Discrete element fatigue damage simulation method based on parallel bonding damage model

Abstract

The invention discloses a discrete element fatigue damage simulation method based on a parallel bonding damage model, belongs to the technical field of discrete element simulation, and aims to solve the problems that an existing PFC embedded model cannot directly simulate fatigue damage, and a fatigue damage model corrected on the basis of a PFC model is poor in applicability and insufficient in theoretical support. The method comprises two core contents of parallel bonding damage model development and discrete element microscopic fatigue damage realization, the Paris law is taken as a fatigue damage rule, integral correction is carried out, a linear parallel bonding model is introduced, then the parallel bonding damage model is proposed, compared with a previous model, the fatigue damage criterion is optimized, and the precision of the parallel bonding damage model is improved. And the mechanical theory support of the damage criterion is ensured, the nonlinear damage evolution under the fatigue load can be accurately represented, and the problems that the linear representation of the traditional model is insufficient and the theoretical basis is lacked are solved.

Description

Technical Field

[0001] This invention relates to the field of discrete element simulation technology, specifically to a discrete element fatigue damage simulation method based on a parallel bond damage model. Background Technology

[0002] In the field of road engineering, cement-stabilized crushed stone and fiber cement-stabilized crushed stone are commonly used road base materials. These materials are prone to fatigue cracking under vehicle cyclic loads. Macroscopically, this manifests as crack initiation, propagation, and eventual penetration, while microscopically, it stems from the gradual deterioration and failure of the bonding bonds between internal particles.

[0003] Discrete Element Method (DEM), especially Particle Flow Program (PFC), has been widely used in the study of the mechanical behavior of materials such as asphalt mixtures and concrete due to its unique advantages in the mechanical analysis of discontinuous systems, simulation of large deformation motion, and visualization of microscopic cracking processes. However, the constitutive models embedded in existing PFC (such as linear models and linear parallel bond models) have inherent defects, as follows: These models assume that the interparticle bonding parameters remain constant during loading and only allow cracking to occur when the stress exceeds the bond strength. However, under fatigue loading, the internal stress of the material is usually less than the bond strength, which makes it impossible for the contact model parameters to deteriorate automatically with the loading process. As a result, PFC cannot directly reflect the degradation of bond performance caused by fatigue damage.

[0004] To overcome the aforementioned shortcomings, two types of methods are typically used in research to simulate fatigue damage: one is the viscoelastic element model represented by the Burgers model, and the other is a modified model based on the reduction of the bond radius. While the Burgers model can describe the viscoelastic mechanical response of asphalt mixtures relatively well, cement-stabilized crushed stone is a brittle material and lacks the self-healing ability of asphalt. Therefore, its fatigue fracture mechanism differs significantly from that of asphalt mixtures, making the model difficult to apply. In the radius reduction type of models, the stress corrosion model (PSC) proposed by David O. Potyondy draws on the subcritical crack propagation law in linear elastic fracture mechanics and can characterize fatigue damage by linearly reducing the bond radius. However, this type of model was originally designed to address rock creep and therefore cannot describe the nonlinear damage evolution under fatigue loading. Furthermore, the nonlinear parallel bond stress corrosion (NPSC) model proposed by Song et al. defines damage as a logarithmic function of time. Although it can simulate cyclic loading, it is essentially a time-dependent model. When the load level and frequency change, the parameters need to be readjusted, resulting in poor extrapolation and a lack of support from fracture damage mechanics theory.

[0005] Furthermore, a core flaw in existing fatigue damage models lies in the lack of physical rationality in the damage reduction criterion. Traditional PSC models rely on... and The two empirical parameters lack theoretical basis during calibration; the essence of fatigue damage is the physical process of crack evolution and energy dissipation under cyclic loading, which is directly related to stress magnitude and energy release rate. Defining damage evolution solely through time or linear rules cannot accurately reflect its physical essence. Paris's law, as a classic theory in fatigue cracking research, not only has a solid foundation in damage mechanics but also has a simple form that aligns with the essence of material fatigue damage. It has been successfully applied to fatigue crack propagation analysis of materials such as metals and concrete. Introducing Paris's law into the PFC model to define the bond radius reduction criterion can significantly improve the model's rationality and logical rigor.

[0006] Existing PFC embedded models cannot directly simulate fatigue damage, and fatigue damage models modified based on them suffer from poor applicability and insufficient theoretical support. Furthermore, they are insufficient to meet the research needs of complex brittle composite materials such as fiber-reinforced cement-stabilized crushed stone. Therefore, it is urgent to develop a discrete element simulation method based on reasonable damage criteria, applicable to brittle composite materials, and capable of accurately capturing the fatigue damage evolution process at the microscale.

[0007] To address the above issues, a discrete element fatigue damage simulation method based on a parallel bond damage model is proposed. Summary of the Invention

[0008] The purpose of this invention is to provide a discrete element fatigue damage simulation method based on a parallel bond damage model. By using this invention, the problems mentioned above, such as the inability of existing PFC embedded models to directly simulate fatigue damage, and the poor applicability and insufficient theoretical support of existing fatigue damage models, are solved.

[0009] To achieve the above objectives, the present invention provides the following technical solution: a discrete element fatigue damage simulation method based on a parallel bond damage model, comprising the development of a parallel bond damage model and the realization of discrete element micro-level fatigue damage, as detailed below: S1: First, establish a discrete element model of the target material and initialize the model to a stable equilibrium state; S2: Develop a parallel bond damage model. The parallel bond damage model is a constitutive model based on the linear parallel bond model, and incorporates... The integral-corrected Paris law serves as a fatigue damage criterion, used to define damage variables, damage assumptions, and radius reduction rules. S3: Determine the microscopic contact parameters and fatigue damage parameters through a system calibration method that combines indoor and virtual tests; S4: Apply fatigue load to the model, traverse all internal contacts, and determine whether the contact stress meets the damage triggering condition in each time step. If it does, calculate the damage increment, then calculate the damage value of the current step, calculate the radius reduction factor based on the damage value of the current step, and then update the bond radius, stiffness matrix and stress; if it does not meet the condition, do not perform damage calculation. S5: Use the damage value obtained in S4 as the initial damage for the current step, and then determine whether the stress meets the damage triggering condition. If it does, calculate the damage increment again; otherwise, do not perform damage calculation. S6: Repeat steps S4-S5 to iterate the damage until the bond breaks or the preset number of cycles is reached. S7: Output simulation results.

[0010] Furthermore, the core of the parallel bond damage model in S2 is the introduction of... The integral-corrected Paris law serves as a fatigue damage criterion, and the radius of the bond bond decreases according to this criterion when the damage condition is met.

[0011] Furthermore, the fatigue damage criterion is expressed as: ,in The length of the bond crack. Where is the bonding diameter, , The bonding radius; Substituting Paris's Law The damage increment can be obtained, and the damage increment is expressed as: ,in It represents the number of loading loops; and These are parameters related to material fatigue. It is the magnitude of the stress intensity factor during cyclic loading; use The Paris law is corrected by integration, as follows: ; in, and For fatigue-related parameters, Determined by the following formula: ; in, Poisson's ratio, The elastic modulus is given; for Type I cracking (opening crack), the stress intensity factor is given. When type II cracking (slip crack) occurs, the stress intensity factor is: The expression for the stress intensity factor is as follows: ; ; ; in, , These represent the maximum and minimum values ​​of the normal stress, respectively. , These represent the maximum and minimum values ​​of tangential stress, respectively. This is the geometric correction factor for Type I cracking (opening crack). This is the geometric correction factor for type II cracking (slip crack); Using Tada to study the shape factor in the single cracking process of a rectangular plate to calculate The points are as follows: ; Will Substitute them separately , and The formula is as follows: ; ; ; As fatigue damage variables evolve and fatigue displacement in the normal and shear directions increases, the fatigue displacement increment is related to the fatigue damage increment variable. Based on the above, the expression for the bond diameter in the linear parallel bond model after damage can be obtained as follows: ; in, Indicates the initial value of the bonding diameter; It is under fatigue loading integral; and For the material constants related to damage, the basic range of values ​​is determined by trial calculations, and then the fatigue damage rate is calculated by orthogonal simulation experiments. These two key parameters are calibrated based on the corresponding indoor test results. This represents the tensile stress between current particles in the parallel bond damage model. This represents the damage stress threshold in the parallel bond damage model. This represents the interparticle bond strength in the parallel bond damage model. The time step for radius reduction.

[0012] Furthermore, the damage assumptions in S2 are as follows: The target material is fiber cement stabilized crushed stone, which includes cement stabilized sand, coarse aggregate and fiber. Fatigue damage only occurs in the contact of the linear parallel bond model, that is, inside the cement stabilized sand, inside a single fiber and at the interface between the cement stabilized sand and the coarse aggregate and fiber. The trigger condition for bond radius reduction is: interparticle tensile stress > damage stress threshold. ; When the interparticle tensile stress is greater than or equal to the bond strength At that time, the adhesive bonds break directly; The fatigue damage rate is controlled by the energy release rate between particles and is causally related to the stress magnitude and the energy release rate.

[0013] Furthermore, the fatigue load applied in S4 can be selected as a half-sine wave load.

[0014] Furthermore, the following computational efficiency optimization measures are adopted in S4, S5, and S6, as detailed below: The stress and strain data between particles are updated every certain number of time steps; A time step amplification factor is introduced when calculating the damage increment.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention uses Paris's law as a fatigue damage rule and performs... By incorporating integral corrections into the linear parallel bond model, a parallel bond damage model is proposed. Compared with other models, this model not only optimizes the fatigue damage criterion but also ensures the mechanical theoretical support for the damage criterion. Furthermore, it can accurately characterize the nonlinear damage evolution under fatigue load, thus solving the problems of insufficient linear characterization and lack of theoretical basis in existing models (PSC, NPSC).

[0016] 2. This invention can be specifically adapted to the complex internal structure of fiber cement stabilized crushed stone, and can intuitively capture the crack initiation location, propagation trend and other states, making up for the shortcomings of existing models that cannot simulate the microscopic fatigue damage mechanism of this type of composite material.

[0017] 3. The simulation results in this invention can output multi-dimensional data such as crack evolution, strain growth and fatigue life, which can accurately reveal the fatigue deterioration law of materials and provide theoretical support for improving the fatigue resistance of fiber cement stabilized crushed stone. Attached Figure Description

[0018] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram illustrating the development of the parallel bond damage model of the present invention; Figure 3This is a schematic diagram of the strain of the two spheres before and after damage in the parallel bond damage model of the present invention; Figure 4 This is a schematic diagram comparing the bonding radii before and after damage in the parallel bond damage model of the present invention; Figure 5 The constants of this invention Relationship with nominal strain growth rate and constant A schematic diagram showing the relationship between the nominal strain growth rate and the strain rate. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] like Figures 1-2 As shown, a discrete element fatigue damage simulation method based on a parallel bond damage model includes the following steps: S1: Establish a discrete element model of the target material, define the model components and internal contact types, and initialize the model environment to a stable equilibrium state, where particle velocity and displacement are zero, and the unbalanced force ratio aratio < 10. -5 The contact model for the discrete element model is selected as follows, specifically: The target material is fiber-cement stabilized crushed stone, which includes cement-stabilized sand, coarse aggregate, and fibers. The contact types of the components within the fiber-cement stabilized crushed stone are as follows: The coarse aggregate-coarse aggregate contact uses a linear model (LM), which can only transmit normal and tangential forces and requires consideration of friction. In contrast, the cement stabilized sand-cement stabilized sand, cement stabilized sand-coarse aggregate, cement stabilized sand-fiber, and single fiber internal contact uses a linear parallel bond model (LPBM), which can transmit forces and bending moments and also supports radius reduction.

[0021] The parallel bond damage model in this invention can not only intuitively capture the initiation location and propagation trend of cracks in fiber cement stabilized crushed stone, but also be used in other related fields, making it widely applicable.

[0022] S2: Develop a parallel bond damage model. This model is a constitutive model based on the linear parallel bond model (LPBM), and incorporates... The integral-corrected Paris law serves as a fatigue damage criterion, used to define damage variables, damage assumptions, and radius reduction rules, as follows: The fatigue damage criterion is expressed as follows: ,in The length of the bond crack. Where is the bonding diameter, , The bonding radius; Substituting Paris's Law The damage increment can be obtained, and the damage increment is expressed as: ,in It represents the number of loading loops; and These are parameters related to material fatigue. It is the stress intensity factor amplitude during cyclic loading; using The Paris law is corrected by integration, as follows: ; in, and These are fatigue-related parameters, and Determined by the following formula: ; in, Poisson's ratio, The elastic modulus is given; for Type I cracking (opening crack), the stress intensity factor is given. When type II cracking (slip crack) occurs, the stress intensity factor is: The expression for the stress intensity factor is as follows: ; ; ; in, , These represent the maximum and minimum values ​​of the normal stress, respectively. , These represent the maximum and minimum values ​​of tangential stress, respectively. This is the geometric correction factor for Type I cracking (opening crack). This is the geometric correction factor for type II cracking (slip crack); Using Tada to study the shape factor in the single cracking process of a rectangular plate to calculate The points are as follows: ; Will Substitute them separately , and The formula is as follows: ; ; ; As fatigue damage variables evolve and fatigue displacement in the normal and shear directions increases, the fatigue displacement increment is related to the fatigue damage increment variable. Based on the above, the expression for the bond diameter in the linear parallel bond model after damage can be obtained as follows: ; in, Indicates the initial value of the bonding diameter; It is under fatigue loading integral; and For the material constants related to damage, the basic range of values ​​is determined by trial calculations, and then the fatigue damage rate is calculated by orthogonal simulation experiments. These two key parameters are calibrated based on the corresponding indoor test results. This represents the tensile stress between current particles in the parallel bond damage model. This represents the damage stress threshold in the parallel bond damage model. This represents the interparticle bond strength in the parallel bond damage model. The time step for radius reduction.

[0023] Radius reduction rule: Bonding radius Decrease as damage increases.

[0024] Fatigue damage only occurs in the contact of the linear parallel bond model, namely inside the cement stabilized sand, inside a single fiber, and at the interface between the cement stabilized sand and the coarse aggregate and fiber. The trigger condition for bond radius reduction is: interparticle tensile stress > damage stress threshold. When the interparticle tensile stress is greater than or equal to the bond strength When the bonding bonds break directly, the fatigue damage rate is controlled by the energy release rate between particles, and is causally related to the stress magnitude and the energy release rate.

[0025] S3: Using a system calibration method combining indoor and virtual experiments, the microscopic contact parameters and fatigue damage parameters of the model are determined, including parameters related to Paris's law. , Damage stress threshold and bond strength Parameters; fixed Value, Adjustment This ensures that the nominal strain growth rate in the virtual experiment is consistent with that in the laboratory experiment; fixed Value, Adjustment Values ​​are used to optimize the matching degree of the nominal strain growth rate; adjustments are made. The fatigue life of the virtual test was made consistent with that of the laboratory test; then, the results of the fatigue life verification were used to determine... The nominal strain is defined as the ratio of actuator displacement to specimen characteristic dimension (in indirect tensile testing, it is the ratio of actuator displacement to specimen diameter); the nominal strain growth rate is defined as the slope of the nominal strain in the steady growth phase; and fatigue life is defined as the number of cycles corresponding to the boundary between the steady growth phase and the accelerated growth phase of the nominal strain.

[0026] S4: Apply fatigue load to the model, traverse all internal contacts, and determine whether the contact stress meets the damage triggering condition at each time step. If it does, calculate the damage increment, then calculate the damage value for the current step, calculate the radius reduction factor based on the damage value for the current step, and then update the bond radius, stiffness matrix, and stress. If the condition is not met, do not perform damage calculation, as detailed below: Apply fatigue loading, for example: select a half-sine wave fatigue load, where the load frequency is 5Hz-10Hz, the amplitude is 60%-90% of the indirect tensile strength, and the interval time is... Duration of load application The values ​​are all between 100ms and 300ms. The specific parameter settings can be adjusted according to the experimental requirements.

[0027] S5: Using the damage value obtained in S4 (damage value of the previous time step) as the initial damage for the current step, within each calculation time step, determine whether the interparticle stress meets the damage triggering condition. If it does, calculate the damage increment according to the damage criterion, then calculate the damage value for the current step, calculate the radius reduction factor based on the damage value of the current step, and then update the bond radius, stiffness matrix, and stress. If it does not meet the condition, do not perform damage calculation, as detailed below: when hour, ,in This is the initial bonding diameter; no radius reduction is performed at this stage. When the radius reduction is applied, the radius reduction of the bond is calculated according to the damage criterion, and the bond diameter and stress are updated; when hour, The bond breaks, breaking out of the damage cycle.

[0028] S6: Repeat steps S4-S5 to perform damage iteration calculations until the bond breaks or the preset number of cycles is reached. Output the simulation results, which include data such as crack evolution, strain growth, and fatigue life.

[0029] S4, S5, and S6 employ the following computational efficiency optimization measures: stress and strain data are updated every 150-200 time steps; the analysis time step is multiplied by a magnification factor to shorten the fatigue failure simulation time without altering the radius reduction rule; and a fixed time step size of 1e is used. -6 s. Example

[0030] The rationality of the "post-damage reduction of bond radius" and "accelerated strain growth" of the parallel bond damage model was verified by double-sphere fatigue damage tests. The specific steps are as follows: Two-sphere model establishment: Two spherical particles, each with a diameter of 1 mm, were created in PFC2D. In the initial contact state, the particle center-to-center distance was 1 mm, the particle density was 2650 kg / m³, and the Poisson's ratio was 0.25. The contact between the two particles was modeled using a linear parallel bond model (LPBM). The microscopic contact parameters were determined based on the indoor test calibration results of cement-stabilized sand, as shown in Table 1. Table 1 Parameters of the linear parallel bonding model in the double-sphere experiment

[0031] Provisional fatigue damage parameters: Paris's law parameters , , Pa, Pa; simultaneously, a semi-sine fatigue loading mode was adopted, with the loading frequency set to 5Hz, and the load amplitude being 80% of the ultimate tensile strength of the double-sphere model (calculated as 4.96MPa), with an interval time of... =200ms, load application time =200ms, loading time is 10000 cycles; then, the strain between the two spheres (defined as "the ratio of the increase in the distance between the two spheres after the load is applied to the original distance between the center of the particles") and the change in the bonding radius are monitored in real time, and the differences in the indicators before and after damage (i.e., the original linear parallel bonding model and the parallel bonding damage model of this invention) are compared for the judgment of subsequent results.

[0032] The experimental results and analysis are as follows: Strain variation: The strain of the two spheres in the undamaged original linear parallel bond model remained stable throughout the loading process without significant increase; while the strain of the two spheres using the parallel bond damage model of this invention exhibited a three-stage characteristic of "initial stability - slow growth - accelerated growth", with specific parameters as follows: Figure 3 As shown, this result demonstrates that the model in this invention can simulate strain accumulation caused by fatigue damage, which is consistent with the macroscopic manifestations of material fatigue deterioration.

[0033] Bond radius variation: The original model showed no reduction in bond radius; the model of this invention gradually reduces the bond radius from its initial value, with specific parameters as follows... Figure 4 As shown, this result proves that the radius reduction rule proposed in this invention is effective, and thus the fatigue damage evolution can be characterized by the reduction of the bonding radius, verifying the rationality of the core logic of the model. Example

[0034] This invention takes fiber-reinforced cement stabilized crushed stone as the research object and uses an indirect tensile (IDT) fatigue test verification model to verify the consistency of crack evolution, fatigue life, and strain growth laws with laboratory tests. Specifically, the model size requirements are as follows: The specimen is a cylinder with a diameter of 150 mm and a height of 80 mm. The width of the upper and lower loading strips is 18.75 mm, and the inner radius is 75 mm. At the same time, the inner diameter of the loading strip is the same as the diameter of the specimen, which makes the contact surface between the loading strip and the specimen fit closely rather than be a single contact point, thus effectively avoiding stress concentration. Model components: Coarse aggregate, nominal maximum particle size 26.5mm, using rigid clusters (clump) to simulate irregular shapes, accounting for 60%; cement-stabilized sand, particle diameter 1.18~2.36mm, accounting for 39.9%; 0.1% of particles with diameter 0.03mm, length 10mm / 15mm / 20mm, dosage 0.9kg / m³ / 2.0kg / m³ / 3.0kg / m³; Model selection and parameter calibration results for the five types of contact within the model. Parameters were calibrated component by component through UCT, IDT, and UTT tests, as shown in Table 2 below. Table 2 Internal Contact Model and Parameters of Fiber Cement Stabilized Crushed Stone

[0035] Based on the results of indoor IDT fatigue tests, fatigue damage parameters under different fiber working conditions were calibrated. , , as well as The calibration process is as follows: First, fix it as =1e -8 ,Adjustment To ensure that the nominal strain growth rate of the virtual test is consistent with that of the laboratory test, determine... The value of ; then, fix . And by adjusting Optimize the matching degree of strain growth rate; adjust To ensure that the virtual fatigue life matches that of laboratory tests; finally, verification. The influence on fracture behavior is then used to determine the final value.

[0036] The calibration results for different operating conditions are shown in Table 3: Table 3. Calibration results of fatigue damage parameters under different fiber working conditions

[0037] The fatigue loading method adopted was half-sine fatigue loading, with the load frequency set to 5Hz and the amplitude being 80% of the indoor IDT intensity under the corresponding working condition, and the interval time being... =200ms, load application time =200ms, calculation time step 1e -6 Loading was stopped when the specimen fractured (nominal strain increased sharply), and then the nominal strain growth curve, fatigue life, number and distribution of cracks were monitored. The results of the virtual test and the laboratory test were compared.

[0038] Nominal strain growth curves: Under different fiber working conditions, the nominal strain growth curves of the virtual tests all exhibited a three-stage characteristic of "initial growth - stable development - rapid failure," which is highly consistent with the results of the indoor tests. Figure 5 As shown, the strain growth trend in the rapid failure stage is completely consistent, proving that the model can accurately simulate the gradual evolution of fatigue damage.

[0039] Fatigue life comparison: The results of the comparison between the virtual test and the laboratory test are shown in Table 4. The relative errors are all within 10%, indicating that the model's fatigue life prediction accuracy can meet the engineering requirements. Under the condition of 15mm fiber length and 0.9kg / m³ content, the virtual fatigue life is 8200 cycles, and the laboratory test is 8900 cycles, with a relative error of 7.9%. The error mainly comes from the microscopic defects of coarse aggregate that were not considered in the model.

[0040] Table 4 Comparison of fatigue life between virtual and indoor tests

[0041] Crack evolution analysis: Virtual experiments can clearly capture the initiation location, propagation trend, and distribution characteristics of cracks, as detailed below: Initial stage (0-30% fatigue life): Cracks mainly initiate at the cement-stabilized sand-coarse aggregate interface (this interface is the weakest area), and are few in number and scattered. Stable stage (30%-80% fatigue life): Cracks extend along the interface and into the cement-stabilized sand. Fibers limit crack propagation through bridging, and the cracks are diffusely distributed. Rapid failure stage (80%-100% fatigue life): diffuse cracks merge to form a through macroscopic crack, and the specimen fractures.

[0042] In addition, the virtual experiment revealed the crack resistance and toughening mechanism of the fiber: in the initial stage of fatigue loading, the fiber, cement-stabilized sand and coarse aggregate share the load; in the stabilization stage, the fiber transmits stress through bridging and inhibits crack propagation; in the failure stage, the fiber is elongated and debonds (short fiber) or breaks (long fiber), which is consistent with the conclusion of the indoor test, and fully proves that the model in this invention can accurately simulate the crack resistance mechanism of the fiber.

[0043] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0044] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A discrete element fatigue damage simulation method based on a parallel bond damage model, characterized in that, This includes the development of a parallel bond damage model and the realization of discrete element micro-level fatigue damage, as detailed below: S1: First, establish a discrete element model of the target material and initialize the model to a stable equilibrium state; S2: Develop a parallel bond damage model. The parallel bond damage model is a constitutive model based on the linear parallel bond model, and incorporates... The integral-corrected Paris law serves as a fatigue damage criterion, used to define damage variables, damage assumptions, and radius reduction rules. S3: Determine the microscopic contact parameters and fatigue damage parameters through a system calibration method that combines indoor and virtual tests; S4: Apply fatigue load to the model, traverse all internal contacts, and determine whether the contact stress meets the damage triggering condition in each time step. If it does, calculate the damage increment, then calculate the damage value of the current step, calculate the radius reduction factor based on the damage value of the current step, and then update the bond radius, stiffness matrix and stress; if it does not meet the condition, do not perform damage calculation. S5: Use the damage value obtained in S4 as the initial damage for the current step, and then determine whether the stress meets the damage triggering condition. If it does, calculate the damage increment again; otherwise, do not perform damage calculation. S6: Repeat steps S4-S5 to iterate the damage until the bond breaks or the preset number of cycles is reached. S7: Output simulation results.

2. The discrete element fatigue damage simulation method based on a parallel bond damage model according to claim 1, characterized in that, The core of the parallel bond damage model in S2 is the introduction of... The integral-corrected Paris law serves as a fatigue damage criterion, and the radius of the bonded bond decreases according to this criterion when the damage condition is met.

3. The discrete element fatigue damage simulation method based on a parallel bond damage model according to claim 2, characterized in that, The fatigue damage criterion is expressed as follows: ,in The length of the bond crack. Where is the bonding diameter, , The bonding radius; Substituting Paris's Law The damage increment can be obtained, and the damage increment is expressed as: ,in It represents the number of loading loops; and These are parameters related to material fatigue. It is the magnitude of the stress intensity factor during cyclic loading; use The Paris law is corrected by integration, as follows: ； in, and For fatigue-related parameters, Determined by the following formula: ； in, Poisson's ratio, The elastic modulus is given; for type I cracking, the stress intensity factor is given. For type II cracking, the stress intensity factor is: The expression for the stress intensity factor is as follows: ; ； ； in, , These represent the maximum and minimum values ​​of the normal stress, respectively. , These represent the maximum and minimum values ​​of tangential stress, respectively. This is the geometric correction factor for type I cracking. This is the geometric correction factor for type II cracking; Using Tada to study the shape factor in the single cracking process of a rectangular plate to calculate The points are as follows: ； Will Substitute them separately , and The formula is as follows: ； ； ； As fatigue damage variables evolve and fatigue displacement in the normal and shear directions increases, the fatigue displacement increment is related to the fatigue damage increment variable. Based on the above, the expression for the bond diameter in the linear parallel bond model after damage can be obtained as follows: ； in, Indicates the initial value of the bonding diameter; It is under fatigue loading integral; and For the material constants related to damage, the basic range of values ​​is determined by trial calculation, and then the fatigue damage rate is calculated by orthogonal simulation test. These two key parameters are calibrated based on the corresponding indoor test results. This represents the tensile stress between current particles in the parallel bond damage model. This represents the damage stress threshold in the parallel bond damage model. This represents the interparticle bond strength in the parallel bond damage model. The time step for radius reduction.

4. The discrete element fatigue damage simulation method based on a parallel bond damage model according to claim 3, characterized in that, The damage assumptions in S2 are as follows: The target material is fiber cement stabilized crushed stone, which includes cement stabilized sand, coarse aggregate and fiber. Fatigue damage only occurs in the contact of the linear parallel bond model, that is, inside the cement stabilized sand, inside a single fiber and at the interface between the cement stabilized sand and the coarse aggregate and fiber. The trigger condition for bond radius reduction is: interparticle tensile stress > damage stress threshold. ; When the interparticle tensile stress is greater than or equal to the bond strength At that time, the adhesive bonds break directly; The fatigue damage rate is controlled by the energy release rate between particles and is causally related to the stress magnitude and the energy release rate.

5. The discrete element fatigue damage simulation method based on a parallel bond damage model according to claim 4, characterized in that, The fatigue load applied in S4 can be selected as a half-sine wave load.

6. The discrete element fatigue damage simulation method based on a parallel bond damage model according to claim 5, characterized in that, The following computational efficiency optimization measures are adopted in S4, S5, and S6, as detailed below: The stress and strain data between particles are updated every certain number of time steps; A time step amplification factor is introduced when calculating the damage increment.

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