Internal pressure bulging test material elastic-plastic-creep constitutive finite element-PSO-NM collaborative inversion calibration method

Abstract

This invention discloses a collaborative inversion calibration method for elastoplastic-creep constitutive finite element-PSO-NM modeling of materials subjected to internal pressure bulging tests. Belonging to the field of material mechanical property testing and numerical simulation technology, this method includes the following steps: S1, acquiring experimental data; S2, establishing a finite element model; S3, constructing an objective function; S4, designing a PSO-NM hybrid optimization algorithm; S5, building an automated integrated program; and S6, performing closed-loop inverse finite element parameter calibration. This invention employs the aforementioned collaborative inversion calibration method for elastoplastic-creep constitutive finite element-PSO-NM modeling of materials subjected to internal pressure bulging tests to establish the relationship between micro-samples and standard constitutive parameters, achieving integrated calibration of multiple performance parameters, balancing global and local search efficiency, and improving parameter calibration accuracy and stability.

Description

Technical Field

[0001] This invention belongs to the field of material mechanical property testing and numerical simulation technology, specifically involving a collaborative inversion calibration method for elastoplastic-creep constitutive finite element-PSO-NM model of materials for internal pressure bulging test. Background Technology

[0002] In engineering fields such as thermal power, aerospace and nuclear energy, structural materials such as heat-resistant steel need to be used for a long time in high temperature, high pressure and complex load environments. Their tensile properties and creep properties are directly related to the safe and stable operation of equipment. Therefore, accurately obtaining the mechanical constitutive parameters of such materials is a core requirement for engineering design and equipment operation and maintenance.

[0003] However, existing technologies have the following shortcomings: Traditional material mechanical parameters rely on standard uniaxial tensile and creep tests. These tests have strict requirements on specimen size, which cannot meet the needs of engineering scenarios where in-service components, equipment, or material samples are limited. Sampling is difficult and may damage the equipment. Although micro-sample testing methods such as internal pressure bulging tests and small punch tests have small sample sizes and low damage, the macroscopic response results obtained from the tests cannot directly correspond to standard constitutive parameters. Numerical inversion methods are required for parameter conversion. Most existing inversion methods are designed for a single test form or are only applicable to the analysis of the elastic-plastic behavior of materials, making it difficult to simultaneously take into account the unified calibration of tensile and creep properties. Existing numerical inversion methods lack efficient optimization algorithms, and are prone to getting trapped in local optima during the identification of complex constitutive parameters, resulting in the accuracy and stability of parameter calibration failing to meet engineering requirements.

[0004] Therefore, a new method is urgently needed. Summary of the Invention

[0005] The purpose of this invention is to provide a collaborative inversion calibration method for elastoplastic-creep constitutive finite element-PSO-NM in internal pressure bulging test materials. This method establishes the relationship between micro-samples and standard constitutive parameters, realizes integrated calibration of multiple performance parameters, takes into account both global and local search efficiency, and improves parameter calibration accuracy and stability.

[0006] To achieve the above objectives, this invention provides a method for the collaborative inversion and calibration of materials for internal pressure bulging tests using elastoplastic-creep constitutive finite element-PSO-NM methods, comprising the following steps: S1. Prepare the sample and complete the internal pressure bulging test, collect experimental response data and construct the experimental response vector, and output the experimental curve and test condition parameters. S2. Based on the test condition parameters of S1, construct a finite element model for the matching internal pressure bulging test, set the geometric dimensions, boundary conditions, loading mode and contact definition, and output the finite element model. S3. Based on the experimental response vector of S1, define the finite element simulation response vector, use the root mean square error (RMSE) to construct the objective function to quantify the deviation between the experimental and simulated responses, and output the objective function and data preprocessing rules. S4. Based on the objective function of S3, construct a hybrid optimization algorithm that integrates the PSO global search module and the Nelder-Mead local refinement module, which combines time-varying parameter control and premature convergence suppression. Complete the algorithm initialization and core rule setting, and output the PSO-NM algorithm logic and parameter value range. S5. Construct an automated iterative closed loop consisting of a parameter correction module, a finite element calculation module, an error evaluation module, and an optimization iteration module. Integrate the finite element model of S2 and the PSO-NM algorithm logic of S4 into the closed loop. Through iteration, until the convergence criterion is met, the final calibrated material constitutive parameters are output.

[0007] Preferably, in S1, the sample is a plate sample, which is a circular thin plate with a diameter of 10-20 mm and a thickness of 0.5-2 mm. The loading modes of the internal pressure bulging test include elastoplastic loading, creep loading and burst loading. Elastic loading applies internal pressure to the target deformation, creep loading uses constant pressure to maintain the load, and burst loading is performed until the specimen fails. The experimental response data includes pressure-center displacement data and center displacement-time data. After collection, outliers are removed and no less than 50 equally spaced valid data points are selected to construct the experimental response vector.

[0008] Preferably, in S2, the establishment of the finite element model includes a three-stage analysis step setting, specifically: In the pre-contact stage, the gap is eliminated by applying 0.01 mm axial displacement through the upper clamp. In the clamping stage, the sample is clamped without slippage by applying 0.1 mm axial displacement through the upper clamp. In the load application stage, the internal pressure is applied according to the loading mode of S1. The boundary conditions are that the lower clamp is fully fixed, the upper clamp restricts radial displacement and in-plane rotation, and the pipe sample is additionally constrained for radial and axial displacement at the pipe end. The finite element model uses S4R shell elements as its element type, and the contact is defined as the finite sliding contact between the fixture and the sample. The tangential friction coefficient is set to 0.3.

[0009] Preferably, in S3, the experimental response vector is: ; In the formula, This is the experimental response vector; For the first The response values ​​corresponding to each valid data point in the experiment; The number of data points; The finite element simulation response vector is: ; In the formula, This represents the response vector in the finite element simulation. For the first The response value corresponding to each finite element simulation data point; The formula for calculating the root mean square error (RMSE) is as follows: ; In the formula, For indexes of data points; The data preprocessing rules include coordinate alignment of experimental and simulated data and linear interpolation resampling to ensure that the number of data points and step size are consistent between the two.

[0010] Preferably, in S4, the initialization settings of the PSO-NM hybrid optimization algorithm are as follows: The upper and lower boundaries of the parameters to be calibrated, the upper limit of velocity, the maximum number of iterations, and the premature convergence threshold are preset; the number of particles is set, the parameter dimension matches the total number of constitutive parameters to be calibrated, and the initial particle positions and initial velocities are randomly generated.

[0011] Preferably, in S4, the time-varying parameter adjustment adopts a strategy of linearly decreasing inertia weights and symmetrically changing learning factors, and the update formulas for the inertia weights and learning factors are as follows: ; ; ; In the formula, This represents the current iteration number. This represents the maximum number of iterations. This represents the maximum value of the inertia weight, ranging from 0.8 to 0.9. This represents the minimum value of the inertia weight, ranging from 0.3 to 0.4. For the first Self-awareness learning factors during the next iteration; For the first Social cognitive learning factors at the next iteration; for The maximum value, for The maximum value, ; for The minimum value, for The minimum value, ;

[0012] Preferably, in S4, the premature convergence suppression strategy includes velocity limiting, boundary projection, and population diversity monitoring, specifically: A velocity limit is imposed on each dimension of the particle, with the following constraints: ; In the formula, For the first The particle in the first The speed corresponding to the dimension parameter; For the first The maximum velocity corresponding to the dimension parameter; For particle indices; The dimension index for the parameter to be calibrated; For particle positions outside the feasible region of parameters, mirror reflection projection is used, and the formula is: ; In the formula, For the first i The particle in the first The position corresponding to the dimension parameter; For the first d The upper boundary of the dimension; For the first The lower boundary of the dimension; Calculate the first The population variance of dimension is given by the formula: ; In the formula, For the first During the nth iteration, the 1st The particle swarm position variance corresponding to the dimension parameter; For the first During the nth iteration, the 1st The average value of all particle positions for the dimensional parameter; The total number of particles in the PSO algorithm; If the total diversity level is below the threshold, the particles are reinitialized using the following formula: ; In the formula, The total dimension of the parameters; This is the preset premature convergence threshold.

[0013] Preferably, in S5, the inter-module data flow logic of the automated iterative closed loop is as follows: The optimization iteration module generates candidate constitutive parameters based on the PSO-NM algorithm logic and passes them to the parameter correction module. The parameter correction module updates the constitutive parameters of the finite element model and passes the updated finite element model file to the finite element calculation module. The finite element calculation module performs finite element solution and outputs simulation response data, which is then passed to the error evaluation module. The error evaluation module calculates the RMSE fitness value based on the objective function of S3 and passes it to the optimization iteration module. The optimization iteration module updates the particle state according to the fitness value and generates new candidate parameters until the convergence criterion is met. The specific functions of the four modules of the automated integration program are as follows: The parameter correction module receives candidate constitutive parameters, updates the elastic-plastic parameters by replacing the Material data in the Abaqus input file and the data in the Plastic section, and updates the creep parameters by writing the preset variable positions in the creep user subroutine and automatically compiling, thus completing the consistency verification of data format, units and order. The finite element calculation module receives the updated finite element model file, generates a unique job name and working directory according to the iteration number, submits the calculation by calling the Abaqus command line interface, automatically configures the compilation and linking parameters for models containing user subroutines, polls and monitors the job status and records the solution log and result database path; The error assessment module receives the simulated response data from the finite element calculation module, extracts the response quantities of the specified nodes and generates simulated curves, combines the experimental curves of S1 to complete data preprocessing, and substitutes them into the objective function to calculate the RMSE fitness value. The optimization iteration module receives the RMSE fitness value from the error evaluation module, executes the PSO-NM hybrid optimization algorithm, updates the individual optimal and global optimal solutions of the particles, generates new candidate constitutive parameters, and realizes the algorithm's driving of the automated closed loop.

[0014] Therefore, the present invention employs the above-mentioned elastoplastic-creep constitutive finite element-PSO-NM collaborative inversion calibration method for internal pressure bulging test materials. Compared with the prior art, the technical solution of the present invention has the following beneficial effects: (1) The internal pressure bulging micro sample test scheme (small sample size, low damage, no need to rely on large-size standard samples) overcomes the technical problems of traditional test having high requirements for sample size and poor adaptability, which cannot meet the difficult sampling conditions of service components and in-service equipment, and thus achieves the technical effect of breaking through the traditional test size limitation and successfully adapting to difficult sampling conditions. (2) By adopting the technical means of constructing a finite element model of internal pressure bulging test and combining experimental curves with numerical simulation results error analysis, the technical problem that the test results of micro specimens are difficult to directly correspond to standard constitutive parameters and cannot be directly applied is overcome, thereby achieving the technical effect of building a bridge between the macroscopic response of micro specimens and the standard constitutive parameters of materials. (3) By adopting the technical means of optimized inversion method, the technical problem of the existing inversion method being limited in function, only able to target a single test form or a single performance, and unable to simultaneously take into account the calibration of tensile and creep performance is overcome. Thus, the technical effect of simultaneously and accurately identifying Ramberg-Osgood elastoplastic parameters and Kachanov-Rabotnov creep damage parameters and realizing the integrated calibration of multiple performance parameters is achieved. (4) By adopting a hybrid optimization algorithm of Particle Swarm Optimization Nelder-Mead (PSO-NM) (including time-varying parameter control, premature convergence suppression, and local refinement strategy) and using Python-Abaqus automated integration program, the technical problems of low accuracy and insufficient stability of existing inversion methods are overcome, thereby achieving the technical effect of balancing global search capability and local convergence efficiency, and improving parameter calibration accuracy and stability.

[0015] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0016] Figure 1 This is a cloud image of the finite element simulation results of an embodiment of the elastoplastic-creep constitutive finite element-PSO-NM co-inversion calibration method for internal pressure bulging test materials according to the present invention; wherein, Figure 1 (a) represents a magnified contour plot. Figure 1 (b) represents the cloud map of the overall forming result; Figure 2 This is a flowchart illustrating the execution of the PSO-NM hybrid optimization algorithm in an embodiment of the elastoplastic-creep constitutive finite element-PSO-NM collaborative inversion calibration method for internal pressure bulging test materials of the present invention. Figure 3 This is an automated closed-loop flowchart of the inverse finite element parameter calibration of an embodiment of the elastic-plastic-creep constitutive finite element-PSO-NM collaborative inversion calibration method for internal pressure bulging test materials of the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Unless otherwise defined, the technical or scientific terms used in the present invention should have the ordinary meaning understood by those skilled in the art.

[0018] Example 1 like Figures 1-3 As shown, this embodiment provides a method for elastoplastic-creep constitutive finite element-PSO-NM co-inversion calibration of materials for internal pressure bulging tests. It should be understood that the specific parameters, models and protocols mentioned in this embodiment are merely examples to help those skilled in the art understand the present invention, and are not intended to limit the present invention.

[0019] The method for elastoplastic-creep constitutive finite element-PSO-NM co-inversion calibration of internal pressure bulging test materials of the present invention includes the following steps: S1. An internal pressure bulging test was conducted, in which a circular thin-plate sample was clamped and sealed, and loaded differently according to the parameter type. When calibrating the elastic-plastic parameters, the pressure was gradually increased and the pressure-center displacement curve was recorded. When calibrating the creep parameters, the pressure was kept constant and the center displacement-time curve was collected to obtain the inversion target data. In this step, a circular thin plate sample with a diameter of 10-20 mm and a thickness of 0.5-2 mm is processed to ensure that the surface is flat and free of defects and to fit the size of the internal pressure bulging test mold. The sample is placed in the circular mold and clamped around the perimeter by the upper and lower clamps. A sealing gasket is used to ensure the airtightness between the sample and the clamps to avoid gas leakage during loading. The gas pressure control system gradually increases the pressure at a rate of 0.1-0.5 MPa / s until the center displacement of the sample reaches the target value or is close to rupture. Displacement and pressure sensors are used to collect data in real time at a sampling frequency of 10 Hz. The pressure is rapidly increased to a preset constant pressure by a pressure control system, and the holding time is set to 100-1000h. The change of the center displacement of the sample over time is continuously collected, and the sampling frequency is adjusted according to the holding time (1Hz for short-term and 0.1Hz for long-term). After removing outliers from the collected raw data, standard format experimental curves are generated, including load-displacement curves and displacement-time curves. Output experimental curves and test parameters; S2. Based on the ABAQUS / Standard platform and four assumptions (uniform and isotropic material, uniform internal pressure distribution, constant loading rate, and maximum displacement at the center), the three-dimensional model is transformed into a two-dimensional axisymmetric model. Shell elements are used to simulate the specimen, and analytical rigid bodies are used to simulate the fixture. Boundary conditions are set in three stages: "pre-contact - clamping - loading". The master-slave contact pairs and friction coefficients are defined to ensure that the simulation and experimental conditions are consistent. In this step, a circular thin plate geometry is created according to the test condition parameters transferred in S1. The mesh is generated using S4R shell elements (four-node reduced integral shell elements) with a mesh size of 0.1-0.3 mm to ensure that the mesh density in the bulging region meets the requirements for large deformation calculation. The upper and lower fixtures are simplified into analytical rigid body surfaces with dimensions consistent with the actual test fixtures. A reference point (RP) is set at the center of the rigid body for applying constraints and transferring loads. Setting boundary conditions includes the following sub-steps: S201. In the pre-contact stage, eliminate the initial gap and establish stable contact; Upper clamp reference point: Apply a small axial displacement to restrict radial displacement and in-plane rotation; Lower clamp reference points: fixed radial displacement, axial displacement, and in-plane rotation; Specimen loading surface: No internal pressure load applied; S202. During the clamping phase, a stable clamping constraint is formed; Upper clamp reference point: Continue to apply axial displacement to maintain radial displacement and in-plane rotation constraints; Lower clamp reference point: Maintains radial displacement, axial displacement, and in-plane rotation at a fixed position; Specimen loading surface: No internal pressure load is applied yet. After this stage, the freedom of the specimen edge is completely restricted. S203. During the loading stage, the sample is driven to bulge and deform. Upper clamp reference point: Continue to apply axial displacement to maintain radial displacement and in-plane rotation constraints; Lower clamp reference point: Maintains radial displacement, axial displacement, and in-plane rotation at a fixed position; Specimen loading surface: No internal pressure load is applied yet. After this stage, the freedom of the specimen edge is completely restricted. The specific settings for boundary conditions and loads are shown in Table 1: Table 1 Boundary Condition and Load Parameter Settings

[0020] in, Indicates radial displacement, in mm. Indicates axial displacement, in mm. Indicates in-plane rotation, with the unit being (rad); Establish a contact pair between the upper fixture rigid body surface and the upper surface of the specimen, and a contact pair between the lower fixture rigid body surface and the lower surface of the specimen, wherein the fixture rigid body surface is the principal surface and the specimen surface is the slave surface. The tangential behavior is based on a friction formula with a penalty function and a friction coefficient of 0.3. Considering the large relative slippage that may occur between the specimen and the fixture during the bulging process, the slippage of the contact pair is described in the form of finite slippage to ensure numerical stability and physical rationality under large deformation conditions. S3. Read the experimental curve data transmitted by S1, use the normalized mean square error (RMSE) as a metric to quantify the difference between the experimental curve and the finite element simulation curve, and establish an objective function that can be used for optimization algorithm search. In this step, n equally spaced valid data points are extracted to construct the experimental response vector, which is represented as: ; In the formula, This is the experimental response vector; For the first The response values ​​corresponding to each valid data point in the experiment; The number of data points; The finite element structure curve vector constructed at the corresponding data points is represented as: ; In the formula, This represents the response vector in the finite element simulation. For the first The response value corresponding to each finite element simulation data point; The difference between the finite element simulation curve and the experimental curve is quantified using the normalized root mean square error (RMSE) as a metric, as shown in the following formula: ; In the formula, For indexes of data points; Output the RMSE objective function; S4 receives the RMSE objective function passed from S3, initializes the particle, velocity, and parameter range; updates the particle state using time-varying inertial weights and symmetric progressive learning factors; suppresses premature convergence through velocity limits, boundary projections, and population diversity monitoring; after entering the convergence phase, extracts the optimal particle to construct a simplex, and calls the Nelder-Mead algorithm for local refinement. In this step, based on the properties of heat-resistant steel, the upper and lower boundaries of the Ramberg-Osgood and Kachanov-Rabotnov parameters are preset; The global search for PSO includes the following sub-steps: S401. Set initial parameters, including basic particle swarm parameters, parameter boundaries, iteration and optimization parameters, and initial particle states; complete the basic parameter configuration before algorithm startup; S402. Using a strategy of linearly decreasing inertia weights and symmetric varying learning factors, the update expression is as follows: ; ; ; In the formula, This represents the current iteration number. This represents the maximum number of iterations. This is the maximum value of the inertia weight, ranging from 0.8 to 0.9. It is used in the early stages of algorithm iteration to enhance the global search capability of particles and avoid getting trapped in local optima too early. This is the minimum value of the inertia weight, ranging from 0.3 to 0.4. It is used in the later stages of algorithm iteration to reduce global exploration and accelerate the convergence of particles to the optimal solution region. For the first Self-awareness learning factors during the next iteration; For the first Social cognitive learning factors at the next iteration; for The maximum value, for The maximum value, ; for The minimum value, for The minimum value, ; S403. Apply a maximum amplitude limit to the velocity in each dimension to prevent particles from skipping the optimal solution or causing search instability due to excessive velocity. The constraint conditions are as follows: ; In the formula, For the first The particle in the first The speed corresponding to the dimension parameter; For the first The maximum velocity corresponding to the dimension parameter; For particle indices; The dimension index for the parameter to be calibrated; When the particle position is outside the feasible region, mirror reflection projection is used, and the formula is: ; In the formula, For the first i The particle in the first The position corresponding to the dimension parameter; For the first d The upper boundary of the dimension; For the first The lower boundary of the dimension; S404. Constructing a criterion based on particle swarm variance, the first... The variance of a population is defined as: ; In the formula, For the first During the nth iteration, the 1st The particle swarm position variance corresponding to the dimension parameter; For the first During the nth iteration, the 1st The average value of all particle positions for the dimensional parameter; The total number of particles in the PSO algorithm; If the total diversity level is below the threshold, the algorithm is considered to have prematurely converged, as shown in the formula: ; In the formula, The total dimension of the parameters; This is the preset premature convergence threshold; S405. When the number of iterations reaches the maximum number of iterations, or the error of the current optimal solution meets the preset convergence criterion, after entering the convergence stage, the optimal particle is extracted to construct the simplex, and the algorithm switches to Nelder-Mead (NM) simplex search for local refinement. S406. Call the Nelder-Mead simplex search algorithm and perform local optimization of the simplex through reflection, expansion, contraction and compression operations until the vertex error of the simplex meets the accuracy requirements. Output the final inverted material parameters after local refinement; S5. Based on Python scripts, four modules are built: the parameter correction module updates the finite element input file / creep subroutine, the finite element calculation module automatically submits the job and monitors the solution status, the error evaluation module completes curve alignment and RMSE calculation, and the optimization iteration module drives the algorithm iteration. In this step, four modular programs are built based on Python scripts (calling the abaqus-pythonAPI). Each module is decoupled through a file interface, specifically: The parameter correction module is used to receive candidate constitutive parameters output by the optimization iteration module, complete the automatic update of the finite element solution input file, and provide the latest constitutive model parameters for each iteration. Read candidate parameters, parse the Material card in the Abaqus input file, replace the stress-plastic strain discrete point data in the elastic parameter row and the Plastic segment, and simultaneously perform consistency checks on data format, units and data order to avoid solution failure due to format errors; write candidate creep parameters into the preset variable positions of the creep user subroutine, automatically call the compiler to generate an executable subroutine file, and output a file structure compatible with the Abaqus solver call; The finite element calculation module is used to receive updated files from the parameter correction module, automatically submit finite element analysis jobs, monitor the solution status, and ensure that the calculation process is robust and controllable. A unique job name and independent working directory are generated based on the current iteration number. The submission command is executed by calling the Abaqus command-line interface via Python. If a creep user subroutine exists, the compilation and linking parameters are automatically configured, and the solver is called to complete the binding of the subroutine and the main model. The job running status is polled every 10 seconds to accurately identify working conditions such as "normal termination", "convergence failure", "hardware interruption", and "format error". The storage paths of the solver log, message file and result database are recorded to ensure subsequent data traceability and problem investigation. The error assessment module is used to receive the result data from the finite element calculation module, establish the error quantification relationship between the experimental response and the finite element response, and output the fitness value for the optimization iteration module to judge the quality of the parameters. The Python script is called to read the Abaqus results database (.odb), locate the center node of the sample, and extract the target response quantity—the elastic-plastic calibration extracts the reaction force and displacement data, and generates a "pressure-center displacement" simulation curve data table; the creep calibration extracts the displacement evolution data over time, and generates a "center displacement-time" simulation curve data table. Read the experimental curve data transmitted by S1, align the time / displacement axis coordinates of the simulated curve and the experimental curve, complete the data resampling by linear interpolation, substitute the difference into the root mean square error (RMSE) formula defined by S3, and output a single scalar error value as the fitness value of this iteration. The optimization iteration module receives the fitness value from the error evaluation module, executes the improved PSO-NM hybrid optimization algorithm, and drives the entire process iteration until the convergence criterion is met. The particle swarm is initialized within the preset upper and lower limits of parameters. The particle state is updated using time-varying inertial weights and symmetric incremental learning factors. The particle velocity and position are limited (to prevent out-of-bounds) and boundary projection (mirror reflection processing) is applied. During the iteration process, a premature convergence detection mechanism is introduced. When insufficient population diversity or stagnation of the objective function is detected, some particles are reinitialized to maintain the global search capability. The individual best (pbest) and global best (gbest) of the particles are updated based on the fitness value, new candidate constitutive parameters are generated and fed back to the parameter correction module to enter the next round of iteration; when the maximum number of iterations or the error threshold condition is met, the algorithm automatically switches to the Nelder-Mead simplex algorithm for local refinement and outputs the final parameters. Driven by the PSO-NM algorithm, the system achieves a closed-loop operation of "parameter update, finite element solution, result extraction, error calculation, and parameter iteration" through an automated program until the convergence criterion is met, and outputs the Ramberg-Osgood elastoplastic parameters and Kachanov-Rabotnov creep damage parameters.

[0021] Therefore, this invention adopts the above-mentioned elastoplastic-creep constitutive finite element-PSO-NM collaborative inversion calibration method for internal pressure bulging test materials. This method establishes the relationship between micro-samples and standard constitutive parameters, realizes integrated calibration of multiple performance parameters, takes into account both global and local search efficiency, and improves parameter calibration accuracy and stability.

[0022] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0023] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for elastoplastic-creep constitutive finite element-PSO-NM co-inversion calibration of materials for internal pressure bulging tests, characterized in that, Includes the following steps: S1. Prepare the sample and complete the internal pressure bulging test, collect experimental response data and construct the experimental response vector, and output the experimental curve and test condition parameters. S2. Based on the test condition parameters of S1, construct a finite element model for the matching internal pressure bulging test, set the geometric dimensions, boundary conditions, loading mode and contact definition, and output the finite element model. S3. Based on the experimental response vector of S1, define the finite element simulation response vector, use the root mean square error (RMSE) to construct the objective function to quantify the deviation between the experimental and simulated responses, and output the objective function and data preprocessing rules. S4. Based on the objective function of S3, construct a hybrid optimization algorithm that integrates the PSO global search module and the Nelder-Mead local refinement module, which combines time-varying parameter control and premature convergence suppression. Complete the algorithm initialization and core rule setting, and output the PSO-NM algorithm logic and parameter value range. S5. Construct an automated iterative closed loop consisting of a parameter correction module, a finite element calculation module, an error evaluation module, and an optimization iteration module. Integrate the finite element model of S2 and the PSO-NM algorithm logic of S4 into the closed loop. Through iteration, until the convergence criterion is met, the final calibrated material constitutive parameters are output.

2. The method for elastoplastic-creep constitutive finite element-PSO-NM co-inversion calibration of materials for internal pressure bulging tests according to claim 1, characterized in that, In S1, the sample is a plate sample, which is a circular thin plate with a diameter of 10-20 mm and a thickness of 0.5-2 mm. The loading modes of the internal pressure bulging test include elastoplastic loading, creep loading and burst loading. Elastic loading applies internal pressure to the target deformation, creep loading uses constant pressure to maintain the load, and burst loading is performed until the specimen fails. The experimental response data includes pressure-center displacement data and center displacement-time data. After collection, outliers are removed and no less than 50 equally spaced valid data points are selected to construct the experimental response vector.

3. The method for elastoplastic-creep constitutive finite element-PSO-NM co-inversion calibration of materials for internal pressure bulging tests according to claim 2, characterized in that, In S2, the establishment of the finite element model includes a three-stage analysis step setting, specifically: In the pre-contact stage, the gap is eliminated by applying 0.01 mm axial displacement through the upper clamp. In the clamping stage, the sample is clamped without slippage by applying 0.1 mm axial displacement through the upper clamp. In the load application stage, the internal pressure is applied according to the loading mode of S1. The boundary conditions are that the lower clamp is fully fixed, the upper clamp restricts radial displacement and in-plane rotation, and the pipe sample is additionally constrained for radial and axial displacement at the pipe end. The finite element model uses S4R shell elements as its element type, and the contact is defined as the finite sliding contact between the fixture and the sample. The tangential friction coefficient is set to 0.

3.

4. The method for elastoplastic-creep constitutive finite element-PSO-NM co-inversion calibration of materials for internal pressure bulging tests according to claim 3, characterized in that, In S3, the experimental response vector is: ； In the formula, This is the experimental response vector; For the first The response values ​​corresponding to each valid data point in the experiment; The number of data points; The finite element simulation response vector is: ； In the formula, This represents the response vector in the finite element simulation. For the first The response values ​​corresponding to each finite element simulation data point; The formula for calculating the root mean square error (RMSE) is as follows: ； In the formula, For indexes of data points; The data preprocessing rules include coordinate alignment of experimental and simulated data and linear interpolation resampling to ensure that the number of data points and step size are consistent between the two.

5. The method for elastoplastic-creep constitutive finite element-PSO-NM co-inversion calibration of materials for internal pressure bulging tests according to claim 4, characterized in that, In S4, the initialization settings of the PSO-NM hybrid optimization algorithm are as follows: The upper and lower boundaries of the parameters to be calibrated, the upper limit of velocity, the maximum number of iterations, and the premature convergence threshold are preset; the number of particles is set, the parameter dimension matches the total number of constitutive parameters to be calibrated, and the initial particle positions and initial velocities are randomly generated.

6. The method for elastoplastic-creep constitutive finite element-PSO-NM co-inversion calibration of materials for internal pressure bulging tests according to claim 5, characterized in that, In S4, the time-varying parameter control adopts a strategy of linearly decreasing inertia weights and symmetrically changing learning factors. The update formulas for the inertia weights and learning factors are as follows: ； ； ； In the formula, This represents the current iteration number. This represents the maximum number of iterations. This represents the maximum value of the inertia weight, ranging from 0.8 to 0.

9. This represents the minimum value of the inertia weight, ranging from 0.3 to 0.

4. For the first Self-awareness learning factors during the next iteration; For the first Social cognitive learning factors at the next iteration; for The maximum value, for The maximum value, ; for The minimum value, for The minimum value, .

7. The method for elastoplastic-creep constitutive finite element-PSO-NM co-inversion calibration of materials for internal pressure bulging tests according to claim 6, characterized in that, In S4, the premature convergence suppression strategy includes velocity limiting, boundary projection, and population diversity monitoring, specifically: A velocity limit is imposed on each dimension of the particle, with the following constraints: ； In the formula, For the first The particle in the first The speed corresponding to the dimension parameter; For the first The maximum velocity corresponding to the dimension parameter; For particle indices; The dimension index for the parameter to be calibrated; For particle positions outside the feasible region of parameters, mirror reflection projection is used, and the formula is: ； In the formula, For the first i The particle in the first The position corresponding to the dimension parameter; For the first d The upper boundary of the dimension; For the first The lower boundary of the dimension; Calculate the first The population variance of dimension is given by the formula: ； In the formula, For the first During the nth iteration, the 1st The particle swarm position variance corresponding to the dimension parameter; For the first During the nth iteration, the 1st The average value of all particle positions for the dimensional parameter; The total number of particles in the PSO algorithm; If the total diversity level is below the threshold, the particles are reinitialized using the following formula: ； In the formula, The total dimension of the parameters; This is the preset premature convergence threshold.

8. The method for elastoplastic-creep constitutive finite element-PSO-NM co-inversion calibration of materials for internal pressure bulging tests according to claim 7, characterized in that, In S5, the inter-module data flow logic of the automated iterative closed loop is as follows: The optimization iteration module generates candidate constitutive parameters based on the PSO-NM algorithm logic and passes them to the parameter correction module; the parameter correction module updates the constitutive parameters of the finite element model and passes the updated finite element model file to the finite element calculation module. The finite element calculation module performs finite element solutions and outputs simulated response data, which is then transmitted to the error evaluation module. The error evaluation module calculates the RMSE fitness value based on the objective function of S3 and passes it to the optimization iteration module. The optimization iteration module updates the particle state and generates new candidate parameters according to the fitness value until the convergence criterion is met. The specific functions of the four modules of the automated integration program are as follows: The parameter correction module receives candidate constitutive parameters, updates the elastic-plastic parameters by replacing the Material data in the Abaqus input file and the data in the Plastic section, and updates the creep parameters by writing the preset variable positions in the creep user subroutine and automatically compiling, thus completing the consistency verification of data format, units and order. The finite element calculation module receives the updated finite element model file, generates a unique job name and working directory according to the iteration number, submits the calculation by calling the Abaqus command line interface, automatically configures the compilation and linking parameters for models containing user subroutines, polls and monitors the job status and records the solution log and result database path; The error assessment module receives the simulated response data from the finite element calculation module, extracts the response quantities of the specified nodes and generates simulated curves, combines the experimental curves of S1 to complete data preprocessing, and substitutes them into the objective function to calculate the RMSE fitness value. The optimization iteration module receives the RMSE fitness value from the error evaluation module, executes the PSO-NM hybrid optimization algorithm, updates the individual optimal and global optimal solutions of the particles, generates new candidate constitutive parameters, and realizes the algorithm's driving of the automated closed loop.

9. A computer device, characterized in that, include: A processor configured to be coupled to memory, read and execute instructions and / or program code in the memory to perform the method as described in any one of claims 1-8.

10. A computer-readable medium, characterized in that, The computer-readable medium stores computer program code that, when executed on a computer, causes the computer to perform the method as described in any one of claims 1-8.

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