Calibration method for bonding strength parameter during simulation of brittle solid material

Abstract

The invention relates to the field of computational mechanics, in particular to a method for calibrating bonding strength parameters during simulation of a brittle solid material, and failure strength data of the brittle solid material is obtained at a preset dynamic strain rate through a split Hopkinson pressure bar (SHPB) iterative test. The failure strength under a certain strain rate is used as an initial bonding strength parameter, and then the bonding strength parameter is updated according to the failure strength of the previous time and the current time in each iteration. And then, constructing a target function, performing parameter optimization by utilizing a simulated annealing algorithm, and judging whether updated bonding strength parameters are accepted or not by adjusting the temperature and the search step size and calculating the increment of the target function. If accepting, continuing iteration until the temperature is lower than the set value, and finally reserving the bonding strength parameter as the calibration value. Based on the calibration method provided by the invention, the real bonding strength of the material can be effectively approached, and the precision and reliability of parameter calibration are improved.

Description

Technical Field

[0001] The present application relates to the field of computational mechanics, and in particular, to a method for calibrating bonding strength parameters when simulating brittle solid materials. Background Art

[0002] Due to the natural advantages of discrete elements in simulating the failure of brittle materials, the discrete element method is widely used in the analysis and research of various solid materials such as rocks, concrete, ceramics, and sea ice. However, since the micro-scale parameters used by the discrete element algorithm are not easy to be directly measured through physical experiments, when using discrete elements to simulate rocks, concrete and other materials, it is necessary to simulate certain conventional strength tests (such as uniaxial compression, three-point bending, Hopkinson pressure bar, etc.), and manually adjust the discrete element micro-parameters until the simulation object is basically consistent with the physical test in terms of the target macro-indicators. The simulation parameters used are regarded as a set of reliable input parameters. However, the traditional manual calibration method is not only time-consuming and labor-intensive, but also difficult to ensure accuracy.

[0003] Bulk materials such as sand are often simulated using linear contact models and Hertz contact models. For cohesive materials such as brittle solids, parallel bonding parameters are usually applied between particle contacts to reflect the characteristics of the cohesive solids. The bond between particles will break under the action of external forces, and continuous bond fractures will cause the instability of the entire material. For cohesive materials such as brittle solids, the breakage of the bond between particles under the action of 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, and the efficiency and accuracy are not ideal.

[0004] To solve the above-mentioned technical problems, the invention patent with publication number CN111610146A discloses an automatic calibration method for discrete element bonding parameters when simulating brittle solids. The compressive strength obtained based on uniaxial compression indoor test and three-point bending indoor test is used as an estimated value of mesoscopic tangential bonding strength and mesoscopic normal bonding strength, and the calibration process is iterated based on an improved adaptive moment estimation optimization algorithm. However, this method may not be able to fully simulate the dynamic loading conditions under actual working conditions, and cannot effectively avoid local optimal solutions, resulting in low efficiency and accuracy of the solution. Therefore, how to provide an efficient and accurate automatic calibration method for inter-particle bonding strength parameters to promote the accurate simulation of brittle solid materials such as rock, concrete, and ceramics by discrete elements has become a technical problem that needs to be solved. Summary of the invention

[0005] In view of this, the present application provides a calibration method for bonding strength parameters when simulating brittle solid materials, which solves the problem that the traditional manual calibration method is time-consuming and labor-intensive and difficult to ensure accuracy.

[0006] The technical solutions provided by this application are as follows:

[0007] A method for calibrating bonding strength parameters when simulating brittle solid materials, comprising:

[0008] S1. Performing a split Hopkinson pressure bar (SHPB) iterative test on samples of brittle solid materials at one or more preset dynamic strain rates, and obtaining the failure strength of the samples at each dynamic strain rate obtained in each iterative test;

[0009] S2, taking the failure strength at any dynamic strain rate in the initial test as the initial bonding strength parameter, and in the iterative test, updating the current bonding strength parameter 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 bonding strength parameter;

[0010] S3. constructing an objective function according to the failure strength and uniaxial compressive strength of the sample at each dynamic strain rate; the uniaxial compressive strength is determined by an indoor Hopkinson uniaxial compression numerical test at each dynamic strain rate performed on the sample according to the initial bond strength parameter;

[0011] S4. Based on the simulated annealing algorithm, the initial temperature, cooling coefficient, minimum temperature and initial search step are set. In the current iteration, the search step is adjusted according to the current temperature, the current bonding strength parameter is updated, and the objective function value corresponding to the current bonding strength parameter is calculated to determine the objective function increment;

[0012] S5. Determine whether to accept the iterative test with the updated bonding strength parameter in the current iteration according to 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 bonding strength parameter as the bonding strength parameter calibration value.

[0013] In one possible implementation, S2 includes:

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

[0015]

[0016] In the formula, := is the assignment symbol, is the initial bonding strength parameter, σ ct2 is the failure strength at any dynamic strain rate;

[0017] The specimens were subjected to secondary SHPB tests to obtain the failure strength at each dynamic strain rate, and the bonding strength parameters were updated, which were expressed as:

[0018]

[0019] In the formula, σ ct1 , σ ct2 , σ ct3 is the average strength at each dynamic strain rate obtained from the initial SHPB test, σ c1 , σ c2 , σ c3 is the failure strength at each dynamic strain rate obtained from the current SHPB test.

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

[0021]

[0022] Among them, λ1, λ2 and λ3 are three weighting coefficients with a value range of [0,1], and λ1+λ2+λ3=1; when the uniaxial compressive strength of three dynamic strain rates is used for calibration at the same time, λ1=λ3=0.3, λ2=0.4; when only the uniaxial compressive strength of two dynamic strain rates is used for calibration, λ1=λ2=0.5; when only the uniaxial compressive strength of one strain rate is used for calibration, λ1=1.

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

[0024] The updating of the current bonding strength parameter in S2 includes:

[0025] Determine the failure strength of the specimen at the current iteration according to the actual dynamic strain rate at the current iteration;

[0026] The current bonding strength parameters are updated according to 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 bonding strength parameters.

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

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

[0029]

[0030] In the formula, is the current bonding strength parameter, Refers to the normalized bonding strength parameter, σ ct2 is the initial bonding strength parameter after assignment;

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

[0032]

[0033] In one possible implementation, S4 includes:

[0034] Set the relevant parameters of simulated annealing, including the initial temperature T0, the minimum temperature T min , cooling coefficient α, initial search step length p0;

[0035] Determine the temperature and search step size for the next iteration; wherein the search step size becomes smaller as the temperature decreases, and is used 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 number of current iterations, T i is the current temperature, p i is the current search step size.

[0039] According to the step size p i , generates a range [-p i ,p i ] is a random number r that follows a uniform distribution i , calculate the updated value of the bonding strength parameter in each iteration step, expressed as:

[0040] r i ∈[-p i ,p i ](7)

[0041]

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

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

[0044] ΔE=L i+1 -L i (9)

[0045] Where ΔE is the increment of the objective function, L i+1is the objective function value corresponding to the current bonding strength parameter, L i is the bonding strength parameter corresponding to the previous iteration.

[0046] In one possible implementation, judging whether to accept the iterative test with the updated bonding strength parameter in the current iteration according to the increment of the objective function includes:

[0047] If the objective function increment ΔE is less than 0, the updated bonding strength parameter is accepted as the current bonding strength parameter, and the iterative test is continued with the current bonding strength parameter;

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

[0049]

[0050] Where, T i is the current temperature;

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

[0052] If R≥P(ΔE), the updated bonding strength parameters are abandoned, and the bonding strength parameters obtained in the previous iteration are retained to continue the iterative test until the current temperature is lower than the minimum temperature, and the current bonding strength parameters are retained as the bonding strength parameter calibration values.

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

[0054] The calibration method of bonding strength parameters when simulating brittle solid materials provided in the embodiment of the present application, by adopting the split Hopkinson pressure bar SHPB iteration test, can accurately obtain the failure strength data of materials under different dynamic strain rates. This method can effectively simulate various dynamic loading conditions that materials may encounter in actual engineering applications, and provides comprehensive and reliable data support for the calibration of bonding strength parameters. Through multi-point measurement of dynamic strain rate, the mechanical behavior characteristics of materials under different strain rates can be more accurately captured, providing a solid foundation for the optimization of subsequent bonding strength parameters. In addition, the method continuously updates the bonding strength parameters in the iteration test, can gradually approach the true bonding strength of the material, and improves the accuracy and reliability of parameter calibration. By introducing the simulated annealing algorithm, the method can effectively avoid the local optimal solution in the parameter search process, so as to find the global optimal bonding strength parameter calibration value. The simulated annealing algorithm can flexibly search in the parameter space by adjusting the temperature and the search step size, and improves the efficiency and accuracy of parameter optimization. Finally, the method can obtain more accurate bonding strength parameter calibration values ​​while ensuring the calculation efficiency, and provides a strong technical guarantee for the engineering application of brittle solid materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a flow chart of a method for calibrating bonding strength parameters when simulating brittle solid materials provided in Example 1 of the present application.

[0056] Figure 2 This is a diagram of the finite difference-discrete element coupled numerical model of the SHPB uniaxial compressive strength test provided in Example 1 of the present application.

[0057] Figure 3 The uniaxial compression stress-strain curves of the C60 concrete specimens provided in Example 1 of the present application at different strain rates. DETAILED DESCRIPTION

[0058] The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present application.

[0059] Embodiment 1

[0060] See also Figure 1 , is a flow chart of a method for calibrating bonding strength parameters when simulating brittle solid materials provided in Example 1 of the present application. Figure 1 As shown in , the specific implementation steps of the above method include:

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

[0062] Specifically, common tests for determining dynamic compressive strength parameters of brittle solid materials include: split Hopkinson bar SHPB test, gravity drop hammer test, etc. From the viewpoint of continuum mechanics, the compressive strength obtained by the split Hopkinson bar SHPB test and the gravity drop hammer test is mainly determined by the shear strength of the sample. Considering that the gravity drop hammer test has a smaller strain rate application range than the split Hopkinson bar SHPB test and may not guarantee the test accuracy, this application adopts the split Hopkinson bar SHPB test as a standard test for calibrating the dynamic compressive mechanical properties of solid materials. In discrete elements, the microscopic parallel bonding parameters that determine the final macroscopic strength index of the sample are mainly the normal bonding parameters (tensile strength parameters) and tangential bonding parameters (shear strength parameters) between particles. The calibrated discrete element model uses the normal bonding parameters and tangential bonding parameters to simulate the macroscopic response of the corresponding split Hopkinson bar SHPB test at the same time.

[0063] In the embodiment of the present application, the split Hopkinson pressure bar SHPB iterative test is performed on the samples of the brittle solid material under one or more preset dynamic strain rates, so as to determine the failure strength of the brittle solid material under different loading conditions, thereby comprehensively capturing the mechanical behavior of the brittle solid material under different strain rates, and providing more accurate data support for the dynamic performance evaluation of the brittle solid material. Through iterative tests, the test parameters can be gradually optimized to ensure that 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 The split Hopkinson pressure bar SHPB test was carried out to measure the dynamic strain rate of the simulated sample at 60s -1 Failure strength at a dynamic strain rate of 85s -1 Failure strength at a dynamic strain rate of 110s -1 Failure strength at .

[0065] Step 2: Take the failure strength at any dynamic strain rate in the initial test as the initial bonding strength parameter, and in the iterative test, update the current bonding strength parameter 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 bonding strength parameter.

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

[0067] For example, the dynamic strain rate of this application embodiment is 85s -1 The failure strength measured at this time is taken as the initial bonding strength parameter and is expressed as:

[0068]

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

[0070] Furthermore, a second SHPB test was performed on the sample to obtain the failure strength at each dynamic strain rate, and the above bond strength parameters were updated and expressed as:

[0071]

[0072] In the formula, σ ct1 , σ ct2 , σ ct3 is the average strength at each dynamic strain rate obtained from the initial SHPB test, σ c1 , σ c2 , σ c3 is the failure strength at each dynamic strain rate obtained from the current SHPB test.

[0073] In a specific application scenario, based on the above initial bonding strength parameters, the brittle solid material is subjected to a dynamic strain rate of 60s. -1 , 85s -1 , 110s -1 The failure strength at each dynamic strain rate obtained from the SHPB test is expressed as σ c1 , σ c2 , σ c3 . With this σ c1 , σ c2 , σ c3 Based on this, the second iteration value of the above bonding strength parameter can be obtained.

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

[0075] Specifically, the embodiment of the present application constructs the above objective function according to the following method, which is expressed as:

[0076]

[0077] Among them, λ1, λ2 and λ3 are three weighting coefficients with a value range of [0,1], and λ1+λ2+λ3=1; when the uniaxial compressive strength of three dynamic strain rates is used for calibration at the same time, λ1=λ3=0.3, λ2=0.4; when only the uniaxial compressive strength of two dynamic strain rates is used for calibration, λ1=λ2=0.5; when only the uniaxial compressive strength of one strain rate is used for calibration, λ1=1.

[0078] The above uniaxial compressive strength is determined by an indoor Hopkinson uniaxial compression numerical test at various dynamic strain rates on the specimen according to the initial bond strength parameters. Figure 2 As shown in , it is a diagram of the finite difference-discrete element coupling numerical model of the SHPB uniaxial compressive strength test provided in Example 1 of the present application. In the numerical simulation of the uniaxial compressive strength test, a half-sine wave represents the input loading waveform, which is used to simulate dynamic loading conditions. The discrete element method is used to simulate the interaction between particles inside the material, and is suitable for describing the destruction process and mechanical behavior of the material. The finite difference rule is used to solve partial differential equations and simulate the deformation and stress distribution of continuous media. The numerical simulation results need to be compared with the actual test results to verify the accuracy of the model, including comparison of stress-strain curves, failure modes, compressive strength and other indicators. Taking the C60 concrete specimen as an example, Figure 3 As shown in , it is the uniaxial compressive stress-strain curve at different strain rates provided in Example 1 of the present application.

[0079] Furthermore, the embodiment of the present application can also use the second iteration value of the above-mentioned bonding strength parameter as the current microscopic tangential bonding strength parameter, that is, the current bonding strength parameter, to perform dynamic strain rate of 60s on the brittle solid material. -1 , 85s -1 , 110s -1 The SHPB numerical simulation test is carried out, and the actual strain rate under each test is deduced based on the simulation results, so as to determine the corresponding failure strength according to the above actual strain rate. Specifically, the failure strength of the sample obtained from any iterative test at each dynamic strain rate is fitted based on the least squares method, and the linear relationship between the failure strength of the sample at each dynamic strain rate and the actual strain rate at the current iteration is determined. Based on the above linear relationship, the failure strength of the brittle solid material sample at the current iteration is determined according to the actual strain rate at the current iteration. Then, the current bonding strength parameters are updated according to the failure strength at each dynamic strain rate in the previous iteration, the failure strength of the sample at the current iteration, and the initial bonding strength parameters.

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

[0081] In the embodiment of the present application, since the bonding strength parameter and the objective function use different units and have a large numerical difference, in order to ensure the convergence performance of the iterative process, the initial bonding strength parameter obtained by the experiment is used to compare the bonding strength parameter on the microscopic scale. After normalization, it is expressed as:

[0082]

[0083] In the formula, is the bonding strength parameter of the current degree, Refers to the normalized bonding strength parameter, σ ct2 is the initial bonding strength parameter after assignment. At this point, the original objective function L can be expressed as a new objective function F with the normalized microscopic bonding strength parameter as the independent variable:

[0084]

[0085] The current bonding strength parameters are updated and iterated according to the simulated annealing algorithm, including: setting the relevant parameters of simulated annealing, including the initial temperature T0, the minimum temperature T min , cooling coefficient α, initial search step size p0, and determine the temperature and search step size for the next iteration.

[0086] Specifically, in each iteration, the search step size is adjusted according to the current temperature. The search step size can become smaller as the temperature decreases. When the initial temperature is high, the step size is large to facilitate the exploration of a larger solution space. As the temperature decreases, the step size gradually decreases to facilitate the refinement of the search. The temperature and search step size are updated as follows, expressed as:

[0087] T i =α i T0 (5)

[0088] p i =α i p0 (6)

[0089] In the formula, i represents the number of current iterations, T i is the current temperature, p i is the current search step size.

[0090] According to the step size p i , generates a range [-p i ,p i] is a random number r that follows a uniform distribution i , calculate the updated value of the bonding strength parameter in each iteration step, expressed as:

[0091] r i ∈[-p i ,p i ] (7)

[0092]

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

[0094] Furthermore, the objective function value L corresponding to the currently used bonding strength parameter is calculated by the numerical model. i+1 , determine the increment ΔE of the objective function, the calculation formula is as follows:

[0095] ΔE=L i+1 -L i (9)

[0096] Where, L i+1 is the objective function value corresponding to the current bonding strength parameter, L i is the bonding strength parameter corresponding to the previous iteration.

[0097] Step 5: Determine whether to accept the iterative test with the updated bonding strength parameter in the current iteration according to the increment ΔE of the objective function. If accepted, continue the iterative test until the current temperature is lower than the minimum temperature, and keep the current bonding strength parameter as the bonding strength parameter calibration value.

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

[0099] Step 51 : According to the increment ΔE of the objective function, if ΔE<0 is satisfied, the updated bonding strength parameter is accepted as the current bonding strength parameter, and the iterative test is continued according to the current bonding strength parameter.

[0100] Step 52: According to the increment ΔE of the objective function, if ΔE>0 is satisfied, the probability P(ΔE) is calculated, and a random number R that follows a uniform distribution in the interval [0,1] is randomly generated to determine whether R is less than P(ΔE). Wherein, P(ΔE) is expressed as:

[0101]

[0102] Where, T i is the current temperature.

[0103] Step 53: If R<P(ΔE), the updated bonding strength parameter is accepted as the current bonding strength parameter, and the iterative test is continued with the current bonding strength parameter.

[0104] Step 54: If R≥P(ΔE), the updated bonding strength parameters are abandoned, and the bonding strength parameters obtained in the previous iteration are retained to continue the iterative test.

[0105] Step 55: until the current temperature is lower than the minimum temperature, the current bonding strength parameter is retained as the bonding strength parameter calibration value.

[0106] The calibration method of the bonding strength parameter when simulating brittle solid materials provided in the embodiment of the present application can accurately obtain the failure strength data of the material under different dynamic strain rates by adopting the separated Hopkinson pressure bar SHPB iteration test. This method can effectively simulate various dynamic loading conditions that the material may encounter in actual engineering applications, thereby providing more comprehensive and reliable data support for the calibration of the bonding strength parameter. Through the multi-point measurement of the dynamic strain rate, the mechanical behavior characteristics of the material under different strain rates can be more accurately captured, providing a solid foundation for the optimization of the subsequent bonding strength parameters. In addition, the method continuously updates the bonding strength parameters in the iteration test, can gradually approach the true bonding strength of the material, and improves the accuracy and reliability of the parameter calibration. Through the introduction of the simulated annealing algorithm, the method can effectively avoid the local optimal solution in the parameter search process, so as to find the global optimal bonding strength parameter calibration value. The simulated annealing algorithm can flexibly search in the parameter space by adjusting the temperature and the search step size, thereby improving the efficiency and accuracy of parameter optimization. Finally, the method can obtain more accurate bonding strength parameter calibration values ​​while ensuring the calculation efficiency, and provides a strong technical guarantee for the engineering application of brittle solid materials.

[0107] Embodiment 2

[0108] In Example 2 of the present application, the method provided by the present application is applied to the calibration of dynamic bonding parameters of a three-dimensional discrete element model of C60 concrete, and the test 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 is measured by the Split Hopkinson Pressure Bar Test (SHPB) at 60s -1 The average failure strength σ ct1 The dynamic strain rate is 66.60MPa and 85s -1The average failure strength σ ct2 is 68.17MPa, and the dynamic strain rate is 110s -1 The average failure strength σ ct3 is 70.23MPa, as shown in the attached Figure 3 The least squares method is used to fit the above data to obtain the dynamic strength relationship of C60 concrete under different strain rate loading. as follows:

[0113]

[0114] in, is 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 was set to 85s -1 The average failure strength at 20° is used as an estimate of the microscopic tangential bond strength.

[0116]

[0117] Among them, ":=" is the assignment symbol. It is the tangential bond strength between particles at the mesoscopic scale.

[0118] Step (3): Use the initial estimate of the microscopic bond strength to perform dynamic strain rate tests at 60 s. -1 , 85s -1 , 110s -1 The failure strengths at different strain rates obtained from the SHPB test 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 size of the objective function L corresponding to the initial estimate of the mesoscopic bond strength.

[0121]

[0122] The second embodiment of the present application simultaneously matches the dynamic strain rate of approximately 60s -1 , 85s -1 , 110s -1 Dynamic uniaxial compressive strength, so take λ1=λ3=0.3, λ2=0.4.

[0123] Step (5): Use the second iteration value of the mesoscopic bond strength (obtained in step (3)) as the current mesoscopic tangential bond strength parameter, and perform dynamic strain tests at a rate of approximately 60 s. -1 , 85s -1 , 110s -1 SHPB numerical simulation test. The actual strain rate under each test is calculated based on the simulation results. According to the dynamic strength relationship of C60 concrete under different strain rate loading obtained in step (1), the corresponding failure strength is calculated using each actual strain rate, and the size of the objective function value L corresponding to the second mesoscopic bond strength iteration value is calculated.

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

[0125] Step (7): Update the value of the objective function with respect to the normalized mesoscopic strength parameter according to the simulated annealing algorithm. Since the units used in the mesoscopic bond strength and the objective function are different and the numerical difference is large, in order 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 test at a dynamic strain rate of 85s-1 ct2 Perform normalization:

[0126]

[0127] in, Refers to the normalized tangential bonding strength. At this point, the original objective function L can be expressed as a new objective function F with the normalized microscopic bonding 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 be reduced as the temperature decreases. When the initial temperature is high, the step size is large to facilitate the exploration of a larger solution space; as the temperature decreases, the step size gradually decreases to facilitate the refinement of the search. Update as follows:

[0130] T i =α i T0

[0131] p i =α i p0

[0132] Where: i is the number of current iterations, T i is the current temperature, p iis the current search step size.

[0133] Step (9): Calculate the candidate mesoscopic tangential bond strength parameters for the next iteration. Based on step (8), the step length p is obtained: i , randomly generate a i ,p i ] is a random number r that follows a uniform distribution i , calculate the updated value of the candidate mesoscopic tangential bond strength 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 bonding strength parameter currently used by the numerical model i+1 , calculate the increment ΔE of the objective function, the calculation formula is as follows:

[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 bonding strength parameter as the current mesoscopic tangential bonding strength parameter. If ΔE > 0, calculate the probability P(ΔE), and the calculation formula is as follows:

[0139]

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

[0141] Step (11): If T i <T min , the calculation is ended, and the current mesoscopic tangential bonding strength parameter currently retained 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 mesoscopic bonding parameters of the C60 concrete model is shown in Table 2. As can be seen from the table, after 6 iterations, the calibration method provided by the present application can simultaneously calibrate the dynamic uniaxial compressive strength of the sample at different strain rates to a smaller error range. -1 , 85s-1 , 110s -1 The errors of dynamic uniaxial compressive strength are 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 the present application have the following beneficial effects:

[0146] (1) High degree of automation, greatly improving the efficiency of parameter calibration. Traditional discrete element simulation parameter calibration methods often require manual repeated experiments and adjustments, which consumes 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 operation links, greatly shortening the parameter calibration cycle, and improving work efficiency, 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) The initial estimation is highly accurate and effectively avoids the risk of local optimality. Based on the potential physical connection between macro and micro strength parameters, this application makes a relatively accurate initial estimation of the micro bonding strength parameters. This estimation method based on physical principles is more scientific and reasonable than the traditional empirical trial and error method. During the iterative calibration process, accurate initial estimates help guide the algorithm to search in the right direction, reduce the risk of the algorithm falling into local optimality due to unreasonable initial values, increase the probability of searching for the global optimal solution, and ensure the accuracy and reliability of the calibration results.

[0148] (3) The algorithm has excellent performance, high calibration accuracy and fast convergence speed. The improved simulated annealing algorithm is used to iterate the calibration process. The simulated annealing algorithm is a classic random optimization algorithm with good global search capabilities and the ability to jump out of local optimality. The improved algorithm, while maintaining its original advantages, further optimizes the parameter setting and iteration strategy, making the algorithm more convergent and more accurate. Within a few iterations, the matching errors of the uniaxial compressive strength parameters of three different strain rates can be converged to a smaller range, which meets the high requirements of discrete element simulation for parameter accuracy and provides a strong guarantee for the accuracy and credibility of the simulation results.

[0149] (4) The implementation process is simple, practical, and has a wide range of applications. The implementation process of this application is concise and clear, easy to understand and operate. Researchers can quickly build a calibration process in commercial discrete element software such as PFC, YADE, and Ligghts according to the provided methods and steps, or they can implement it by programming themselves. This flexibility and convenience make this application very practical and can be widely used in discrete element simulation projects in different fields and of different scales. It provides an effective parameter calibration tool for the numerical simulation of various complex engineering problems, and promotes the application and development of discrete element technology in practical engineering.

[0150] In summary, the present invention is an efficient, stable, clear implementation process and highly adaptable calibration method. The invention can provide technical support for the calibration of bond strength parameters in discrete elements, and promote the accurate simulation of brittle solid materials such as rock, concrete, and ceramics by discrete elements.

[0151] Finally, it should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

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

[0153] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be 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 the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for calibrating bonding strength parameters when simulating brittle solid materials, characterized in that: include: S1. Performing a split Hopkinson pressure bar (SHPB) iterative test on samples of brittle solid materials at one or more preset dynamic strain rates, and obtaining the failure strength of the samples at each dynamic strain rate obtained in each iterative test; S2, taking the failure strength at any dynamic strain rate in the initial test as the initial bonding strength parameter, and in the iterative test, updating the current bonding strength parameter 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 bonding strength parameter; S3. constructing an objective function according to the failure strength and uniaxial compressive strength of the sample at each dynamic strain rate; the uniaxial compressive strength is determined by an indoor Hopkinson uniaxial compression numerical test at each dynamic strain rate performed on the sample according to the initial bond strength parameter; S4. Based on the simulated annealing algorithm, the initial temperature, cooling coefficient, minimum temperature and initial search step are set. In the current iteration, the search step is adjusted according to the current temperature, the current bonding strength parameter is updated, and the objective function value corresponding to the current bonding strength parameter is calculated to determine the objective function increment; S5. Determine whether to accept the iterative test with the updated bonding strength parameter in the current iteration according to 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 bonding strength parameter as the bonding strength parameter calibration value.

2. The method for calibrating bonding strength parameters when simulating brittle solid materials according to claim 1, characterized in that: S2 includes: The failure strength at any dynamic strain rate in the initial SHPB test is taken as the initial bond strength parameter, which is expressed as: In the formula, := is the assignment symbol, is the initial bonding strength parameter, σ ct2 is the failure strength at any dynamic strain rate; The specimens were subjected to secondary SHPB tests to obtain the failure strength at each dynamic strain rate, and the bonding strength parameters were updated, which are expressed as: In the formula, σ ct1 , σ ct2 , σ ct3 is the average strength at each dynamic strain rate obtained from the initial SHPB test, σ c1 , σ c2 , σ c3 is the failure strength at each dynamic strain rate obtained from the current SHPB test.

3. The method for calibrating bonding strength parameters when simulating brittle solid materials according to claim 2, characterized in that: The objective function constructed in S3 is expressed as: Among them, λ1, λ2 and λ3 are three weighting coefficients with a value range of [0,1], and λ1+λ2+λ3=1; when the uniaxial compressive strength of three dynamic strain rates is used for calibration at the same time, λ1=λ3=0.3, λ2=0.4; when only the uniaxial compressive strength of two dynamic strain rates is used for calibration, λ1=λ2=0.5; when only the uniaxial compressive strength of one strain rate is used for calibration, λ1=1.

4. The method for calibrating bonding strength parameters when simulating brittle solid materials according to claim 1, characterized in that: Based on the least square method, the failure strength of the sample obtained in any iterative test at each dynamic strain rate is fitted to determine the linear relationship between the failure strength of the sample at each dynamic strain rate and the actual strain rate at the current iteration; The updating of the current bonding strength parameter in S2 includes: Determine the failure strength of the specimen at the current iteration according to the actual strain rate at the current iteration; The current bonding strength parameters are updated according to 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 bonding strength parameters.

5. The method for calibrating bonding strength parameters when simulating brittle solid materials according to claim 1, characterized in that: Before S4, the method further includes: Based on the initial bonding strength parameters, the current bonding strength parameters are normalized and expressed as: In the formula, is the current bonding strength parameter, Refers to the normalized bonding strength parameter, σ ct2 is the initial bonding strength parameter after assignment; The objective function L is expressed as an objective function F with the normalized bonding strength parameter as the independent variable, expressed as:

6. The method for calibrating bonding strength parameters when simulating brittle solid materials according to claim 1, characterized in that: The S4 includes: Set the relevant parameters of simulated annealing, including the initial temperature T0, the minimum temperature T min , cooling coefficient α, initial search step length p0; Determine the temperature and search step size for the next iteration; wherein the search step size becomes smaller as the temperature decreases, and is used to refine the search, and is expressed as: T i =α i T0 (5) p i =a i p0 (6) In the formula, i is the number of current iterations, T i is the current temperature, p i is the current search step size. According to the step size p i , generates a range [-p i ,p i ] is a random number r that follows a uniform distribution i , calculate the updated value of the bonding strength parameter in each iteration step, expressed as: r i ∈[-p i ,p i ](7) In the formula, := is the assignment symbol, σ ct2 is the initial bonding strength parameter after assignment.

7. The method for calibrating bonding strength parameters when simulating brittle solid materials according to claim 1, characterized in that: Calculate the objective function value corresponding to the current bonding strength parameter and determine the objective function increment, which is expressed as: ΔE=L i+1 -L i (9) Where ΔE is the increment of the objective function, L i+1 is the objective function value corresponding to the current bonding strength parameter, L i is the bonding strength parameter corresponding to the previous iteration.

8. The method for calibrating bonding strength parameters when simulating brittle solid materials according to claim 7, characterized in that: Judging whether to accept the iterative test with the updated bonding strength parameter in the current iteration according to the objective function increment includes: If the objective function increment ΔE is less than 0, the updated bonding strength parameter is accepted as the current bonding strength parameter, and the iterative test is continued with the current bonding strength parameter until the current temperature is less than the minimum temperature, and the current bonding strength parameter is retained as the bonding strength parameter calibration value; If the objective function increment ΔE>0, the probability P(ΔE) is calculated, which is expressed as: Where, T i is the current temperature; A random number R is randomly generated and follows a uniform distribution in the interval [0,1]. If R < P(ΔE), the updated bonding strength parameter is accepted as the current bonding strength parameter, and the iterative test is continued with the current bonding strength parameter until the current temperature is less than the minimum temperature, and the current bonding strength parameter is retained as the bonding strength parameter calibration value; If R≥P(ΔE), the updated bonding strength parameters are abandoned, and the bonding strength parameters obtained in the previous iteration are retained to continue the iterative test until the current temperature is lower than the minimum temperature, and the current bonding strength parameters are retained as the bonding strength parameter calibration values.

Images