Brittle material cyclic loading and unloading test simulation method based on discrete elements

Abstract

The invention provides a brittle material cyclic loading and unloading test simulation method based on discrete elements. The method comprises the steps that a cyclic loading and unloading constitutive model used for describing the mechanical state of particles when a brittle material is affected by cyclic loading is constructed; based on a discrete element method and a cyclic loading and unloading constitutive model, inputting parameters and conditions, and if the time step length is not reached, calculating particle stress information; if the time step length is reached, directly outputting a calculation result and drawing a cloud picture; traversing all the particles, calculating the speed and displacement of the particles according to the stress information of the particles, outputting a calculation result, and drawing a cloud picture. According to the invention, reference can be provided for mechanical characteristics of cyclic loading and unloading tests of the fragile material, cyclic loading, fatigue and plastic failure of the fragile material under the cyclic loading condition can be reflected, and production safety in the construction process can be guaranteed; the technical problem that an existing cyclic loading and unloading test simulation method depends on experience judgment of linear regression and cannot meet the scene requirements of a nonlinear relation and plastic failure is solved.

Description

Technical Field

[0001] The invention relates to the technical field of geotechnical engineering, and in particular to a discrete element-based brittle material cyclic loading and unloading test simulation method. Background Art

[0002] The discrete element method has good adaptability to discontinuous medium problems and is relatively mature in studying large displacement deformation and nonlinear relationships. It is widely used in various fields such as geotechnical engineering, structural geology, geophysics, mining engineering, and has achieved many important results.

[0003] In the discrete element method, interparticle bond contact provides different microstructural models in the form of constitutive models. Currently, the mainstream constitutive model for brittle materials is the parallel bond model, which can effectively simulate the specimen failure process. However, its limitation lies in treating the entire deformation process as elastic, which does not fully reflect the elastic-plastic properties of the material.

[0004] To address this phenomenon, some researchers have proposed models, such as bilinear models, that improve upon the consideration of elastic deformation during loading. On the other hand, in constitutive models, if all forces are removed after plastic deformation between particles, the interparticle spacing will not return to its original position. If an external force is applied to restore it, a certain repulsive force will be generated between the particles during the recovery process. Furthermore, existing models struggle to simulate indoor cyclic loading and unloading tests. Furthermore, these constitutive models are primarily designed for rock materials and have not been validated for use with other brittle materials. Summary of the Invention

[0005] In response to the shortcomings of the existing technology, the present invention provides a discrete element-based simulation method for cyclic loading and unloading tests of brittle materials to solve the technical problem that the existing cyclic loading and unloading test simulation method relies on empirical judgment of linear regression and cannot meet the requirements of scenarios with nonlinear relationships and plastic failure.

[0006] The technical solution of the present invention is: a discrete element-based brittle material cyclic loading and unloading test simulation method, comprising the following steps:

[0007] S1) Constructing a cyclic loading and unloading constitutive model for describing the mechanical state of particles of brittle materials when subjected to cyclic loading;

[0008] S2) Based on the discrete element method and cyclic loading and unloading constitutive model, input parameters and conditions to determine whether the time step has been reached; if the time step has not been reached, calculate the particle force information; if the time step has been reached, directly output the calculation results and draw a cloud map;

[0009] S3) traverse all particles, calculate the particle velocity and displacement according to the particle force information, and obtain the calculation results; output the calculation results and draw a cloud map.

[0010] Preferably, in step S1), constructing a cyclic loading and unloading constitutive model specifically includes the following steps:

[0011] Detecting whether particles are in contact within the generated particle model, and if so, generating adhesion;

[0012] Define the relevant parameters of the cyclic loading and unloading constitutive model, including tensile strength, calculation boundary radius, normal stiffness, tangential stiffness, and damping coefficient;

[0013] A cyclic loading and unloading constitutive model is applied to the resulting bond.

[0014] Preferably, in step S2), it is determined whether the time step is reached; if the time step is not reached, the particle force information is calculated; specifically, the following steps are included:

[0015] S21), initializing the parameters of the cyclic loading and unloading constitutive model, inputting material parameters, and determining the model size;

[0016] S22), determining the coordinates of discrete particles;

[0017] S23), numbering the discrete particles and inputting corresponding data information;

[0018] S24), applying initial boundary conditions and determining the time step;

[0019] S25) Calculate the particle force information according to the calculation rules of the cyclic loading and unloading constitutive model.

[0020] Preferably, in step S2), the cyclic loading and unloading constitutive model is divided into an elastic deformation stage, a plastic deformation stage and a strain softening stage.

[0021] Preferably, in step S2), during the elastic deformation stage, the rock material exhibits linear elastic behavior.

[0022] Preferably, in step S2), when the relative displacement continues to increase and exceeds a preset critical value, microscopic damage begins to occur inside the rock, entering the plastic deformation stage. The normal force growth rate in the plastic deformation stage is lower than that in the initial stage, which is manifested as a gentle curve slope.

[0023] Preferably, in step S2), after entering the strain softening region, the mechanical properties of the rock material enter a peak, and the slope of the strain softening region is negative, indicating that the normal force of the material gradually decreases and a certain residual strength is retained.

[0024] The beneficial effects of the present invention are:

[0025] 1. This invention constructs a cyclic loading and unloading constitutive model for the elastic-plastic failure state of brittle materials such as rocks during cyclic loading and unloading processes, and applies it to discrete element software to form a method for describing the unloading and loading mechanical characteristics of rocks;

[0026] 2. The present invention can provide a reference for the mechanical characteristics of cyclic loading and unloading tests of brittle materials, reflecting the cyclic loading, fatigue and plastic failure of brittle materials under cyclic loading conditions, and ensuring production safety during the construction process;

[0027] 3. The present invention can solve the technical problem that the existing cyclic loading and unloading test simulation method relies on the empirical judgment of linear regression and cannot meet the requirements of scenarios with nonlinear relationships and plastic failure. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 Schematic diagram of the process of the present invention;

[0029] Figure 2 This is a schematic diagram of discrete element particle contact in the present invention;

[0030] Figure 3 A relationship diagram between the normal force and the relative normal displacement increment of the cyclic loading and unloading elastic-plastic constitutive model of the present invention;

[0031] Figure 4 This is a comparison diagram of the curve before and after the sudden change of the present invention;

[0032] Figure 5 This is a diagram of a cyclic loading and unloading test model of the present invention;

[0033] Figure 6 This is a stress-strain relationship diagram of the cyclic loading and unloading test of the present invention;

[0034] Figure 7 This is a displacement cloud diagram of the simulated cyclic loading and unloading test of the present invention;

[0035] Figure 8 This is a stress cloud diagram of the simulated cyclic loading and unloading test of the present invention. DETAILED DESCRIPTION

[0036] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings:

[0037] like Figure 1 As shown, the present invention provides a discrete element-based simulation method for brittle material cyclic loading and unloading tests, comprising the following steps:

[0038] S1) Constructing a cyclic loading and unloading constitutive model for describing the mechanical state of particles of brittle materials when subjected to cyclic loading; specifically comprising the following steps:

[0039] Detecting whether particles are in contact within the generated particle model, and if so, generating adhesion;

[0040] Define the relevant parameters of the cyclic loading and unloading constitutive model, including tensile strength, calculation boundary radius, normal stiffness, tangential stiffness, and damping coefficient;

[0041] A cyclic loading and unloading constitutive model is applied to the resulting bond.

[0042] S2) Based on the discrete element method and cyclic loading and unloading constitutive model, input parameters and conditions to determine whether the time step has been reached; if the time step has not been reached, calculate the particle force information; specifically, the following steps are included:

[0043] S21) Initialize the parameters of the cyclic loading and unloading constitutive model, input material parameters, and determine the model dimensions. In this embodiment, the input parameters include, but are not limited to, damping coefficient, stiffness, calculation boundary radius, neighborhood radius, elastic modulus, bulk modulus, critical elongation, boundary conditions, etc. The model dimensions include, but are not limited to, length, width, elastic modulus, density, and damping coefficient.

[0044] S22), determining the coordinates of discrete particles;

[0045] This embodiment determines the coordinates of discrete particles based on the initial generation coordinates of the particles and the displacement information within each time step;

[0046] S23), numbering the discrete particles and inputting corresponding data information, including but not limited to coordinates, radius, speed, force, torque, bonding state, etc.;

[0047] S24), applying initial boundary conditions and determining the time step; in this embodiment, the bottom of the sample is a fixed boundary, and the rest are free boundaries; too short a time step will result in excessive instantaneous displacement of the particles, and too long a time step will result in low computational efficiency, so it is necessary to select a suitable time step value;

[0048] S25) Calculate the particle force information according to the calculation rules of the cyclic loading and unloading constitutive model.

[0049] In this embodiment, Figure 2 As shown, based on the discrete element method, the overlap between particles is defined as when When it is greater than zero, the particles overlap and are judged to be in contact. For the contact between particles and walls, the overlap is calculated using the particle coordinates and the wall coordinates. The contact determination procedure is built into the constitutive model. When particles overlap, the parallel bonding forces between the particles are divided into normal forces and tangential forces:

[0050]

[0051] Where, is the normal force, is the tangential force; represents the contact normal unit vector.

[0052] Wherein, the normal force The calculation expression is:

[0053]

[0054] Where, is the normal force in the time step, is the normal force in the previous time step, is the normal stiffness, is the cross-sectional area, set to the diameter of the smaller particle of the two particles. n is the relative normal displacement increment, which can be obtained by the overlap The size of c bond represents the calculation boundary radius; when particles overlap, the normal force increases with the increase of the overlap; when particles do not overlap, the normal force increases with the increase of the distance between particles until it exceeds the calculation boundary, and the normal force returns to zero after fracture.

[0055] The tangential force The calculation formula is as follows:

[0056]

[0057] in, represents the tangential force in the current step; represents the tangential force in the previous time step; is the tangential stiffness, Δδ s is the relative tangential displacement increment, τ bond Indicates the threshold value of bonding strength; 0<δ s <τ bond When δ s As the force increases, when it exceeds the failure limit, the bond breaks and the tangential force returns to zero. s <0, there is no tangential force.

[0058] In this embodiment, the cyclic loading and unloading constitutive model is divided into an elastic deformation stage, a plastic deformation stage, and a strain softening stage. In the elastic deformation stage, the rock material exhibits linear elastic behavior.

[0059] When the relative displacement continues to increase and exceeds a preset critical value, microscopic damage begins to occur inside the rock, entering the plastic deformation stage. The normal force growth rate in the plastic deformation stage is lower than that in the initial stage, which is manifested as a gentle curve slope.

[0060] After entering the strain softening region, the mechanical properties of the rock material enter a peak, and the slope of the strain softening region is negative, indicating that the normal force of the material gradually decreases and a certain residual strength is retained.

[0061] like Figure 3 As shown, when entering the elastic and plastic deformation stages, the degree of deformation between particles will be recorded. and in, It represents the maximum interparticle distance reached by the particles during each round of loading. Indicates the minimum inter-particle distance reached during each round of unloading. When particles are unloaded, the inter-particle normal force calculation will use the unloading stiffness Therefore, its uninstall path is different from the original path.

[0062] like Figure 4 As shown in Figure 1, if the slope of the curve is directly changed while ensuring the calculation of the elastic deformation stage, a sudden change will occur between the curves of the two stages. To ensure the continuity of the curve, a reloading intercept is introduced into the cyclic loading and unloading constitutive model.

[0063] During the elastic deformation phase:

[0064] The change in the normal force of the parallel bonding force between the particles is expressed as:

[0065]

[0066] in, represents the normal force during the elastic deformation stage, represents the normal force in the previous time step, represents the normal stiffness in the elastic deformation stage, represents the cross-sectional area, Δδ n is the relative normal displacement increment, is the normal reloading intercept, which is determined by the deformation degree and the original loading curve;

[0067] The change in the tangential force of the parallel bonding force between the particles is expressed as:

[0068]

[0069] in, represents the tangential force in the elastic deformation stage, represents the tangential force in the previous time step, represents the tangential stiffness in the elastic deformation stage, represents the cross-sectional area, Δδ s is the relative normal displacement increment, is the tangential reloading intercept, which is determined by the recorded deformation degree and the original loading curve.

[0070] During the plastic deformation stage:

[0071] The change in the normal force of the parallel bonding force between the particles is expressed as:

[0072]

[0073] in, is the normal force in the plastic deformation stage, It represents the stiffness of the plastic deformation stage, a is the ratio of the displacement corresponding to the turning point of the two stages to the displacement corresponding to the peak, and c is the ratio of the displacement corresponding to the turning point of the two stages to the displacement corresponding to the peak. b represents the computational boundary of the bond;

[0074] The change in the tangential force of the parallel bonding force between the particles is expressed as:

[0075]

[0076] in, is the tangential force in the plastic deformation stage, It represents the stiffness of the plastic deformation stage, a is the ratio of the displacement corresponding to the turning point of the two stages to the displacement corresponding to the peak, and c is the ratio of the displacement corresponding to the turning point of the two stages to the displacement corresponding to the peak. b Represents the computational boundary of the bond.

[0077] During the strain softening phase:

[0078] The change in the normal force of the parallel bonding force between the particles is expressed as:

[0079]

[0080] in, is the normal force in the plastic deformation stage, δ n,TH1 Indicates the relative displacement increment corresponding to the peak normal force, F n,OF represents the normal force offset in the critical stage, represents the stiffness in the strain softening stage;

[0081] The change in the tangential force of the parallel bonding force between the particles is expressed as:

[0082]

[0083] in, is the tangential force in the plastic deformation stage, δ S,TH1 Indicates the relative displacement increment corresponding to the peak tangential force, F s,OF represents the tangential force offset in the critical stage, Represents the stiffness in the strain softening stage.

[0084] As a preferred embodiment of this invention, for inter-particle unloading, the normal force is expressed as:

[0085]

[0086] in, is the normal unloading force in the parallel key, represents the normal force during loading, represents the unloading stiffness, represents the contact area of the parallel bond, Δδ n represents the normal relative displacement, It is the intercept of the unloading curve, which is determined by the deformation degree recorded by the program and the original loading curve.

[0087] The tangential force is not adjusted during the unloading stage and is calculated using the loading method, i.e.:

[0088]

[0089] in, represents the tangential force in the elastic deformation stage, represents the tangential force in the previous time step, represents the tangential stiffness in the elastic deformation stage, represents the cross-sectional area, Δδ s is the relative normal displacement increment, is the tangential reloading intercept, which is determined by the recorded deformation degree and the original loading curve; is the tangential force in the plastic deformation stage; Indicates the stiffness in the plastic deformation stage; δ s,TH Indicates the relative displacement increment corresponding to the peak tangential force, F s,OF represents the tangential force offset in the critical stage; is the tangential force in the plastic deformation stage; represents the stiffness in the strain softening stage; a is the ratio of the displacement corresponding to the turning point of the two stages to the displacement corresponding to the peak; c b Represents the computational boundary of the bond.

[0090] The final particle force f is expressed as:

[0091]

[0092] Among them, f x and f y is the force on the particle in the x and y directions, and we have:

[0093]

[0094] Among them, l n is the number of particles produced, θ lF is the bonding inclination angle; n and F s are the normal force and tangential force of the bond, respectively. The calculation method of different deformation stages in the non-unloading state is as follows:

[0095]

[0096] When the bond corresponding to the particle is in the unloading state, its normal force F n =F n,unload .

[0097] When the interparticle overlap is greater than zero, the same calculation method as the elastic stage is used, but the direction of the bonding force is opposite. When the interparticle normal tension reaches 70% of the peak strength, the calculation method of the plastic deformation stage is used. After the interparticle normal tension reaches the peak, the calculation method of the strain softening stage is used.

[0098] After the bond breaks, no tension can be generated between the particles. If the particles overlap again at this time, the situation will be treated as if the bond has not broken.

[0099] For the tangential force generated between particles, the tangential relative displacement is proportional to the magnitude of the tangential force.

[0100] If the time step has been reached, the calculation results are directly output and the cloud map is drawn.

[0101] S3) traverse all particles, calculate the particle velocity and displacement according to the particle force information, and obtain the calculation results; output the calculation results and draw a cloud map.

[0102] In this embodiment, the particle velocity v is calculated based on the particle force result:

[0103]

[0104] Among them, f is the final calculated particle force, d m is the damping coefficient, Δt is the unit time step, and m is the unit mass of the particle.

[0105] In this embodiment, based on the particle velocity results, the relative particle displacement Δs at each time step is obtained by multiplying the particle velocity by the unit time step:

[0106] Δs=vΔt.

[0107] like Figure 5As shown in the figure, this example used the MTS815 multifunctional loading system to conduct uniaxial compression and cyclic loading experiments on granite. The specimen was fixed at the bottom and loaded from the top. The cyclic loading and unloading tests used sinusoidal loading at a loading rate of 1 Hz, with 10 cycles. The upper and lower limits of the cyclic loading and unloading were 4 MPa and 15 MPa, respectively. After the cyclic loading and unloading tests, the granite specimen was uniaxially compressed to failure, and the stress and strain data were recorded.

[0108] Prior to conducting cyclic loading-unloading tests on the numerical model, uniaxial compression tests were performed, followed by parameter calibration of the discrete element model. A trial-and-error approach was used to calibrate the parameters to obtain a DEM model that closely resembled the specimen characteristics. This model was then used to simulate the cyclic loading-unloading tests. The final model contained 220 particles, had a damping ratio of 0.8, an effective modulus set to 31.46 GPa, a normal to tangential stiffness ratio of 1.5, and a friction coefficient of 0.4. After uniaxial compression test parameter calibration, a compressive strength of 60.7 MPa and an elastic modulus of 14.2 GPa were obtained.

[0109] In addition, the particle flow software PFC was used to simulate the same experiment, in which the constitutive model used the parallel bonding model built into PFC. The simulation results of the parallel bonding model were compared with the cyclic loading and unloading elastic-plastic model newly constructed in this paper.

[0110] like Figure 6 As shown in the figure, the indoor test results are relatively close to the results of the cyclic loading and unloading elastic-plastic model, but there is a large gap with the results obtained by the parallel bonding model simulation in the PFC. The curves simulated by the cyclic loading and unloading elastic-plastic constitutive model are highly consistent with the experimental results. During the cyclic loading-unloading stage, the program can well simulate the degree of plastic deformation of the material, and the peak value and overall slope of the curve are very similar to the actual experiment. In addition, the obtained compressive strength and elastic modulus are also very close to the experimental data. At the same time, the simulation curves show ideal results, especially in the cyclic loading-unloading stage, where the constitutive model used effectively captures the curve shape of the hysteresis loop segment.

[0111] In the simulation results obtained by PFC during the cyclic loading and unloading part, the loading curve is relatively close to the unloading curve, which cannot show the characteristics of the plastic deformation of the specimen. Due to the low loading upper limit of this test scheme, at this stress level, the PFC parallel bond model regards deformation as elastic deformation, ignoring the damage and plastic accumulation effects inside the material. Therefore, it fails to capture the gradual accumulation of damage inside the rock, which will significantly affect the subsequent mechanical behavior of the material. On the other hand, in the monotonic loading part after cyclic loading and unloading, the peak strength and elastic modulus of the specimens obtained by PFC simulation at different numbers of cycles do not change significantly, indicating that PFC cannot show the changes in the internal mechanical properties of the specimens caused by cyclic loading and unloading, especially the changes in strength and stiffness due to accumulated damage. This deficiency makes it have certain limitations in reflecting the damage evolution process of the material.

[0112] During the cyclic loading and unloading process, energy dissipation is usually caused by certain plastic deformation and microcrack expansion inside the specimen. The larger the area of the hysteresis loop, the more energy the material dissipates in each cycle. The hysteresis loop in the actual test is more obvious, indicating that there is a lot of irreversible energy dissipation in the specimen during the loading and unloading process, reflecting the accumulation of damage. The hysteresis loop in the PFC example is not obvious, that is, the energy dissipation caused by the cyclic strain between particles is not simulated. Therefore, the number of cycles has little effect on the final strength of the specimen. The cyclic loading and unloading elastic-plastic constitutive model defined in this embodiment better reflects the plastic failure and energy dissipation phenomena.

[0113] like Figure 7 As shown in the figure, the discrete element software can present the displacement cloud diagram of the specimen particles under cyclic loading and unloading. Figure 8 As shown in Figure 2, the discrete element software can present the stress cloud diagram of the specimen particles under cyclic loading and unloading.

[0114] The above embodiments and descriptions are only for explaining the principles and best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements, which shall fall within the scope of the invention to be protected.

Claims

1. A method for simulating cyclic loading and unloading tests of brittle materials based on discrete elements, characterized in that: The following steps are involved: S1) Constructing a cyclic loading and unloading constitutive model for describing the mechanical state of particles of brittle materials when subjected to cyclic loading; S2) Based on the discrete element method and cyclic loading and unloading constitutive model, input parameters and conditions to determine whether the time step has been reached; if the time step has not been reached, calculate the particle force information; if the time step has been reached, directly output the calculation results and draw a cloud map; S3) traverse all particles, calculate the particle velocity and displacement according to the particle force information, and obtain the calculation results; output the calculation results and draw a cloud map.

2. The method for simulating cyclic loading and unloading tests of brittle materials based on discrete element analysis according to claim 1, characterized in that: In step S2), the force f on the particles is expressed as: Among them, f x and f y is the force on the particle in the x and y directions, and we have: Among them, l n is the number of particles produced, θ l F is the bonding inclination angle; n and F s are the normal force and tangential force of the bond respectively; when the bond corresponding to the particle is in the unloading state, its normal force F n =F n,unload .

3. The method for simulating cyclic loading and unloading tests of brittle materials based on discrete element analysis according to claim 2, characterized in that: In step S2), based on the discrete element method, the overlap between particles is defined as when When it is greater than zero, the particles overlap and are judged to be in contact. For the contact between particles and walls, the overlap is calculated using the particle coordinates and the wall coordinates. The contact determination procedure is built into the constitutive model. When particles overlap, the parallel bonding forces between the particles are divided into normal forces and tangential forces: Where, is the normal force parallel to the adhesive force, is the tangential force parallel to the adhesive force; represents the contact normal unit vector.

4. The method for simulating cyclic loading and unloading tests of brittle materials based on discrete element analysis according to claim 2, characterized in that: The normal force parallel to the adhesive force The calculation expression is: Where, is the normal force in the time step, is the normal force in the previous time step, is the normal stiffness, is the cross-sectional area; Δδ n is the relative normal displacement increment, through the overlap The size of c bond Represents the calculation boundary radius; when particles overlap, the normal force increases with the increase in the amount of overlap; when particles do not overlap, the normal force increases with the increase in the distance between particles until it exceeds the calculation boundary, and the normal force returns to zero after breaking; The tangential force parallel to the bonding force The calculation formula is as follows: in, represents the tangential force in the current step; represents the tangential force in the previous time step; is the tangential stiffness, Δδ s is the relative tangential displacement increment, τ bond Indicates the threshold value of bonding strength; 0<δ s <τ bond When δ s As the force increases, when it exceeds the failure limit, the bond breaks and the tangential force returns to zero; if δ s <0, there is no tangential force.

5. The method for simulating cyclic loading and unloading tests of brittle materials based on discrete element analysis according to claim 3, characterized in that: In step S2), the cyclic loading and unloading constitutive model is divided into an elastic deformation stage, a plastic deformation stage and a strain softening stage.

6. The method for simulating cyclic loading and unloading tests of brittle materials based on discrete element analysis according to claim 5, characterized in that: In step S2), during the elastic deformation phase: The change in the normal force of the parallel bonding force between the particles is expressed as: in, represents the normal force during the elastic deformation stage, represents the normal force in the previous time step, represents the normal stiffness in the elastic deformation stage, represents the cross-sectional area, Δδ n is the relative normal displacement increment, is the normal reloading intercept, which is determined by the deformation degree and the original loading curve; The change in the tangential force of the parallel bonding force between the particles is expressed as: in, represents the tangential force in the elastic deformation stage, represents the tangential force in the previous time step, represents the tangential stiffness in the elastic deformation stage, represents the cross-sectional area, Δδ s is the relative normal displacement increment, is the tangential reloading intercept, which is determined by the recorded deformation degree and the original loading curve.

7. The method for simulating cyclic loading and unloading tests of brittle materials based on discrete element analysis according to claim 5, characterized in that: In step S2), during the plastic deformation stage: The change in the normal force of the parallel bonding force between the particles is expressed as: in, is the normal force in the plastic deformation stage, represents the stiffness of the plastic deformation stage, a is the ratio of the corresponding displacement at the turning point of the two stages to the corresponding displacement at the peak; Δδ n is the relative normal displacement increment; c b represents the computational boundary of the bond; is the normal reloading intercept, which is determined by the deformation degree and the original loading curve; The change of the tangential force of the parallel bonding force between the particles is expressed as: in, is the tangential force in the plastic deformation stage, It represents the stiffness of the plastic deformation stage, a is the ratio of the displacement corresponding to the turning point of the two stages to the displacement corresponding to the peak, and c is the ratio of the displacement corresponding to the turning point of the two stages to the displacement corresponding to the peak. b Represents the computational boundary of the bond.

8. The method for simulating cyclic loading and unloading tests of brittle materials based on discrete element analysis according to claim 5, characterized in that: In step S2), during the strain softening stage: The change in the normal force of the parallel bonding force between the particles is expressed as: in, is the normal force in the plastic deformation stage, δ n,TH Indicates the relative displacement increment corresponding to the peak normal force, F n,OF represents the normal force offset in the critical stage, represents the stiffness in the strain softening stage; The change of the tangential force of the parallel bonding force between the particles is expressed as: in, is the tangential force in the plastic deformation stage, δ s,TH Indicates the relative displacement increment corresponding to the peak tangential force, F s,OF represents the tangential force offset in the critical stage, Represents the stiffness in the strain softening stage.

9. The method for simulating cyclic loading and unloading tests of brittle materials based on discrete element analysis according to claim 5, characterized in that: In step S2), when the particles are unloaded, the normal force between the particles is calculated using the unloading stiffness For inter-particle unloading, the normal force is expressed as: in, is the normal unloading force in the parallel key, represents the normal force during loading, represents the unloading stiffness, represents the contact area of the parallel bond, Δδ n represents the normal relative displacement, is the intercept of the unloading curve, which is determined by the deformation degree recorded by the program and the original loading curve; The tangential force is not adjusted during the unloading stage and is calculated using the loading method, i.e.: in, represents the tangential force in the elastic deformation stage, represents the tangential force in the previous time step, represents the tangential stiffness in the elastic deformation stage, represents the cross-sectional area, Δδ s is the relative normal displacement increment, is the tangential reloading intercept, which is determined by the recorded deformation degree and the original loading curve; is the tangential force in the plastic deformation stage; Indicates the stiffness in the plastic deformation stage; δ s,TH Indicates the relative displacement increment corresponding to the peak tangential force, F s,OF represents the tangential force offset in the critical stage; is the tangential force in the plastic deformation stage; represents the stiffness in the strain softening stage; a is the ratio of the displacement corresponding to the turning point of the two stages to the displacement corresponding to the peak; c b Represents the computational boundary of the bond.

10. The discrete element-based simulation method for cyclic loading and unloading tests of brittle materials according to claim 5, characterized in that: In step S2), when the inter-particle overlap is greater than zero, the same calculation method as in the elastic stage is used, but the direction of the bonding force is opposite. When the inter-particle normal tension reaches 70% of the peak strength, the calculation method of the plastic deformation stage is used. After the inter-particle normal tension reaches the peak, the calculation method of the strain softening stage is used. After the bond breaks, no tension can be generated between the particles. If the particles overlap again at this time, the situation will be treated as if the bond has not broken. For the tangential force generated between particles, the tangential relative displacement is proportional to the magnitude of the tangential force.

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