A method for calibrating bond strength parameters when simulating brittle solid materials

Abstract

This application relates to the field of computational mechanics, and more particularly to a method for calibrating bond strength parameters when simulating brittle solid materials. It utilizes a split Hopkinson bar (SHPB) iterative test to obtain failure strength data of the brittle solid material at a preset dynamic strain rate. The failure strength at a certain strain rate is used as the initial bond strength parameter, and then updated in each iteration based on the previous and current failure strengths. Next, an objective function is constructed, and the parameters are optimized using a simulated annealing algorithm. By adjusting the temperature and search step size, the increment of the objective function is calculated, and the updated bond strength parameter is determined. If accepted, iteration continues until the temperature is below a set value; the final retained bond strength parameter is the calibration value. Based on the calibration method provided in this application, the true bond strength of the material can be effectively approximated, improving the accuracy and reliability of parameter calibration.

Description

Technical Field

[0001] This application relates to the field of computational mechanics, and more specifically, to a method for calibrating the bond strength parameter when simulating brittle solid materials. Background Technology

[0002] Due to its inherent advantages in simulating the failure of brittle materials, the Discrete Element Method (DEM) is widely used in the analysis and research of various solid materials such as rocks, concrete, ceramics, and sea ice. However, because the mesoscale parameters used in the DEM algorithm are not easily obtained directly through physical experiments, current DEM simulations of materials such as rocks and concrete require simulating certain conventional strength tests (such as uniaxial compression, three-point bending, Hopkinson bar compression, etc.). The mesoscale parameters of the DEM are then manually adjusted until the simulated object's macroscopic properties are essentially consistent with those of the physical tests. Only then are the simulated parameters considered a reliable set of input parameters. However, traditional manual calibration methods are not only time-consuming and labor-intensive but also difficult to guarantee accuracy.

[0003] For granular materials such as sand and soil, linear contact models and Hertzian contact models are commonly used for simulation. For bonded materials such as brittle solids, parallel bonding parameters are typically applied between particle contacts to reflect the characteristics of bonded solids. The bond between particles can fracture under external forces, and continuous bond fracture can lead to the instability of the entire material. For brittle solids and other bonded materials, the fracture of the bond between particles under external forces is a key factor leading to material instability. Existing simulation methods often require the application of parallel bonding parameters, but the determination of these parameters also relies on trial and error, resulting in unsatisfactory efficiency and accuracy.

[0004] To address the aforementioned technical problems, invention patent CN111610146A discloses an automatic calibration method for discrete element method (DEM) bonding parameters when simulating brittle solids. It uses compressive strength obtained from uniaxial compression and three-point bending tests as estimates of mesoscopic tangential and mesoscopic normal bond strengths, and iterates the calibration process using an improved adaptive moment estimation optimization algorithm. However, this method may not fully simulate the dynamic loading conditions under actual working conditions and cannot effectively avoid local optima, resulting in low efficiency and accuracy. Therefore, providing an efficient and accurate automatic calibration method for interparticle bond strength parameters to promote accurate DEM simulation of brittle solid materials such as rocks, concrete, and ceramics has become a technical problem that needs to be solved. Summary of the Invention

[0005] In view of this, this application provides a method for calibrating the bond strength parameter when simulating brittle solid materials, which solves the problems of traditional manual calibration methods being time-consuming, labor-intensive, and difficult to guarantee accuracy.

[0006] The technical solution provided in this application is as follows:

[0007] A method for calibrating bond strength parameters when simulating brittle solid materials includes:

[0008] S1. Perform split Hopkinson bar (SHPB) iterative tests on brittle solid material specimens at one or more preset dynamic strain rates to obtain the failure strength of the specimens at each dynamic strain rate obtained in each iterative test.

[0009] S2. The initial bond strength parameter is the failure strength at any dynamic strain rate in the first test. In the iterative test, the current bond strength parameter is updated based on the failure strength at each dynamic strain rate in the previous iteration, the failure strength at each dynamic strain rate in the current iteration, and the initial bond strength parameter.

[0010] S3. Construct an objective function based on the failure strength and uniaxial compressive strength of the specimen at various dynamic strain rates; the uniaxial compressive strength is determined by indoor Hopkinson uniaxial compression numerical tests of the specimen at various dynamic strain rates based on the initial bond strength parameters.

[0011] S4. Based on the simulated annealing algorithm, set the initial temperature, cooling coefficient, minimum temperature and initial search step size. In the current iteration, adjust the search step size according to the current temperature, update the current bond strength parameters, calculate the objective function value corresponding to the current bond strength parameters, and determine the objective function increment.

[0012] S5. Determine whether to accept the iterative test with the updated bond strength parameter in the current iteration based on the increment of the objective function; if accepted, continue the iterative test until the current temperature is lower than the minimum temperature, and retain the current bond strength parameter as the bond strength parameter calibration value.

[0013] One possible implementation includes S2, which includes:

[0014] The initial bond strength parameter, taken as the failure strength at any dynamic strain rate in the initial SHPB test, is expressed as:

[0015]

[0016] In the formula, := is the assignment symbol. Let σ be the initial bond strength parameter. ct2 The failure strength is given by any dynamic strain rate.

[0017] The failure strength at various dynamic strain rates was obtained by performing a second SHPB test on the specimen, and the bond strength parameter was updated as follows:

[0018]

[0019] In the formula, σ ct1 , σ ct2 , σ ct3 σ represents the average strength obtained from the initial SHPB test at various dynamic strain rates. c1 , σ c2 , σ c3 The failure strength is obtained under various dynamic strain rates in the current SHPB test.

[0020] In one possible implementation, the objective function constructed in S3 is expressed as:

[0021]

[0022] Wherein, λ1, λ2, and λ3 are three weighting coefficients with a value range of [0,1], and λ1+λ2+λ3=1; when calibrating the uniaxial compressive strength using three dynamic strain rates simultaneously, λ1=λ3=0.3, λ2=0.4; when calibrating the uniaxial compressive strength using only two dynamic strain rates, λ1=λ2=0.5; when calibrating the uniaxial compressive strength using only one strain rate, λ1=1.

[0023] In one possible implementation, the failure strength of the specimen obtained in any iteration of the test is fitted at each dynamic strain rate based on the least squares method to determine the linear relationship between the failure strength of the specimen at each dynamic strain rate and the actual dynamic strain rate in the current iteration.

[0024] The S2 step of updating the current bond strength parameters includes:

[0025] The failure strength of the specimen in the current iteration is determined based on the actual dynamic strain rate in the current iteration.

[0026] The current bond strength parameters are updated based on the failure strength at each dynamic strain rate in the previous iteration, the failure strength of the specimen in the current iteration, and the initial bond strength parameters.

[0027] In one possible implementation, before S4, the method further includes:

[0028] Based on the initial bond strength parameters, the current bond strength parameters are normalized and expressed as follows:

[0029]

[0030] In the formula, The current bond strength parameters are as follows: The normalized bond strength parameter, σ ct2 These are the initial bond strength parameters after assignment;

[0031] The objective function L is expressed as an objective function F with the normalized bond strength parameter as the independent variable, as follows:

[0032]

[0033] In one possible implementation, S4 includes:

[0034] Set the relevant parameters for simulated annealing, including the initial temperature T0 and the minimum temperature T. min Cooling coefficient α, initial search step size p0;

[0035] Determine the temperature and search step size for the next iteration; wherein the search step size decreases as the temperature decreases to refine the search, and is expressed as:

[0036] T i =α i T0 (5)

[0037] p i =α i p0 (6)

[0038] In the formula, i is the current iteration number, and T i Given the current temperature, p i This represents the current search step size.

[0039] Based on step size p i Generate a value in the range [-p] i ,p i A random number r that follows a uniform distribution within the range i The updated value of the bond strength parameter in each iteration step is calculated and expressed as:

[0040] r i ∈[-p i ,p i (7)

[0041]

[0042] In the formula, := is the assignment symbol, σ ct2 This represents the initial bond strength parameter after assignment.

[0043] In one possible implementation, the objective function value corresponding to the current bond strength parameter is calculated, and the objective function increment is determined, expressed as follows:

[0044] ΔE=L i+1 -L i (9)

[0045] In the formula, ΔE is the increment of the objective function, and L i+1L represents the objective function value corresponding to the current bond strength parameters. i This refers to the bond strength parameter corresponding to the previous iteration.

[0046] One possible implementation involves determining whether to accept iterative testing with the updated bond strength parameters in the current iteration based on the objective function increment, including:

[0047] If the objective function increment ΔE < 0, then the updated bond strength parameter is accepted as the current bond strength parameter, and the iterative experiment continues with the current bond strength parameter;

[0048] If the objective function increment ΔE > 0, then the probability P(ΔE) is calculated and expressed as:

[0049]

[0050] In the formula, T i The current temperature;

[0051] A random number R is randomly generated that follows a uniform distribution in the interval [0,1]. If R < P(ΔE), the updated bond strength parameter is accepted as the current bond strength parameter, and the iterative test is continued with the current bond strength parameter.

[0052] If R≥P(ΔE), then the updated bond strength parameter is discarded, and the bond strength parameter obtained in the previous iteration is retained to continue the iterative test until the current temperature is lower than the minimum temperature. The current bond strength parameter is then retained as the bond strength parameter calibration value.

[0053] Compared with the prior art, the technical solution provided in this application has the following beneficial effects:

[0054] The method for calibrating bond strength parameters in simulating brittle solid materials provided in this application employs a split Hopkinson bar (SHPB) iterative test, enabling accurate acquisition of material failure strength data under different dynamic strain rates. This method effectively simulates various dynamic loading conditions that materials may encounter in practical engineering applications, providing comprehensive and reliable data support for bond strength parameter calibration. Multi-point measurement of dynamic strain rates allows for more accurate capture of the material's mechanical behavior characteristics at different strain rates, providing a solid foundation for subsequent optimization of bond strength parameters. Furthermore, the method continuously updates bond strength parameters during iterative experiments, gradually approximating the material's true bond strength, thus improving the accuracy and reliability of parameter calibration. By introducing a simulated annealing algorithm, this method effectively avoids local optima during parameter search, thereby finding the globally optimal bond strength parameter calibration value. The simulated annealing algorithm, by adjusting temperature and search step size, allows for flexible searching in the parameter space, improving the efficiency and accuracy of parameter optimization. Ultimately, this method achieves more accurate bond strength parameter calibration values ​​while maintaining computational efficiency, providing strong technical support for the engineering application of brittle solid materials. Attached Figure Description

[0055] Figure 1 This is a flowchart illustrating a method for calibrating bond strength parameters when simulating brittle solid materials, as provided in Embodiment 1 of this application.

[0056] Figure 2 The diagram shows the finite difference-discrete element coupled numerical model of the SHPB uniaxial compressive strength test provided in Embodiment 1 of this application.

[0057] Figure 3 Uniaxial compressive stress-strain curves of C60 concrete specimens provided in Embodiment 1 of this application at different strain rates. Detailed Implementation

[0058] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the embodiments of this application. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0059] Example 1

[0060] See Figure 1 This is a flowchart illustrating a method for calibrating bond strength parameters when simulating brittle solid materials, as provided in Embodiment 1 of this application. Figure 1 As shown, the specific implementation steps of the above method include:

[0061] Step 1: Perform split Hopkinson bar (SHPB) iterative tests on brittle solid material specimens at one or more preset dynamic strain rates to obtain the failure strength of the specimens at each dynamic strain rate obtained in each iteration test.

[0062] Specifically, common tests for determining the dynamic compressive strength parameters of brittle solid materials include the split Hopkinson bar (SHPB) test and the drop weight test. From the perspective of continuum mechanics, the compressive strength obtained from the SHPB test and the drop weight test is mainly determined by the shear strength of the specimen. Considering that the drop weight test has a smaller applicable strain rate range and may not guarantee test accuracy compared to the SHPB test, this application adopts the SHPB test as the standard test for calibrating the dynamic compressive mechanical properties of solid materials. In the discrete element method (DEM), the mesoscopic parallel bond parameters that determine the final macroscopic strength index of the specimen are mainly the normal bond parameters (tensile strength parameters) and tangential bond parameters (shear strength parameters) between particles. The calibrated DEM model uses normal and tangential bond parameters that simultaneously and well simulate the macroscopic response of the corresponding SHPB test.

[0063] In this embodiment, split Hopkinson bar (SHPB) iterative tests are performed on brittle solid material samples under one or more preset dynamic strain rates. This allows for the determination of the failure strength of brittle solid materials under different loading conditions, thereby comprehensively capturing the mechanical behavior of brittle solid materials at different strain rates and providing more accurate data support for the dynamic performance evaluation of brittle solid materials. Through iterative testing, test parameters can be gradually optimized to ensure reliable failure strength values ​​are obtained under various strain rate conditions.

[0064] In some embodiments, the dynamic strain rate is 60s. -1 85s -1 and 110s -1 A split Hopkinson bar (SHPB) test was conducted to measure the dynamic strain rate of the simulated specimen at 60 s⁻¹. -1 The failure strength at 85 s⁻¹, with a dynamic strain rate of 85 s⁻¹ -1 The failure strength at a dynamic strain rate of 110 s⁻¹ -1 Failure strength at that time.

[0065] Step 2: Take the failure strength at any dynamic strain rate in the initial test as the initial bond strength parameter, and update the current bond strength parameter in the iterative test according to the failure strength at each dynamic strain rate in the previous iteration, the failure strength at each dynamic strain rate in the current iteration, and the initial bond strength parameter.

[0066] Specifically, the failure strength at any dynamic strain rate in the initial SHPB test is used as the initial bond strength parameter to preliminarily determine the estimated value of the mesoscopic tangential bond strength.

[0067] For example, in this embodiment of the application, a dynamic strain rate of 85s is selected. -1 The failure strength measured at that time is used as the initial bond strength parameter, and is expressed as:

[0068]

[0069] In the formula, := is the assignment symbol. Let σ be the initial bond strength parameter. ct2 The failure strength is the value at any selected dynamic strain rate.

[0070] Furthermore, a second SHPB test was performed on the specimen to obtain the failure strength at various dynamic strain rates, and the above bond strength parameters were updated as follows:

[0071]

[0072] In the formula, σ ct1 , σ ct2 , σ ct3 σ represents the average strength obtained from the initial SHPB test at various dynamic strain rates. c1 , σ c2 , σ c3 The failure strength is obtained under various dynamic strain rates in the current SHPB test.

[0073] In a specific application scenario, based on the initial bond strength parameters mentioned above, the brittle solid material is subjected to dynamic strain at a rate of 60 s⁻¹. -1 85s -1 110s -1 The failure strength obtained from the SHPB test at various dynamic strain rates is expressed as σ. c1 σ c2 σ c3 . Therefore σ c1 σ c2 σ c3 Based on this, the second iterative values ​​of the aforementioned bond strength parameters can be obtained.

[0074] Step 3: Construct the objective function based on the failure strength and uniaxial compressive strength of the specimen at various dynamic strain rates.

[0075] Specifically, the objective function described above is constructed in the embodiments of this application as follows:

[0076]

[0077] Wherein, λ1, λ2, and λ3 are three weighting coefficients with a value range of [0,1], and λ1+λ2+λ3=1; when calibrating the uniaxial compressive strength using three dynamic strain rates simultaneously, λ1=λ3=0.3, λ2=0.4; when calibrating the uniaxial compressive strength using only two dynamic strain rates, λ1=λ2=0.5; when calibrating the uniaxial compressive strength using only one strain rate, λ1=1.

[0078] The aforementioned uniaxial compressive strength was determined by indoor Hopkinson uniaxial compression numerical tests at various dynamic strain rates performed on the specimens based on initial bond strength parameters. For example... Figure 2 The diagram shown is a finite difference-discrete element coupled numerical model diagram of the SHPB uniaxial compressive strength test provided in Embodiment 1 of this application. In the numerical simulation of the uniaxial compressive strength test, a half-sine wave represents the input loading waveform, used to simulate dynamic loading conditions. The discrete element method is used to simulate the interaction between particles within the material, suitable for describing the failure process and mechanical behavior of the material. The finite difference method is used to solve partial differential equations, simulating the deformation and stress distribution of a continuous medium. The numerical simulation results need to be compared with actual experimental results to verify the accuracy of the model, including comparing stress-strain curves, failure modes, compressive strength, and other indicators. Taking a C60 concrete sample as an example, as... Figure 3 The figure shows uniaxial compressive stress-strain curves at different strain rates provided in Embodiment 1 of this application.

[0079] Furthermore, in this embodiment, the second iteration value of the above-mentioned bond strength parameter can also be used as the current mesoscopic tangential bond strength parameter, i.e., the current bond strength parameter, and dynamic strain rate of 60s can be applied to the brittle solid material. -1 85s -1 110s -1 SHPB numerical simulation experiments were conducted, and the actual strain rates under each test were calculated based on the simulation results. The corresponding failure strengths were then determined based on these actual strain rates. Specifically, the failure strengths of the specimens obtained from any iteration of the experiment were fitted using the least squares method at each dynamic strain rate to determine the linear relationship between the failure strength of the specimens at each dynamic strain rate and the actual strain rate in the current iteration. Based on this linear relationship, the failure strength of the brittle solid material specimen in the current iteration was determined according to the actual strain rate in the current iteration. Furthermore, the current bond strength parameters were updated based on the failure strengths at each dynamic strain rate in the previous iteration, the failure strength of the specimen in the current iteration, and the initial bond strength parameters.

[0080] Step 4: Based on the simulated annealing algorithm, set the initial temperature, minimum temperature, cooling coefficient and initial search step size. In the current iteration, adjust the search step size according to the current temperature, update the current bond strength parameters, calculate the objective function value corresponding to the current bond strength parameters, and determine the objective function increment.

[0081] In this embodiment, the bond strength parameter and the objective function use different units and have significantly different values. To ensure the convergence performance of the iterative process, the initial bond strength parameter obtained experimentally is used to adjust the bond strength parameter at the mesoscale. After normalization, it is represented as:

[0082]

[0083] In the formula, This represents the current bond strength parameter. The normalized bond strength parameter, σ ct2 Let L be the initial bond strength parameter after assignment. At this point, the original objective function L can be expressed as a new objective function F with the normalized mesoscopic bond strength parameter as the independent variable:

[0084]

[0085] The current bond strength parameters are updated iteratively based on the simulated annealing algorithm, specifically including: setting relevant parameters for simulated annealing, including the initial temperature T0 and the minimum temperature T. min The system determines the cooling coefficient α, the initial search step size p0, and the temperature and search step size for the next iteration.

[0086] Specifically, in each iteration, the search step size is adjusted based on the current temperature. The search step size can decrease as the temperature decreases. At higher initial temperatures, the step size is larger to explore a larger solution space. As the temperature decreases, the step size gradually decreases to refine the search. The temperature and search step size are updated as follows:

[0087] T i =α i T0 (5)

[0088] p i =α i p0 (6)

[0089] In the formula, i represents the current iteration number, and T i Given the current temperature, p i This represents the current search step size.

[0090] Based on step size p i Generate a value in the range [-p] i ,p iA random number r that follows a uniform distribution within the range i The updated value of the bond strength parameter in each iteration step is calculated and expressed as:

[0091] r i ∈[-p i ,p i (7)

[0092]

[0093] In the formula, := is the assignment symbol, σ ct2 This represents the initial bond strength parameter after assignment.

[0094] Furthermore, the objective function value L corresponding to the currently used bond strength parameters is calculated using a numerical model. i+1 The increment ΔE of the objective function is determined by the following formula:

[0095] ΔE=L i+1 -L i (9)

[0096] In the formula, L i+1 L represents the objective function value corresponding to the current bond strength parameters. i This refers to the bond strength parameter corresponding to the previous iteration.

[0097] Step 5: Determine whether to accept iterative testing with the updated bond strength parameters in the current iteration based on the objective function increment ΔE. If accepted, continue iterative testing until the current temperature is lower than the minimum temperature, and retain the current bond strength parameters as the bond strength parameter calibration value.

[0098] Specifically, such as Figure 1 As shown, step 5 may further include:

[0099] Step 51: Based on the objective function increment ΔE, if ΔE<0 is satisfied, then the updated bond strength parameter is accepted as the current bond strength parameter, and iterative experiments are continued based on the current bond strength parameter.

[0100] Step 52: Based on the objective function increment ΔE, if ΔE > 0, calculate the probability P(ΔE), and randomly generate a random number R that follows a uniform distribution on the interval [0,1]. Determine whether R is less than P(ΔE). Here, P(ΔE) is expressed as:

[0101]

[0102] In the formula, T i This is the current temperature.

[0103] Step 53: If R < P(ΔE), then accept the updated bond strength parameter as the current bond strength parameter, and continue the iterative test with the current bond strength parameter.

[0104] Step 54: If R≥P(ΔE), then discard the updated bond strength parameters and retain the bond strength parameters obtained in the previous iteration to continue the iterative experiment.

[0105] Step 55: Until the current temperature is lower than the minimum temperature, retain the current bond strength parameter as the bond strength parameter calibration value.

[0106] The method for calibrating bond strength parameters in simulating brittle solid materials provided in this application employs a split Hopkinson bar (SHPB) iterative test, which accurately obtains the material's failure strength data under different dynamic strain rates. This method effectively simulates various dynamic loading conditions that materials may encounter in practical engineering applications, thus providing more comprehensive and reliable data support for the calibration of bond strength parameters. Through multi-point measurement of dynamic strain rates, the mechanical behavior characteristics of the material under different strain rates can be captured more accurately, providing a solid foundation for subsequent optimization of bond strength parameters. Furthermore, this method continuously updates the bond strength parameters in iterative experiments, gradually approximating the material's true bond strength, improving the accuracy and reliability of parameter calibration. By introducing a simulated annealing algorithm, this method effectively avoids local optima during parameter search, thereby finding the globally optimal bond strength parameter calibration value. The simulated annealing algorithm, by adjusting the temperature and search step size, can flexibly search within the parameter space, improving the efficiency and accuracy of parameter optimization. Ultimately, this method can obtain more accurate bond strength parameter calibration values ​​while ensuring computational efficiency, providing strong technical support for the engineering application of brittle solid materials.

[0107] Example 2

[0108] In Embodiment 2 of this application, the method provided in this application is applied to the calibration of dynamic bond parameters of a three-dimensional discrete element model of C60 concrete. The experimental parameters are as follows:

[0109] Table 1 Particle Model Parameters

[0110]

[0111] The simulation steps are as follows:

[0112] Step (1): The dynamic strain rate of C60 concrete was measured to be 60 s using the split Hopkinson bar test (SHPB). -1 The average failure strength σ at that time ct1 The pressure is 66.60 MPa, and the dynamic strain rate is 85 s⁻¹. -1The average failure strength σ at that time ct2 The pressure is 68.17 MPa, and the dynamic strain rate is 110 s⁻¹. -1 The average failure strength σ at that time ct3 It is 70.23 MPa, as shown in the attached document. Figure 3 As shown. The data above were fitted using the least squares method to obtain the dynamic strength relationship of C60 concrete under different strain rate loading. as follows:

[0113]

[0114] in, This represents the actual average strain rate of the concrete specimen measured in each test.

[0115] Step (2): Initial estimation of microscopic strength parameters. Based on the macroscopic strength parameters obtained from the experiment, the dynamic strain rate is set to 85 s⁻¹. -1 The average failure strength at that time is used as an estimate of the mesoscopic tangential bond strength. As follows:

[0116]

[0117] In this context, ":=" is the assignment operator. It is the tangential bonding strength between particles at a microscopic scale.

[0118] Step (3): Using the initial estimate of the microscopic bond strength, dynamic strain rate of 60s was measured. -1 85s -1 110s -1 The failure strengths obtained from the SHPB test at various strain rates are σ c1 σ c2 σ c3 Calculate the second iteration value of the mesoscopic bond strength:

[0119]

[0120] Step (4): Construct the objective function L as follows, and calculate the magnitude of the objective function L corresponding to the initial estimate of the microscopic bond strength.

[0121]

[0122] In Embodiment 2 of this application, the dynamic strain rate is simultaneously matched to approximately 60s. -1 85s -1 110s -1 The dynamic uniaxial compressive strength is determined, therefore λ1=λ3=0.3, λ2=0.4.

[0123] Step (5): Using the second iteration value of the micro-bond strength (obtained in step (3)) as the current micro-tangential bond strength parameter, dynamic strain rates of approximately 60 s are applied. -1 85s -1 110s -1 The SHPB numerical simulation test was conducted. Based on the simulation results, the actual strain rate under each test was calculated. According to the dynamic strength relationship of C60 concrete under different strain rates obtained in step (1), the corresponding failure strength was calculated using each actual strain rate, and the objective function value L corresponding to the second microscopic bond strength iteration value was calculated.

[0124] Step (6): Set the relevant parameters for simulated annealing. The initial temperature T0 is generally set to 100; the minimum temperature T min The initial search step size is typically set to 0.01; the cooling coefficient α is typically set to 0.95; and the initial search step size p0 is typically set to 0.1.

[0125] Step (7): Update the objective function with respect to the normalized mesoscopic strength parameters according to the simulated annealing algorithm. Since the units used for the mesoscopic bond strength and the objective function are different, and the numerical differences are significant, to ensure the convergence performance of the iterative process, the tangential bond strength at the mesoscopic scale is... The average failure strength σ obtained from the experiment at a dynamic strain rate of 85 s⁻¹ was used. ct2 Normalization is performed:

[0126]

[0127] in, This refers to the normalized tangential bond strength. In this case, the original objective function L can be expressed as a new objective function F with the normalized mesoscopic bond strength parameter as the independent variable:

[0128]

[0129] Step (8): Calculate the temperature and search step size for the next iteration. The step size can decrease as the temperature decreases. A larger step size is used when the initial temperature is higher to explore a larger solution space; as the temperature decreases, the step size gradually decreases to refine the search. Update as follows:

[0130] T i =α i T0

[0131] p i =α i p0

[0132] Where: i is the current iteration number, T i Given the current temperature, p iThis represents the current search step size.

[0133] Step (9): Calculate the candidate mesoscopic tangential bond strength parameters for the next iteration. The step size p is obtained based on step (8). i Randomly generate a value in the range [-p] i ,p i A random number r that follows a uniform distribution within the range i The updated value of the candidate mesoscopic tangential bond strength is calculated in each iteration step, and the update formula is as follows:

[0134] r i ∈[-p i ,p i ]

[0135]

[0136] Step (10): Calculate the objective function value L corresponding to the candidate mesoscopic tangential bond strength parameter currently used through a numerical model. i+1 The increment ΔE of the objective function is calculated using the following formula:

[0137] ΔE=L i+1 -L i

[0138] Determine whether to accept the current new solution. If ΔE < 0, then accept the candidate mesoscopic tangential bond strength parameter as the current mesoscopic tangential bond strength parameter. If ΔE > 0, then calculate the probability P(ΔE) using the following formula:

[0139]

[0140] A random number R is randomly generated that follows a uniform distribution on the interval [0,1]. If R < P(ΔE), the candidate tangential bond strength parameter is accepted as the latest tangential bond strength parameter. Otherwise, the candidate tangential bond strength parameter is discarded, and the current mesoscopic tangential bond strength parameter from the previous iteration is retained.

[0141] Step (11): If T i <T min The calculation ends, and the current microscopic tangential bond strength parameter is the calibration parameter. If the temperature requirement is not met, the parameter value is updated and recalculated according to steps (6)-(10) until the current temperature meets the requirement.

[0142] The calibration process of the microstructure bond parameters of the C60 concrete model is shown in Table 2. As can be seen from the table, after six iterations, the calibration method provided in this application can simultaneously calibrate the dynamic uniaxial compressive strength of the specimen at different strain rates to a relatively small error range. The dynamic strain rate is 60 s⁻¹. -1 85s-1 110s -1 The dynamic uniaxial compressive strength errors were 1.3%, 3.1%, and 2.0%, respectively.

[0143] Table 2 Iterative verification process of microscopic bonding parameters

[0144]

[0145] Compared with the prior art, the embodiments of this application have the following beneficial effects:

[0146] (1) High degree of automation, significantly improving parameter calibration efficiency. Traditional discrete element simulation parameter calibration methods often require repeated manual trials and adjustments, consuming a lot of manpower and time. However, this application can automatically and quickly calibrate the parallel bonding parameters required for discrete element simulation, eliminating tedious manual operations, greatly shortening the parameter calibration cycle, improving work efficiency, and allowing researchers to devote more energy to core work such as simulation analysis and result interpretation, laying a solid foundation for the widespread application and in-depth research of discrete element simulation.

[0147] (2) High initial estimation accuracy effectively avoids the risk of local optima. This application uses the potential physical relationship between macroscopic and microscopic strength parameters to make a relatively accurate initial estimation of microscopic bond strength parameters. This estimation method based on physical principles is more scientific and reasonable than the traditional empirical trial-and-error method. In the iterative calibration process, accurate initial estimates help guide the algorithm to search in the correct direction, reduce the risk of the algorithm getting trapped in local optima due to unreasonable initial values, increase the probability of finding the global optimal solution, and ensure the accuracy and reliability of the calibration results.

[0148] (3) The algorithm exhibits superior performance, high calibration accuracy, and fast convergence. An improved simulated annealing algorithm is used for the iterative calibration process. Simulated annealing is a classic stochastic optimization algorithm with excellent global search capabilities and the ability to escape local optima. The improved algorithm, while maintaining its original advantages, further optimizes the parameter settings and iteration strategy, resulting in better convergence and higher accuracy. Within a few iterations, the matching error of the uniaxial compressive strength parameters for three different strain rates can be converged to a small range, meeting the high requirements of discrete element simulation for parameter accuracy and providing a strong guarantee for the accuracy and reliability of the simulation results.

[0149] (4) The implementation process is simple, highly practical, and widely applicable. The implementation process of this application is concise and clear, easy to understand and operate. Researchers can quickly build calibration processes in commercial discrete element software such as PFC, YADE, and Lightning based on the provided methods and steps, or they can implement it themselves through programming. This flexibility and convenience make this application highly practical and widely applicable to discrete element simulation projects of different fields and scales. It provides an effective parameter calibration tool for numerical simulation of various complex engineering problems, promoting the application and development of discrete element technology in practical engineering.

[0150] In summary, this invention is an efficient, stable, and adaptable calibration method with a clear implementation process. This invention can provide technical support for the calibration of bond strength parameters in discrete element methods and promote the accurate simulation of brittle solid materials such as rocks, concrete, and ceramics by discrete element methods.

[0151] Finally, 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 a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0152] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0153] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for calibrating bond strength parameters when simulating brittle solid materials, characterized in that, include: S1. Under various preset dynamic strain rates, separate Hopkinson bar (SHPB) iterative tests were conducted on brittle solid material samples to obtain the failure strength of the samples under each dynamic strain rate in each iterative test. S2. The initial bond strength parameter is the failure strength at any dynamic strain rate in the first test. In the iterative test, the current bond strength parameter is updated based on the failure strength at each dynamic strain rate in the previous iteration, the failure strength at each dynamic strain rate in the current iteration, and the initial bond strength parameter. S3. Construct an objective function based on the failure strength and uniaxial compressive strength of the specimen at various dynamic strain rates; the uniaxial compressive strength is determined by indoor Hopkinson uniaxial compression numerical tests of the specimen at various dynamic strain rates based on the initial bond strength parameters. S4. Based on the simulated annealing algorithm, set the initial temperature, cooling coefficient, minimum temperature and initial search step size. In the current iteration, adjust the search step size according to the current temperature, update the current bond strength parameters, calculate the objective function value corresponding to the current bond strength parameters, and determine the objective function increment. S5. Determine whether to accept iterative testing with the updated bond strength parameters in the current iteration based on the increment of the objective function. If accepted, continue iterative testing until the current temperature is lower than the minimum temperature, and retain the current bond strength parameter as the bond strength parameter calibration value; S2 includes: The initial bond strength parameter, taken as the failure strength at any dynamic strain rate in the initial SHPB test, is expressed as: ； In the formula, For assignment operator, These are the initial bond strength parameters. The failure strength is given by any dynamic strain rate. The failure strength at various dynamic strain rates was obtained by performing a second SHPB test on the specimen, and the bond strength parameter was updated as follows: ； In the formula, , , The average strength at various dynamic strain rates obtained from the initial SHPB test. , , The failure strength is obtained at various dynamic strain rates in the current SHPB test.

2. The method for calibrating the bond strength parameter when simulating brittle solid materials according to claim 1, characterized in that, The objective function constructed in S3 is expressed as follows: ； in, , and Let be three weighted coefficients with a value range of [0,1], and When calibrating uniaxial compressive strength using three different dynamic strain rates simultaneously, , When calibrating uniaxial compressive strength using only two dynamic strain rates, .

3. The method for calibrating the bond strength parameter when simulating brittle solid materials according to claim 1, characterized in that, The failure strength of the specimen obtained in any iteration of the test is fitted by the least squares method at each dynamic strain rate to determine the linear relationship between the failure strength of the specimen at each dynamic strain rate and the actual strain rate in the current iteration. The S2 step of updating the current bond strength parameters includes: The failure strength of the specimen in the current iteration is determined based on the actual strain rate in the current iteration. The current bond strength parameters are updated based on the failure strength at each dynamic strain rate in the previous iteration, the failure strength of the specimen in the current iteration, and the initial bond strength parameters.

4. The method for calibrating the bond strength parameter when simulating brittle solid materials according to claim 1, characterized in that, Prior to S4, the method further includes: Based on the initial bond strength parameters, the current bond strength parameters are normalized and expressed as follows: ； In the formula, The current bond strength parameters are as follows: Refers to the normalized bond strength parameter. These are the initial bond strength parameters after assignment; The objective function L is expressed as an objective function F with the normalized bond strength parameter as the independent variable, as follows: 。 5. The method for calibrating the bond strength parameter when simulating brittle solid materials according to claim 1, characterized in that, S4 includes: Set the relevant parameters for simulated annealing, including the initial temperature. Minimum temperature Cooling coefficient Initial search step size ; Determine the temperature and search step size for the next iteration; wherein the search step size decreases as the temperature decreases to refine the search, and is expressed as: ； ； In the formula, This represents the current iteration number. The current temperature, This is the current search step size; Based on step size Generate a range Random numbers that follow a uniform distribution The updated value of the bond strength parameter in each iteration step is calculated and expressed as: ； ； In the formula, Assignment operator, The initial bond strength parameters after assignment.

6. The method for calibrating the bond strength parameter when simulating brittle solid materials according to claim 1, characterized in that, Calculate the objective function value corresponding to the current bond strength parameters, determine the objective function increment, and express it as: ； In the formula, The increment of the objective function, The objective function value corresponding to the current bond strength parameters. This refers to the bond strength parameter corresponding to the previous iteration.

7. The method for calibrating the bond strength parameter when simulating brittle solid materials according to claim 6, characterized in that, Determining whether to accept iterative testing with updated bond strength parameters in the current iteration based on the objective function increment includes: If the objective function increment If the updated bond strength parameter is accepted as the current bond strength parameter, the iterative test will continue with the current bond strength parameter until the current temperature is lower than the minimum temperature, and the current bond strength parameter will be retained as the bond strength parameter calibration value. If the objective function increment Then calculate the probability. , is represented as: ； In the formula, The current temperature; Randomly generate a value in the interval Random numbers that follow a uniform distribution ,like If the updated bond strength parameter is accepted as the current bond strength parameter, the iterative test will continue with the current bond strength parameter until the current temperature is lower than the minimum temperature, and the current bond strength parameter will be retained as the bond strength parameter calibration value. like If the updated bond strength parameter is not obtained, the bond strength parameter obtained in the previous iteration is retained and iterative experiments are continued until the current temperature is lower than the minimum temperature. The current bond strength parameter is then retained as the bond strength parameter calibration value.

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