters. Taking rock mass engineering as an example, the initiation and propagation of cracks in intact rock or fractured rock mass often trigger geological disasters such as rockfall, collapse, landslide, and tunnel collapse after forming a through-sliding surface. Revealing the failure mechanism of brittle materials helps predict the location of crack initiation and the path of crack propagation, so as to take 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 approaches for 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 the propagation of multiple cracks in materials. 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. The basic computational unit of both methods is a discrete block. A bonding model is required to bond the discrete blocks together into a whole. When the failure condition is met, crack propagation is simulated by destroying the bond between the two bonded blocks. Compared with DEM, DDA has the following advantages: 1. Higher solution accuracy; 2. No need for very small time steps and 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 the computational efficiency is low. Summary of the Invention

[0005] In view of the shortcomings of the existing technology, one of the objectives of the present invention is to provide a numerical simulation method and system for the progressive failure process of elastic-brittle materials based on the circular element discontinuous deformation analysis method (DDDA), which can accurately predict the progressive failure process of elastic-brittle materials and has the characteristics of high simulation accuracy and strong practicality.

[0006] A second object of the present invention is to provide a system for realizing the numerical simulation method and system of the progressive failure process of elastic-brittle materials based on DDDA.

[0007] The present invention provides a method and system for numerically simulating the progressive failure process of elastic-brittle materials based on DDDA, comprising the following steps:

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

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

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

[0011] S4. Calibrate the input parameters of the three-spring bonded circular element DDA numerical model using the mechanical parameters of real elastic-brittle material specimens as a benchmark;

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

[0013] Step S1 is specifically as follows:

[0014] According to the geometric parameters of the real elastic-brittle material, the initial two-dimensional DDDA numerical model is constructed;

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

[0016] in is the displacement of the circular element; is the translation of the center of the circular unit in the x direction; is the translation of the center of the circular unit in the y direction; is the rotation angle of the circular element around its center.

[0017] The circular element discontinuous deformation analysis adopts an implicit solution method, and in each time step of the stepwise time integration, the overall equilibrium equation is constructed based on the minimum potential energy principle;

[0018] The overall balance equation is expressed as follows:

[0019] Among them, when hour, is the interaction stiffness submatrix between circular element i and circular element j, and the interaction stiffness submatrix is matrix; is the radius correlation matrix of circular unit i, and the radius correlation matrix is matrix; is the unknown quantum matrix of the displacement of circular unit i, denoted as ,in is the displacement of circular element i in the x direction, is the displacement of circular element i in the y direction, is the rotation angle of circular unit i around its center; is the generalized force matrix of circular unit i, denoted as ,in is the generalized force of circular element i in the x-direction, is the generalized force of circular element i in the y direction, is the generalized force of circular element i around its center;

[0020] In each calculation step, the circular element discontinuous deformation analysis assembles a set of simultaneous equilibrium equations based on information about contact pairs and various external loads acting on the circular element system; solves the equations to obtain the displacement increments of the circular elements; and updates the calculation model data, including the velocity and coordinates of the circular elements and the interaction forces between the circular elements.

[0021] Step S2 specifically comprises: based on the compression-to-tension ratio of the real elastic-brittle material, with the outer contour of the initial two-dimensional DDDA numerical model as the boundary, circular units are grouped based on spatial position or other criteria related to the compression-to-tension ratio performance, and the discrete particles in the initial two-dimensional DDDA numerical model are divided into multiple particle groups, wherein the particles in the same particle group are configured to synergistically respond to the mechanical behavior related to the compression-to-tension ratio in subsequent simulations, and finally a two-dimensional DDDA numerical model is obtained.

[0022] Specifically, the criteria based on spatial position or other criteria related to the compression-to-pull ratio performance include grouping based on Thiessen polygon meshes.

[0023] Step S3 specifically comprises: 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;

[0024] The three-spring bonded circular element DDA numerical model is a bonded contact model between circular elements, using three springs as load-bearing elements to bond discrete circular elements into a whole; the three springs include a tangential spring and two normal springs;

[0025] Based on the principle of minimum potential energy, the tangential spring submatrix is ​​superimposed on the simultaneous equilibrium equations and expressed using the following formula:

[0026] in, is the tangential spring stiffness; is the cumulative relative displacement of the tangential spring connection end points in the tangential direction at the beginning of the time step; is the first intermediate matrix, and ; is the second intermediate matrix, and ; is the x-direction component of the tangential direction vector of circular element i and circular element j; is the y-direction component of the tangential direction vector of circular element i and circular element j; is the radius of circular element i;

[0027] Based on the principle of minimum potential energy, the normal spring submatrix is ​​superimposed on the simultaneous equilibrium equations and expressed using the following formula:

[0028] in, is the normal spring stiffness; is the third intermediate matrix, and ; is the distance between the normal spring and the center line of the bonded element, ; The width of the bonding unit is , ; is the radius of circular element i; is the radius of circular element j; is the cumulative relative displacement of the connection end points of normal spring 1 in the normal direction;

[0029] The elastic-brittle constitutive model is used as the bond failure criterion, and the following three sub-criterions are used in sequence to determine whether the bond element has failed:

[0030] in, is the input value of the tensile strength of the bonded element; is the input value of the internal friction angle; is the input value of cohesion; is the normal spring compression; when hour, ,otherwise .

[0031] When at least one spring is broken according to the judgment criteria, the bonded element is considered to be broken. After the bond between the two bonded circular elements is broken, the two circular elements will be regarded as ordinary circular element-circular element contact pairs, and their normal contact submatrix is:

[0032] in, is the normal spring stiffness between circular element i and circular element j; is the fourth intermediate matrix, and ; is the fifth intermediate matrix, and ; is the x-coordinate of the connection point between the normal spring and circular element i; is the x-coordinate of the connection point between the normal spring and circular element j; is the y-coordinate of the connection point between the normal spring and the circular element i; is the y coordinate of the connection point between the normal spring and the circular element j;

[0033] For a normal circular element-circular element contact pair, the tangential contact submatrix is:

[0034] in, is the tangential spring stiffness between circular element i and circular element j; is the displacement transformation matrix of circular unit i; , is the center coordinate of circular unit i; , is the center coordinate of circular unit i.

[0035] Step S4 is specifically as follows:

[0036] The input parameters of the DDA numerical model of three-spring bonded circular elements are calibrated based on the mechanical parameters of real elastic-brittle material specimens.

[0037] The input parameter calibration includes calibration of elastic parameters and calibration of strength parameters;

[0038] Elastic parameters including Poisson's ratio input and elastic modulus input value , the corresponding relationship 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:

[0039] in, is half the width of the bonding unit; is the initial length of the bonding unit; H is the thickness of the entire model;

[0040] The calibration of the elastic parameters comprises the following steps:

[0041] (1) A numerical sample with an aspect ratio of 2 was established, with the number of particles ranging from 6000 to 10000. The radius range and distribution of the circular units in the sample were consistent with the calculation model;

[0042] (2) Order Equal to the elastic modulus of the real elastic-brittle material , using several different Poisson's ratios , numerical experiments were carried out respectively, and several groups of and data, where is the Poisson's ratio of the real elastic-brittle material;

[0043] (3) Based on the Logistic function, fit the Relationships and The Logistic function of the relationship, the Logistic function expression is:

[0044] Among them, x is the independent variable; y is the dependent variable; is the first undetermined coefficient; is the second undetermined coefficient; is the third undetermined coefficient; p is the fourth undetermined coefficient;

[0045] (4) Obtained by fitting Relationship between Logistic function and Relational Logistic function, calculated to obtain the specified Corresponding , and the Corresponding , thus calculating the specified Corresponding ;

[0046] (5) Using the calculated and , a numerical experiment is conducted to verify the obtained and Is it the specified value? If it meets the requirements, the elastic parameter calibration is ended. Otherwise, the value obtained in this numerical test is and Add data to the dataset and fit again Relationships and Logistic function of the relationship and return to step (4).

[0047] The strength parameters include the input value of the tensile strength of the bonding element , input value of internal friction angle , input value of cohesion ;

[0048] The calibration of the intensity parameters is specifically as follows:

[0049] Maintain Poisson's ratio input value and elastic modulus input value unchanged, by adjusting the tensile strength input value and the input value of cohesion , so that the compressive strength of the numerical model and tensile strength Corresponding to the compressive strength and tensile strength of real elastic-brittle materials.

[0050] The calibration of the intensity parameters comprises the following steps:

[0051] The circular unit groups in step S2 are bonded, the circular unit groups are bonded again, and the bonding units inside the circular unit groups are bonded. Increased 10 times;

[0052] Take the input value of the internal friction angle A value between 30° and 50° is used as the input value of the tensile strength of the bonding unit. The tensile strength is 1.54 times of the specified tensile strength. A direct tensile test is carried out on the numerical sample, and the result is ,Sure The linear function expression of Corresponding ;

[0053] Take the input value of the internal friction angle The values ​​are 5, 20, 35, 50, 65 and 80, and 6 uniaxial compression tests are carried out on the numerical samples to obtain 6 groups of Data is fitted by Logistic function Curve expression, calculate the specified Corresponding .

[0054] Step S5 is specifically as follows:

[0055] Determine the input parameters of the numerical model;

[0056] According to the actual working conditions of the target elastic-brittle material in actual engineering or experiments, corresponding boundary conditions are applied to the numerical model;

[0057] Under the boundary conditions, the numerical model is driven to perform mechanical calculations, dynamically simulating the entire progressive destruction process of the elastic-brittle material from initial deformation, microcrack initiation and expansion to macroscopic fracture, and obtaining dynamic change data such as the displacement field, stress field and energy loss inside the model to complete the numerical simulation of the progressive destruction process of the elastic-brittle material.

[0058] The boundary conditions include displacement boundary conditions, force / load boundary conditions, and velocity boundary conditions.

[0059] The present invention also provides a system for realizing the numerical simulation method and system of the progressive failure process of elastic-brittle materials based on DDDA, comprising a numerical model construction module, a model circular unit grouping module, a three-spring bonding module, a model parameter calibration module, and an elastic-brittle material progressive failure simulation module;

[0060] The numerical model construction module uses the geometric parameters of the real elastic-brittle material specimen as a benchmark to construct the initial two-dimensional DDDA numerical model and upload the data to the model circular unit grouping module;

[0061] The model circular element grouping module groups the circular elements in the two-dimensional DDDA numerical model based on the received data and the compression-tension ratio of the real elastic-brittle material, obtains the two-dimensional DDDA numerical model, and uploads the data to the three-spring bonding module;

[0062] The three-spring bonding module bonds the circular elements in the two-dimensional DDDA numerical model based on 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;

[0063] 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 elastic-brittle material specimen, and uploads the data to the elastic-brittle material progressive failure simulation module;

[0064] The progressive failure simulation module for brittle materials adds boundary conditions to the three-spring bonded circular element DDA numerical model based on the actual working conditions of the target brittle material in actual engineering or experiments to simulate the progressive failure process of the brittle material.

[0065] The present invention discloses a numerical simulation method and system for the progressive failure process of elastic-brittle materials based on DDDA. The method of the present invention provides effective principles, algorithms, processes and program operation equipment for exploring the fracture failure mechanism of elastic-brittle materials, realizes accurate prediction of the progressive failure process of elastic-brittle materials, and has the characteristics of high simulation accuracy and strong practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 It is a schematic flow diagram of the method of the present invention;

[0067] Figure 2 Schematic diagram of the three-spring bonded particle model proposed by the method of the present invention;

[0068] Figure 3 This is a schematic diagram of a common circular element-circular element contact pair proposed by the method of the present invention;

[0069] Figure 4 is a calculation model diagram 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 a two-dimensional DDDA numerical model constructed in the embodiment; Figure 4 (c) is the DDA numerical model of three-spring bonded circular elements constructed in the embodiment;

[0070] Figure 5 1 is a schematic diagram of a parameter calibration process in an embodiment of the method of the present invention;

[0071] Figure 6 1 is a comparison chart of numerical test results and physical experimental results of splitting of a single-crack Brazilian circle element in an embodiment of the method of the present invention;

[0072] Figure 7 1. This is a comparison chart of numerical test results of progressive failure of uniaxial compression of square specimens with cross cracks and physical test results in an embodiment of the method of the present invention;

[0073] Figure 8 It is the numerical result of the progressive failure process of elastic-brittle materials in the engineering field in the embodiment of the method of the present invention. DETAILED DESCRIPTION

[0074] The present invention provides a numerical simulation method and system for the progressive failure process of elastic-brittle materials based on DDDA, the flow diagram of which is shown in FIG. Figure 1 As shown, the following steps are included:

[0075] S1. Based on the geometric parameters of real elastic-brittle material specimens, an initial two-dimensional DDDA numerical model is constructed;

[0076] Step S1 is specifically as follows:

[0077] According to the geometric parameters of the real elastic-brittle material, the initial two-dimensional DDDA numerical model is constructed;

[0078] The initial two-dimensional DDDA numerical model uses rigid circular elements as basic calculation units. Each circular element has three degrees of freedom, which are expressed as:

[0079] in is the displacement of the circular element; is the translation of the center of the circular unit in the x direction; is the translation of the center of the circular unit in the y direction; is the rotation angle of the circular unit around its center;

[0080] The circular element discontinuous deformation analysis adopts an implicit solution method, and in each time step of the stepwise time integration, the overall equilibrium equation is constructed based on the minimum potential energy principle;

[0081] The overall balance equation is expressed as follows:

[0082] Among them, when hour, is the interaction stiffness submatrix between circular element i and circular element j, and the interaction stiffness submatrix is matrix; is the radius correlation matrix of circular unit i, and the radius correlation matrix is matrix; is the unknown quantum matrix of the displacement of circular unit i, denoted as ,in is the displacement of circular element i in the x direction, is the displacement of circular element i in the y direction, is the rotation angle of circular unit i around its center; is the generalized force matrix of circular unit i, denoted as ,in is the generalized force of circular element i in the x-direction, is the generalized force of circular element i in the y direction, is the generalized force of circular element i around its center;

[0083] In each calculation step, the circular element discontinuous deformation analysis assembles a set of simultaneous equilibrium equations based on information about contact pairs and various external loads acting on the circular element system; solves the equations to obtain the displacement increments of the circular elements; and updates the calculation model data, including the velocity and coordinates of the circular elements and the interaction forces between the circular elements.

[0084] S2. Based on the compression-tension ratio of the real elastic-brittle material, the circular elements in the two-dimensional DDDA numerical model obtained in step S1 are grouped to obtain a two-dimensional DDDA numerical model;

[0085] Step S2 specifically comprises: based on the compression-to-tension ratio of the real elastic-brittle material, with the outer contour of the initial two-dimensional DDDA numerical model as the boundary, circular units are grouped based on spatial position or other criteria related to the compression-to-tension ratio performance, and the discrete particles in the initial two-dimensional DDDA numerical model are divided into multiple particle groups, wherein the particles in the same particle group are configured to synergistically respond to the mechanical behavior related to the compression-to-tension ratio in subsequent simulations, and finally a two-dimensional DDDA numerical model is obtained.

[0086] Specifically, the criteria based on spatial position or other criteria related to the compression-to-pull ratio performance include grouping based on Thiessen polygon meshes.

[0087] S3. Bond the circular element in the two-dimensional DDDA numerical model and add bonded elements to obtain a three-spring bonded circular element DDA numerical model;

[0088] Step S3 specifically comprises: 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;

[0089] The three-spring bonded circular element DDA numerical model is a bonded contact model between circular elements, which uses three springs as load-bearing elements to bond discrete circular elements into a whole. Figure 2 As shown; the three springs include a tangential spring and two normal springs;

[0090] Based on the principle of minimum potential energy, the tangential spring submatrix is ​​superimposed on the simultaneous equilibrium equations and expressed using the following formula:

[0091] in, is the tangential spring stiffness; is the cumulative relative displacement of the tangential spring connection end points in the tangential direction at the beginning of the time step; is the first intermediate matrix, and ; is the second intermediate matrix, and ; is the x-direction component of the tangential direction vector of circular element i and circular element j; is the y-direction component of the tangential direction vector of circular element i and circular element j; is the radius of circular element i;

[0092] Based on the principle of minimum potential energy, the normal spring submatrix is ​​superimposed on the simultaneous equilibrium equations and expressed using the following formula:

[0093] in, is the normal spring stiffness; is the third intermediate matrix, and ; is the distance between the normal spring and the center line of the bonded element, ; The width of the bonding unit is , ; is the radius of circular element i; is the radius of circular element j; is the cumulative relative displacement of the connection end points of normal spring 1 in the normal direction;

[0094] The elastic-brittle constitutive model is used as the bond failure criterion, and the following three sub-criterions are used in sequence to determine whether the bond element has failed:

[0095] in, is the input value of the tensile strength of the bonded element; is the input value of the internal friction angle; is the input value of cohesion; is the normal spring compression; when hour, ,otherwise .

[0096] When at least one spring is broken according to the judgment criteria, the bonding unit is considered to be broken. After the bonding between the two bonded circular units is broken, the two circular units will be regarded as ordinary circular unit-circular unit contact pairs, such as Figure 3 As shown, its normal contact matrix is:

[0097] in, is the normal spring stiffness between circular element i and circular element j; is the fourth intermediate matrix, and ; is the fifth intermediate matrix, and ; is the x-coordinate of the connection point between the normal spring and circular element i; is the x-coordinate of the connection point between the normal spring and circular element j; is the y-coordinate of the connection point between the normal spring and the circular element i; is the y coordinate of the connection point between the normal spring and the circular element j;

[0098] For a normal circular element-circular element contact pair, the tangential contact submatrix is:

[0099] in, is the tangential spring stiffness between circular element i and circular element j; is the displacement transformation matrix of circular unit i; , is the center coordinate of circular unit i; , is the center coordinate of circular unit i.

[0100] S4. Calibrate the input parameters of the three-spring bonded circular element DDA numerical model using the mechanical parameters of real elastic-brittle material specimens as a benchmark;

[0101] Step S4 is specifically as follows:

[0102] The input parameters of the DDA numerical model of three-spring bonded circular elements are calibrated based on the mechanical parameters of real elastic-brittle material specimens.

[0103] The input parameter calibration includes calibration of elastic parameters and calibration of strength parameters;

[0104] Elastic parameters including Poisson's ratio input and elastic modulus input value , the corresponding relationship 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:

[0105] in, is half the width of the bonding unit; is the initial length of the bonding unit; H is the thickness of the entire model;

[0106] The calibration of the elastic parameters comprises the following steps:

[0107] (1) A numerical sample with an aspect ratio of 2 was established, with the number of particles ranging from 6000 to 10000. The radius range and distribution of the circular units in the sample were consistent with the calculation model;

[0108] (2) Order Equal to the elastic modulus of the real elastic-brittle material , using several different Poisson's ratios , numerical experiments were carried out respectively, and several groups of and data, where is the Poisson's ratio of the real elastic-brittle material;

[0109] (3) Based on the Logistic function, fit the Relationships and The Logistic function of the relationship, the Logistic function expression is:

[0110] Among them, x is the independent variable; y is the dependent variable; is the first undetermined coefficient; is the second undetermined coefficient; is the third undetermined coefficient; p is the fourth undetermined coefficient;

[0111] (4) Obtained by fitting Relationship between Logistic function and Relational Logistic function, calculated to obtain the specified Corresponding , and the Corresponding , thus calculating the specified Corresponding ;

[0112] (5) Using the calculated and , a numerical experiment is conducted to verify the obtained and Is it the specified value? If it meets the requirements, the elastic parameter calibration ends. Otherwise, the value obtained in this numerical test is and Add data to the dataset and fit again Relationships and Logistic function of the relationship and return to step (4).

[0113] The strength parameters include the input value of the tensile strength of the bonding element , input value of internal friction angle , input value of cohesion ;

[0114] The calibration of the intensity parameters is specifically as follows:

[0115] Maintain Poisson's ratio input value and elastic modulus input value unchanged, by adjusting the tensile strength input value and the input value of cohesion , so that the compressive strength of the numerical model and tensile strength Corresponding to the compressive strength and tensile strength of real elastic-brittle materials.

[0116] The calibration of the intensity parameters comprises the following steps:

[0117] The circular unit groups in step S2 are bonded, the circular unit groups are bonded again, and the bonding units inside the circular unit groups are bonded. Increased 10 times;

[0118] Take the input value of the internal friction angle A value between 30° and 50° is used as the input value of the tensile strength of the bonding unit. The tensile strength is 1.54 times of the specified tensile strength. A direct tensile test is carried out on the numerical sample, and the result is ,Sure The linear function expression of Corresponding ;

[0119] Take the input value of the internal friction angle The values ​​are 5, 20, 35, 50, 65 and 80, and 6 uniaxial compression tests are carried out on the numerical samples to obtain 6 groups of Data is fitted by Logistic function Curve expression, calculate the specified Corresponding .

[0120] S5. Based on the actual working conditions of the target elastic-brittle material in actual engineering or experiments, boundary conditions are added to the three-spring bonded circular element DDA numerical model to simulate the progressive failure process of the elastic-brittle material.

[0121] Step S5 is specifically as follows:

[0122] Determine the input parameters of the numerical model;

[0123] According to the actual working conditions of the target elastic-brittle material in actual engineering or experiments, corresponding boundary conditions are applied to the numerical model;

[0124] Under the boundary conditions, the numerical model is driven to perform mechanical calculations, dynamically simulating the entire progressive destruction process of the elastic-brittle material from initial deformation, microcrack initiation and expansion to macroscopic fracture, and obtaining dynamic change data such as the displacement field, stress field and energy loss inside the model to complete the numerical simulation of the progressive destruction process of the elastic-brittle material.

[0125] The boundary conditions include displacement boundary conditions, force / load boundary conditions, and velocity boundary conditions.

[0126] The present invention also provides a system for realizing the numerical simulation method and system of the progressive failure process of elastic-brittle materials based on DDDA, comprising a numerical model construction module, a model circular unit grouping module, a three-spring bonding module, a model parameter calibration module, and an elastic-brittle material progressive failure simulation module;

[0127] The numerical model construction module uses the geometric parameters of the real elastic-brittle material specimen as a benchmark to construct the initial two-dimensional DDDA numerical model and upload the data to the model circular unit grouping module;

[0128] The model circular element grouping module groups the circular elements in the two-dimensional DDDA numerical model based on the received data and the compression-tension ratio of the real elastic-brittle material, obtains the two-dimensional DDDA numerical model, and uploads the data to the three-spring bonding module;

[0129] The three-spring bonding module bonds the circular elements in the two-dimensional DDDA numerical model based on 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;

[0130] 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 elastic-brittle material specimen, and uploads the data to the elastic-brittle material progressive failure simulation module;

[0131] The progressive failure simulation module for brittle materials adds boundary conditions to the three-spring bonded circular element DDA numerical model based on the actual working conditions of the target brittle material in actual engineering or experiments to simulate the progressive failure process of the brittle material.

[0132] The method of the present invention is further described below with reference to an embodiment:

[0133] According to the geometric parameters of elastic-brittle materials, a two-dimensional DDDA numerical model is constructed. Its basic calculation unit is a rigid circular unit, which contains 17022 circular units, such as Figure 4 (a)

[0134] According to the compression-tension ratio of the elastic-brittle material of 6.6, it is divided into groups according to the Thiessen polygon mesh, and the number of circular elements in each group is 6 to 12, such as Figure 4 (b)

[0135] Bond the particles, add bonding units, and bond the discrete circular units into a whole, such as Figure 4 (c)

[0136] According to the attached Figure 3 The parameter calibration process in the calibration is used to calibrate the input parameters. The flow chart is as follows Figure 5 As shown;

[0137] After the input parameters are calibrated, a Brazilian splitting test is performed on the equipment and compared with the experimental phenomena, such as Figure 6 As shown;

[0138] In addition, based on the above process, the uniaxial compression crack initiation, expansion and failure of cross-crack cement mortar specimens were also simulated, such as Figure 7 In addition to the experimental scale simulation of progressive failure of elastic-brittle materials, the present invention can also be applied to engineering fields, such as the simulation of the progressive failure process of discontinuous jointed rock slope excavation and unloading, as shown in Figure 8 shown.

[0139] Although the present invention has been disclosed above with reference to preferred embodiments, this is not intended to limit the present invention. Any person skilled in the art can, without departing from the scope of the technical solution of the present invention, utilize the technical content disclosed above to make many possible changes and modifications to the technical solution of the present invention, or modify it into an equivalent embodiment with equivalent changes. Therefore, any simple modification, equivalent change, and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the scope of protection of the technical solution of the present invention.

Claims

1. A numerical simulation method for the progressive failure process of elastic-brittle materials based on DDDA, characterized in that: The following steps are involved: S1. Based on the geometric parameters of real elastic-brittle material specimens, an initial two-dimensional DDDA numerical model is constructed; S2. Based on the compression-tension ratio of the real elastic-brittle material, the circular elements in the two-dimensional DDDA numerical model obtained in step S1 are grouped to obtain a two-dimensional DDDA numerical model; S3. Bond the circular element in the two-dimensional DDDA numerical model and add bonded elements to obtain a three-spring bonded circular element DDA numerical model; S4. Calibrate the input parameters of the three-spring bonded circular element DDA numerical model using the mechanical parameters of real elastic-brittle material specimens as a benchmark; S5. Based on the actual working conditions of the target elastic-brittle material in actual engineering or experiments, boundary conditions are added to the three-spring bonded circular element DDA numerical model to simulate the progressive failure process of the elastic-brittle material.

2. The numerical simulation method for the progressive failure process of elastic-brittle materials based on DDDA according to claim 1 is characterized in that: Step S1 is specifically as follows: According to the geometric parameters of the real elastic-brittle material, the initial two-dimensional DDDA numerical model is constructed; The initial two-dimensional DDDA numerical model uses rigid circular elements as basic calculation units. Each circular element has three degrees of freedom, which are expressed as: in is the displacement of the circular element; is the translation of the center of the circular unit in the x direction; is the translation of the center of the circular unit in the y direction; is the rotation angle of the circular element around its center.

3. The numerical simulation method for the progressive failure process of elastic-brittle materials based on DDDA according to claim 2 is characterized in that: The initial two-dimensional DDDA numerical model adopts an implicit solution method to construct the overall equilibrium equation based on the minimum potential energy principle in each time step of stepwise time integration; The overall balance equation is expressed as follows: Among them, when hour, is the interaction stiffness submatrix between circular element i and circular element j, and the interaction stiffness submatrix is matrix; is the radius correlation matrix of circular unit i, and the radius correlation matrix is matrix; is the unknown quantum matrix of the displacement of circular unit i, denoted as ,in is the displacement of circular element i in the x direction, is the displacement of circular element i in the y direction, is the rotation angle of circular unit i around its center; is the generalized force matrix of circular unit i, denoted as ,in is the generalized force of circular element i in the x-direction, is the generalized force of circular element i in the y direction, is the generalized force of circular element i around its center; In each calculation step, the circular element discontinuous deformation analysis assembles a set of simultaneous equilibrium equations based on information about contact pairs and various external loads acting on the circular element system; solves the equations to obtain the displacement increments of the circular elements; and updates the calculation model data, including the velocity and coordinates of the circular elements and the interaction forces between the circular elements.

4. The numerical simulation method for the progressive failure process of elastic-brittle materials based on DDDA according to claim 1 is characterized in that: Step S2 specifically comprises: based on the compression-to-tension ratio of the real elastic-brittle material, with the outer contour of the initial two-dimensional DDDA numerical model as the boundary, circular units are grouped based on spatial position or other criteria related to the compression-to-tension ratio performance, and the discrete particles in the initial two-dimensional DDDA numerical model are divided into multiple particle groups, wherein the particles in the same particle group are configured to synergistically respond to the mechanical behavior related to the compression-to-tension ratio in subsequent simulations, and finally a two-dimensional DDDA numerical model is obtained.

5. The numerical simulation method for the progressive failure process of elastic-brittle materials based on DDDA according to claim 1 is characterized in that: Step S3 specifically comprises: 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 bonded contact model between circular elements, using three springs as load-bearing elements to bond discrete circular elements into a whole; the three springs include a tangential spring and two normal springs; Based on the principle of minimum potential energy, the tangential spring submatrix is ​​superimposed on the simultaneous equilibrium equations and expressed using the following formula: in, is the tangential spring stiffness; is the cumulative relative displacement of the tangential spring connection end points in the tangential direction at the beginning of the time step; is the first intermediate matrix, and ; is the second intermediate matrix, and ; is the x-direction component of the tangential direction vector of circular element i and circular element j; is the y-direction component of the tangential direction vector of circular element i and circular element j; is the radius of circular element i; Based on the principle of minimum potential energy, the normal spring submatrix is ​​superimposed on the simultaneous equilibrium equations and expressed using the following formula: in, is the normal spring stiffness; is the third intermediate matrix, and ; is the distance between the normal spring and the center line of the bonded element, ; The width of the bonding unit is , ; is the radius of circular element j; is the cumulative relative displacement of the end points of the normal spring (1) in the normal direction at the beginning of the time step; The elastic-brittle constitutive model is used as the bond failure criterion, and the following three sub-criterions are used in sequence to determine whether the bond element has failed: in, is the input value of the tensile strength of the bonded element; is the input value of the internal friction angle; is the input value of cohesion; is the normal spring compression; when hour, ,otherwise .

6. The numerical simulation method for the progressive failure process of elastic-brittle materials based on DDDA according to claim 5 is characterized in that: When at least one spring is broken according to the judgment criteria, the bonded element is considered to be broken. After the bond between the two bonded circular elements is broken, the two circular elements will be regarded as ordinary circular element-circular element contact pairs, and their normal contact submatrix is: in, is the normal spring stiffness between circular element i and circular element j; is the fourth intermediate matrix, and ; is the fifth intermediate matrix, and ; is the x-coordinate of the connection point between the normal spring and circular element i; is the x-coordinate of the connection point between the normal spring and circular element j; is the y-coordinate of the connection point between the normal spring and the circular element i; is the y coordinate of the connection point between the normal spring and the circular element j; For a normal circular element-circular element contact pair, the tangential contact submatrix is: in, is the tangential spring stiffness between circular element i and circular element j; is the displacement transformation matrix of circular unit i; , is the center coordinate of circular unit i; , are the center coordinates of circular unit j.

7. The numerical simulation method for the progressive failure process of elastic-brittle materials based on DDDA according to claim 1 is characterized in that: Step S4 is specifically as follows: The input parameters of the DDA numerical model of three-spring bonded circular elements are calibrated based on the mechanical parameters of real elastic-brittle material specimens. The input parameter calibration includes calibration of elastic parameters and calibration of strength parameters; Elastic parameters including Poisson's ratio input and elastic modulus input value , the corresponding relationship 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, is half the width of the bonding unit; is the initial length of the bonding unit; H is the thickness of the entire model; The calibration of the elastic parameters comprises the following steps: (1) A numerical sample with an aspect ratio of 2 was established, with the number of particles ranging from 6000 to 10000. The radius range and distribution of the circular units in the sample were consistent with the calculation model; (2) Order Equal to the elastic modulus of the real elastic-brittle material , using several different Poisson's ratios , numerical experiments were carried out respectively, and several groups of and data, where is the Poisson's ratio of the real elastic-brittle material; (3) Based on the Logistic function, fit the Relationships and The Logistic function of the relationship, the Logistic function expression is: Among them, x is the independent variable; y is the dependent variable; is the first undetermined coefficient; is the second undetermined coefficient; is the third undetermined coefficient; p is the fourth undetermined coefficient; (4) Obtained by fitting Relationship between Logistic function and Relational Logistic function, calculated to obtain the specified Corresponding , and the Corresponding , thus calculating the specified Corresponding ; (5) Using the calculated and , a numerical experiment is conducted to verify the obtained and Is it the specified value? If it meets the requirements, the elastic parameter calibration is ended; otherwise, the value obtained in this numerical test is and Add data to the dataset and fit again Relationships and Logistic function of the relationship and return to step (4).

8. The numerical simulation method for the progressive failure process of elastic-brittle materials based on DDDA according to claim 7 is characterized in that: The strength parameters include the input value of the tensile strength of the bonding element , input value of internal friction angle , input value of cohesion ; The calibration of the intensity parameters is specifically as follows: Maintain Poisson's ratio input value and elastic modulus input value unchanged, by adjusting the tensile strength input value and the input value of cohesion , so that the compressive strength of the numerical model and tensile strength Corresponding to the compressive strength and tensile strength of real elastic-brittle materials; The calibration of the intensity parameters comprises the following steps: The circular unit groups in step S2 are bonded, the circular unit groups are bonded again, and the bonding units inside the circular unit groups are bonded. Increased 10 times; Take the input value of the internal friction angle A value between 30° and 50° is used as the input value of the tensile strength of the bonding unit. The tensile strength is 1.54 times of the specified tensile strength. A direct tensile test is carried out on the numerical sample, and the result is ,Sure The linear function expression of Corresponding ; Take the input value of the internal friction angle The values ​​are 5, 20, 35, 50, 65 and 80, and 6 uniaxial compression tests are carried out on the numerical samples to obtain 6 groups of Data is fitted by Logistic function Curve expression, calculate the specified Corresponding .

9. The numerical simulation method for the progressive failure process of elastic-brittle materials based on DDDA according to claim 1 is characterized in that: Step S5 is specifically as follows: Determine the input parameters of the numerical model; According to the actual working conditions of the target elastic-brittle material in actual engineering or experiments, corresponding boundary conditions are applied to the numerical model; Under the boundary conditions, the numerical model is driven to perform mechanical calculations to dynamically simulate the entire progressive failure process of the elastic-brittle material from initial deformation, microcrack initiation and expansion to macroscopic fracture, and dynamic change data such as displacement field, stress field, and energy loss within the model are obtained to complete 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.

10. A system for implementing the numerical simulation method of the progressive failure process of elastic-brittle materials based on DDDA according to any one of claims 1 to 9, characterized in that: It includes numerical model construction module, model circular unit grouping module, three-spring bonding module, model parameter calibration module, and elastic-brittle material progressive failure simulation module; The numerical model construction module uses the geometric parameters of the real elastic-brittle material specimen as a benchmark to construct the initial two-dimensional DDDA numerical model and upload the data to the model circular unit grouping module; The model circular element grouping module groups the circular elements in the two-dimensional DDDA numerical model based on the received data and the compression-tension ratio of the real elastic-brittle material, obtains 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 based on 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 elastic-brittle material specimen, and uploads the data to the elastic-brittle material progressive failure simulation module; The progressive failure simulation module for brittle materials adds boundary conditions to the three-spring bonded circular element DDA numerical model based on the actual working conditions of the target brittle material in actual engineering or experiments to simulate the progressive failure process of the brittle material.

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