Parameter construction method and system of nonlinear constitutive model of ultra-high performance concrete

Abstract

The application discloses a kind of ultra-high performance concrete nonlinear constitutive model parameter construction method and system, belong to concrete material numerical simulation technical field, this method includes: obtaining the basic parameters and test response data of ultra-high performance concrete obtained by actual test;According to the completeness of the data obtained, determine the highest parameter construction level that can be executed and execute parameter construction according to the level preset logic, in the construction process, the parameter set calculated by the previous low level is used as the input of the current level parameter solving, and the construction of each parameter in the model parameter system is completed step by step, and the final calibrated complete parameter set is output;Wherein the parameter construction level includes low data parameter generation level, partial data correction level, error driven iterative calibration level from low to high.The present application can generate a complete parameter set under the condition of incomplete test data, and the usability of the parameter set under the low data scene and the accuracy of the parameter set under the high data condition are considered.

Description

Technical Field

[0001] This invention belongs to the field of numerical simulation technology of concrete materials, and in particular relates to a method and system for constructing parameters of a nonlinear constitutive model of ultra-high performance concrete. Background Technology

[0002] Concrete is a multiphase material composed of cementitious matrix, aggregates, fibers, etc. Under stress, it exhibits mechanical characteristics such as tension-compression asymmetry, confining pressure sensitivity, post-peak softening, crack propagation, and unloading stiffness degradation. A single linear elastic model is difficult to describe the above nonlinear behaviors, while a nonlinear constitutive model can characterize the plastic deformation, damage evolution, and stiffness degradation process of materials under complex stress states. It is now widely used in the analysis of nonlinear mechanical behavior of concrete materials and structures. Finite element simulation software equipped with a nonlinear material model of concrete can simulate the response of concrete under various loading conditions such as uniaxial or multiaxial forces.

[0003] The parameters of nonlinear constitutive models of concrete in existing simulation software are mostly determined based on test data of ordinary concrete. However, for ultra-high performance concrete (UHPC), since UHPC differs from ordinary concrete in terms of composition, strength, tensile properties, post-peak softening, confining pressure response, and damage evolution, directly applying ordinary concrete parameters or general default parameters to UHPC simulation can easily cause the simulated stress-strain curves of UHPC under multiple working conditions to deviate from the actual test results, reducing the accuracy of component bearing capacity, deformation, and damage prediction.

[0004] Currently, the parameters of the UHPC nonlinear constitutive model are mostly calibrated through actual experimental engineering. However, considering the large number of UHPC model parameters and the coupling relationship between various parameters, and the fact that only a few basic parameters such as compressive strength can usually be obtained through a small number of experiments in the early stages of engineering, it is difficult to support the accurate calibration of the entire constitutive parameter set. If a complete experimental calibration method is adopted, multiple sets of tests such as uniaxial compression and uniaxial tension are required to complete the parameter calibration, which is costly and difficult to obtain data. Summary of the Invention

[0005] To address the challenges of obtaining complete parameter sets for existing UHPC nonlinear constitutive model parameter calibration under low data conditions and the high cost of using complete experimental calibration, this invention provides a method and system for constructing parameters for an ultra-high performance concrete nonlinear constitutive model. The method involves hierarchical construction of model parameters based on the completeness of experimental data. Under low data conditions, empirical relationships are introduced, and a complete parameter set is derived theoretically. This complete parameter set is then corrected based on various measured fundamental parameters. Finally, error-driven iterative calibration is performed using measured experimental response data. This approach balances the usability of the calibration parameter set under low data scenarios with the accuracy of the calibration parameter set under high data conditions, reduces the cost of complete experimental calibration, and ensures simulation accuracy and adaptability for UHPC applications.

[0006] In a first aspect, the present invention provides a method for constructing parameters of a nonlinear constitutive model for ultra-high performance concrete.

[0007] A method for constructing parameters for a nonlinear constitutive model of ultra-high performance concrete includes: A parameter system for the nonlinear constitutive model of ultra-high performance concrete was established, including elastic parameters, yield criterion parameters, flow rule parameters, hardening parameters, and damage parameters. Obtain the ultra-high performance concrete foundation parameters and test response data obtained through actual testing; the foundation parameters include at least the compressive strength in the yield criterion parameters, and the other foundation parameters and test response data are selectively obtained according to the actual test conditions. Based on the completeness of the acquired data, the highest executable parameter construction level is determined, and parameter construction is performed according to the preset logic of that level. During the construction process, the parameter set calculated by the previous lower level is used as the input for the parameter solution of the current level, and the construction of each parameter in the model parameter system is completed step by step. Among them, the parameter construction levels include the low data parameter generation level from low to high, the partial data correction level, and the error-driven iterative calibration level. Based on the parameters in the constructed model parameter system, the final calibrated complete parameter set is output, and a material parameter file that can be called by finite element software is generated.

[0008] In a further technical solution, the basic parameters other than compressive strength include one or more of the following: tensile strength, elastic modulus, Poisson's ratio, density, steel fiber length, steel fiber diameter, steel fiber volume fraction, and maximum aggregate particle size; the test response data include one or more of the following: uniaxial compression test curve, uniaxial compression cycle test curve, triaxial compression test curve, and uniaxial tensile test curve.

[0009] A further technical solution includes the following elastic parameters: elastic modulus, Poisson's ratio, and density; yield criterion parameters: compressive strength, tensile strength, biaxial compressive strength, eccentricity parameter, and friction parameter; flow rule parameters: parameters that control the direction of plastic flow; hardening parameters: initial hardening parameter, hardening modulus, and hardening ductility parameter; and damage parameters: inelastic strain threshold, compressive damage ductility parameter, tensile strength threshold, ultimate crack opening displacement, and crack opening displacement threshold.

[0010] Further technical solutions, based on the completeness of the acquired data, determine the highest executable parameter construction level, including: When the acquired data only contains compressive strength and not test response data, the highest parameter construction level that can be executed is determined to be the low data parameter generation level. When the acquired data includes compressive strength and one or more other basic parameters, but lacks test response data, the highest parameter construction level that can be executed is determined to be the partial data correction level. When the acquired data includes compressive strength, one or more other basic parameters, and at least one test response data, the highest parameter construction level that can be executed is determined to be the error-driven iterative calibration level.

[0011] A further technical solution involves pre-defined parameter construction logic at each parameter construction level: In the low data parameter generation level, compressive strength is the main control input, and the initial calibration complete parameter set is generated based on the preset empirical relationship of ultra-high performance concrete. In some data correction levels, using existing measured basic parameters, one or more of the elastic parameters, yield criterion parameters, flow rule parameters, hardening parameters, and damage parameters in the initially calibrated complete parameter set are grouped and corrected accordingly to obtain the corrected complete parameter set; In the error-driven iterative calibration hierarchy, the initial complete parameter set is used as the basis. The current parameter set is formed by correcting the existing measured basic parameters. The material parameter file is generated based on the current parameter set. The nonlinear constitutive model in the finite element software is called to perform numerical simulation at the element level to obtain numerical simulation response data. Then, the error value corresponding to the current parameter set is calculated by combining the experimental response data to update the parameter set. Through continuous iterative updates, the optimized complete parameter set is obtained.

[0012] A further technical solution is that the iterative update process in the error-driven iterative calibration level is as follows: An error objective function is constructed; the error objective function includes one or more of the following: uniaxial compression error term, uniaxial tensile error term, uniaxial cyclic compression error term, and triaxial compression error term. Each error term includes one or more of the following: peak strength error, peak strain error, elastic segment slope error, post-peak softening segment error, unloading stiffness error, residual deformation error, and confining pressure response error. Based on the error objective function, the error value corresponding to the current parameter set is calculated according to the numerical simulation response data and the experimental response data. If the error value is greater than the preset error threshold, the current parameter set is updated under the constraints of the preset parameter value range and parameter update rules, and the numerical simulation and error calculation are performed again according to the updated parameter set. Repeatedly iterate through parameter updates, numerical simulations, and error calculations until the error value is no greater than the preset error threshold or the preset maximum number of iterations is reached, and output the final calibrated complete parameter set and the corresponding material parameter file.

[0013] A further technical solution involves using the nonlinear constitutive model built into LS-DYNA, which is a nonlinear material model for concrete, and outputting a material parameter file that can be directly accessed by LS-DYNA, which is a material keyword file.

[0014] A further technical solution involves constructing a multi-dimensional parameter vector from the parameter set when updating the current parameter set. The update of the parameter vector is represented as: ; In the above formula, For the first The possible values ​​of each parameter For the first During the nth iteration The possible values ​​of each parameter The objective function is the comprehensive error. For the first During the nth iteration The possible values ​​of each parameter For the first The update step size for each parameter; This is a parametric projection function used to limit the updated parameters to their minimum value. and maximum value between; The parameter update rule constraint is as follows: parameters in the current parameter set are updated step by step according to parameter sensitivity or according to a preset parameter update order to reduce parameter tuning errors caused by parameter coupling; wherein, the parameter sensitivity of each parameter is calculated, and the parameters are sorted according to their sensitivity and updated sequentially; the formula for calculating the parameter sensitivity is: ; In the above formula, For the first Sensitivity of each parameter For the first One parameter to be updated. For the first The disturbance of each parameter, The objective function is the comprehensive error. This is the current parameter vector; The preset parameter update order is as follows: first update the yield criterion parameters and flow law parameters to reduce peak strength error and confining pressure response error; then update the hardening parameters to reduce peak strain error and pre-peak nonlinear segment error; then update the compression damage parameters to reduce post-peak softening segment error, unloading stiffness error and residual response error; finally update the tensile damage parameters to reduce uniaxial tensile response error or bending response error.

[0015] Secondly, the present invention provides a parameter construction system for a nonlinear constitutive model of ultra-high performance concrete.

[0016] A parameter construction system for a nonlinear constitutive model of ultra-high performance concrete includes: The model parameter system construction module is used to build the parameter system of the nonlinear constitutive model of ultra-high performance concrete, including elastic parameters, yield criterion parameters, flow law parameters, hardening parameters, and damage parameters. The data acquisition module is used to acquire the ultra-high performance concrete foundation parameters and test response data obtained through actual testing; the foundation parameters include at least the compressive strength in the yield criterion parameters, and the other foundation parameters and test response data are selectively acquired according to the actual test conditions. The model parameter construction module is used to determine the highest executable parameter construction level based on the completeness of the acquired data and execute parameter construction according to the preset logic of that level. During the construction process, the parameter set calculated by the previous lower level is used as the input for solving the parameters of the current level, and the construction of each parameter in the model parameter system is completed step by step. The parameter construction levels include the low data parameter generation level from low to high, the partial data correction level, and the error-driven iterative calibration level. The results output module is used to output the final calibrated complete parameter set based on each parameter in the constructed model parameter system, and generate a material parameter file that can be called by finite element software.

[0017] Thirdly, the present invention also provides an electronic device, comprising: a memory for storing executable instructions; and a processor for implementing the above-described method for constructing parameters of the nonlinear constitutive model of ultra-high performance concrete when executing the executable instructions stored in the memory.

[0018] Fourthly, the present invention also provides a computer-readable storage medium storing executable instructions for inducing a processor to execute the executable instructions to implement the above-described method for constructing parameters of a nonlinear constitutive model for ultra-high performance concrete.

[0019] The above one or more technical solutions have the following beneficial effects: This invention provides a method and system for constructing parameters for a nonlinear constitutive model of ultra-high performance concrete (UHPC). It solves the problems of existing nonlinear constitutive model parameters for ordinary concrete being difficult to directly apply to numerical simulations of UHPC, and the high cost of relying on complete experimental calibration of UHPC parameters due to the difficulty in obtaining a complete parameter set under low data conditions. In this invention, considering the large number of parameters, strong parameter coupling, and difficulty in obtaining complete experimental data for the UHPC nonlinear constitutive model, a hierarchical parameter construction strategy based on data completeness is designed. According to the type and quantity of obtained data, the corresponding parameter construction steps are executed progressively according to the data completeness: when only compressive strength parameters are available, or only compressive strength parameters and material composition parameters are available, but no experimental response data is available, empirical formulas are introduced. Based on preset empirical relationships, material composition parameters, and default constraints, an initial complete parameter set is generated, reducing the dependence of parameter determination on multiple types of experimental data such as uniaxial tension, cyclic compression, and triaxial compression, and ensuring the completeness of parameter calibration; when further data such as elastic modulus, tensile strength, Poisson's ratio, density, steel fiber parameters, or maximum aggregate particle size are available, the method continues. When measured basic parameters are available but test response data is unavailable, the parameter sets directly generated in the low-data parameter generation level may lack adaptability under different loading conditions because they are initial values. Therefore, the measured basic data is used to group and correct the corresponding parameter groups to obtain a corrected and calibrated complete parameter set, improving the adaptability of the parameter construction process to different basic data conditions. When compressive strength, one or more other measured basic parameters, and at least one test response data are available, the corrected and calibrated complete parameter set is used as the current parameter set. The finite element model is used to call the simulation, and the parameters are iteratively updated based on the deviation between the simulation results and the test response results, improving the accuracy of parameter calibration. This allows the parameter calibration process to correct the corresponding parameter groups based on available test response data, further improving the applicability of the parameter system under different loading conditions. Through the above methods, this invention establishes a hierarchical parameter construction process of low-data parameter generation, partial data correction, and error-driven iterative calibration. This enables the nonlinear constitutive model of ultra-high performance concrete to obtain a complete parameter set even when complete experimental data is lacking. As experimental data gradually becomes richer, the applicability of calibration parameters is gradually improved, the cost of experimental calibration is reduced, and the availability of parameters in low-data scenarios is balanced with the simulation accuracy and working condition adaptability under experimental response data conditions.

[0020] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0021] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0022] Figure 1 This is a flowchart illustrating the method for constructing parameters of the nonlinear constitutive model of ultra-high performance concrete proposed in this embodiment of the invention. Figure 2 This is a schematic diagram of the structure of the nonlinear constitutive model parameter construction system for ultra-high performance concrete proposed in this embodiment of the invention; Figure 3 This is a schematic diagram illustrating the construction of the comprehensive error objective function in an embodiment of the present invention; Figure 4 This is a schematic diagram of the data completeness identification and parameter classification construction process in an embodiment of the present invention; Figure 5 This is a graph showing the relationship between the elastic modulus and compressive strength of ultra-high performance concrete in an embodiment of the present invention. Figure 6 This is a graph showing the relationship between the tensile strength and compressive strength of ultra-high performance concrete in an embodiment of the present invention. Figure 7 This is a schematic diagram of the biaxial failure surface of ultra-high performance concrete in an embodiment of the present invention; Figure 8 This is a diagram showing the correction relationship of the failure surface parameters of the nonlinear constitutive model of ultra-high performance concrete in an embodiment of the present invention. Figure 9 This is a diagram showing the relationship between parameters for determining the flow law of ultra-high performance concrete in an embodiment of the present invention. Figure 10 This is a diagram showing the relationship between the hardening ductility parameters of ultra-high performance concrete in an embodiment of the present invention. Figure 11 The diagram shows the relationship between the compressive damage ductility parameters of ultra-high performance concrete in the embodiments of the present invention; wherein, (a) is the diagram showing the relationship between the compressive damage ductility parameters under uniaxial compression, and (b) is the diagram showing the relationship between the compressive damage ductility parameters and the confining pressure under triaxial compression. Figure 12 This is a comparison diagram of the four-point bending load-displacement curves of the ultra-high performance concrete beam in Example 1 of this invention. Figure 13 This is a comparison of stress-strain curves from uniaxial compression tests and numerical simulations of ultra-high performance concrete in Example 2 of this invention. Figure 14This is a comparison chart of the stress-strain curves of ultra-high performance concrete in uniaxial tensile test and numerical simulation in Example 2 of this invention; Figure 15 This is a comparison chart of the stress-strain curves of ultra-high performance concrete in uniaxial compression cycle test and numerical simulation in Example 2 of this invention; Figure 16 The figure shows a comparison of the stress-strain curves of ultra-high performance concrete in triaxial compression test and numerical simulation in Example 3 of the present invention; where (a) is the triaxial compression response under low confining pressure and (b) is the triaxial compression response under high confining pressure. Figure 17 This is a comparison diagram of the four-point bending load-displacement curves of the ultra-high performance concrete beam in Example 4 of this invention. Figure 18 The image shows a comparison of the uniaxial compressive load-axial displacement curves of ultra-high performance concrete-filled steel pipe columns in Example 5 of this invention; where (a) is a comparison image of steel pipe group 1, (b) is a comparison image of steel pipe group 2, and (c) is a comparison image of steel pipe group 3. Detailed Implementation

[0023] It should be noted that the following detailed descriptions are exemplary and are intended only to describe specific embodiments and to provide further explanation of the invention, and are not intended to limit the scope of exemplary embodiments of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0024] As noted in the background section, existing nonlinear constitutive model parameters for ordinary concrete are difficult to directly apply to the numerical simulation of ultra-high performance concrete (UHVPC). Therefore, it is necessary to accurately calibrate or construct nonlinear constitutive model parameters for UHVPC. The construction of existing UHVPC nonlinear constitutive model parameters relies on experimental engineering. In actual engineering or preliminary numerical analysis, only a few basic parameters such as compressive strength, elastic modulus, or steel fiber length are typically obtained, which is insufficient to support the accurate determination of a complete parameter set. To calibrate all model parameters, a large number of experiments are required. Because the model has many parameters (including elastic parameters, yield criterion parameters, flow law parameters, hardening parameters, and damage parameters) and there are coupling relationships between them, parameter calibration through complete experiments usually requires multiple types of test data, such as uniaxial compression, uniaxial tension, cyclic compression, and triaxial compression. This results in high experimental costs and difficulty in data acquisition. If tensile, cyclic compression, or triaxial compression test data is missing, the model cannot be effectively applied.

[0025] To address the aforementioned problems, this invention proposes a method and system for constructing parameters for a nonlinear constitutive model of ultra-high performance concrete (UHPC). Based on the completeness of experimentally acquired data (including basic data and experimental data), the method employs a hierarchical approach, performing low-data parameter generation, partial data correction, and error-driven iterative calibration to construct a complete parameter set for the UHPC nonlinear constitutive model. Hierarchical construction refers to dividing parameter construction into three levels based on the completeness of basic parameters and experimental data: low-data parameter generation, partial data correction, and error-driven iterative calibration. Low-data parameter generation, when experimental response data is lacking, uses compressive strength as the primary input, combined with available material composition parameters and preset empirical relationships, to generate an initial, complete parameter set for calibration. Partial data correction, based on the initial calibration, introduces relatively complete data (i.e., one or more other measured basic parameters, such as elastic modulus, tensile strength, Poisson's ratio, density, steel fiber parameters, or maximum aggregate size), and uses the measured basic parameters to replace or correct the corresponding parameter sets to obtain a corrected, complete parameter set. Parameter set; Error-driven iterative calibration refers to introducing more complete data (i.e., one or more experimental response data) on the basis of the corrected calibration, evaluating the deviation between the numerical simulation results and the experimental results through the error objective function, and iteratively correcting the model parameters under the constraints of the preset parameter value range and parameter update rules to obtain the final optimized complete parameter set. In this way, the nonlinear constitutive model of ultra-high performance concrete can still obtain a complete parameter set when complete experimental data is lacking, and gradually improve the applicability of the calibration parameters as the experimental data becomes richer, reduce the cost of calibration experiments, and take into account the availability of parameters in low data scenarios and the simulation accuracy and working condition adaptability under experimental response data conditions.

[0026] Example 1 This embodiment provides a method for constructing parameters for a nonlinear constitutive model of ultra-high performance concrete under conditions of incomplete experimental data, such as... Figure 1 As shown, this method mainly includes steps such as data acquisition, data completeness identification, initial parameter generation, parameter grouping and correction, error-driven iterative calibration, and result output. Through low-data parameter generation, partial data correction, and error-driven iterative calibration, it balances the usability of the parameter set in low-data scenarios with the simulation accuracy and adaptability to operating conditions under experimental response data conditions. The specific steps of this method are as follows: Step S1: Establish the parameter system of the nonlinear constitutive model of ultra-high performance concrete, including elastic parameters, yield criterion parameters, flow law parameters, hardening parameters, and damage parameters.

[0027] Specifically, before implementing the entire parameter construction scheme, it is necessary to clarify the specific parameters of the UHPC nonlinear constitutive model to be constructed, and establish the parameter system of the ultra-high performance concrete nonlinear constitutive model to lay the foundation for subsequent parameter solution and calibration (i.e., construction).

[0028] In this embodiment, the nonlinear constitutive model refers to a constitutive model capable of describing the plastic deformation, damage evolution, and stiffness degradation processes of concrete materials. In the finite element simulation software LS-DYNA, the nonlinear constitutive model is a nonlinear material model of concrete that includes elastic parameters, yield criterion parameters, flow rule parameters, hardening parameters, and damage parameters. The material parameter file output by this model is a material keyword file that can be directly called by LS-DYNA. Based on this, a UHPC nonlinear constitutive model parameter vector (i.e., parameter set) is established. This parameter vector includes at least elastic parameters, yield criterion parameters, flow rule parameters, hardening parameters, and damage parameters, which can be expressed as: ; in, For the parameter vector to be constructed, For the elasticity parameter vector, Let be the yield criterion parameter vector. For the flow rule parameter vector, For hardening parameter vectors, This is the damage parameter vector.

[0029] Furthermore, elastic parameters include elastic modulus, Poisson's ratio, density, etc.; yield criterion parameters include compressive strength, tensile strength, biaxial compressive strength, eccentricity parameter, friction parameter, etc.; flow rule parameters are parameters that control the direction of plastic flow; hardening parameters include initial hardening parameter, hardening modulus, hardening ductility parameter, etc.; damage parameters include inelastic strain threshold, compressive damage ductility parameter, tensile strength threshold, ultimate crack opening displacement, crack opening displacement threshold, etc.

[0030] Step S2: Obtain the ultra-high performance concrete foundation parameters and test response data obtained through experimental testing. The foundation parameters must include at least the compressive strength from the yield criterion parameters; other foundation parameters and test response data are selectively obtained based on the experimental conditions.

[0031] Specifically, preliminary parameter data is obtained through a small number of experimental tests. This data includes at least compressive strength, and can also be selectively obtained according to the experimental conditions. Other basic parameters besides compressive strength include one or more of the following: tensile strength, elastic modulus, Poisson's ratio, density, steel fiber length, steel fiber diameter, steel fiber volume fraction, and maximum aggregate particle size. Test response data includes one or more of the following: uniaxial compression test curve (uniaxial compressive stress-strain curve), uniaxial compression cycle test curve (uniaxial compression cycle stress-strain curve), triaxial compression test curve, and uniaxial tensile test curve (uniaxial tensile stress-strain curve). The triaxial compression test curve includes peak stress, peak strain, post-peak softening response, and residual response under different confining pressure conditions, which can be used to correct subsequent yield criterion parameters, flow rule parameters, hardening parameters, and damage parameters.

[0032] Step S3: Based on the completeness of the acquired data, determine the highest executable parameter construction level and execute parameter construction according to the preset logic of that level. During the construction process, the parameter set calculated by the previous lower level is used as the input for solving the parameters of the current level, and the construction of each parameter in the model parameter system is completed step by step.

[0033] Specifically, such as Figure 4 As shown, the execution process of step S3 is as follows: Step S3.1: Determine the highest executable parameter construction level based on the completeness of the acquired data. In this embodiment, the parameter construction levels include a low-data parameter generation level, a partial data correction level, and an error-driven iterative calibration level, from low to high. The criteria for dividing these three levels are as follows: When the acquired data only has compressive strength or only has compressive strength and material composition parameters, but no test response data, the highest parameter construction level that can be executed is determined to be the low data parameter generation level. When the acquired data includes compressive strength and one or more other measured basic parameters (such as tensile strength, elastic modulus, Poisson's ratio, density, steel fiber length, steel fiber diameter, steel fiber volume fraction, maximum aggregate particle size, etc.), and there is no experimental response data, the highest parameter construction level that can be executed is determined to be the partial data correction level. When the acquired data includes compressive strength, one or more other measured basic parameters, and at least one test response data (one or more of uniaxial compression test curve, uniaxial tensile test curve, uniaxial compression cycle test curve, and triaxial compression test curve), the highest executable parameter construction level is determined to be the error-driven iterative calibration level.

[0034] Step S3.2: Based on the predetermined logic of the highest executable parameter, construct the parameter construction level and execute the parameter construction. During the construction process, the parameter set calculated by the previous lower level is used as the input for solving the parameter of the current level, and the construction of each parameter in the model parameter system is completed step by step.

[0035] Specifically, the preset parameter construction logic in each parameter construction level is as follows: 1) In the low data parameter generation level, compressive strength is the main control input. Combined with the available material composition parameters, and relying on the preset empirical relationships and default constraints of ultra-high performance concrete, the initial calibration complete parameter set is generated.

[0036] In this embodiment, the preset empirical relationships include: the relationship between elastic modulus and compressive strength; the relationship between tensile strength and compressive strength; the relationship between biaxial compressive strength and compressive strength; the relationship between eccentricity parameter and compressive strength, tensile strength, and biaxial compressive strength; the relationship between friction parameter and compressive strength, tensile strength, and eccentricity parameter; the relationship between hardening parameter and peak plastic strain or confining pressure; the relationship between compressive damage parameter and confining pressure; and the relationship between tensile damage parameter and steel fiber length, etc.

[0037] To establish the aforementioned pre-defined empirical relationships, this embodiment selects experimental data of ultra-high performance concrete materials published in multiple literatures as the fitting basis. All selected literatures disclose basic mechanical properties or constitutive response data related to parameter construction, including compressive strength, elastic modulus, tensile strength, triaxial compressive response, and axial plastic strain corresponding to peak stress. This data covers the commonly used strength range and typical mix design conditions of ultra-high performance concrete and can be used to establish initial parameter relationships in the low-data parameter generation level. It should be noted that the literature data is only used to establish initial empirical relationships for the parameters of the nonlinear constitutive model of ultra-high performance concrete. When the target material has measured basic parameters or experimental response data, subsequent partial data correction levels and error-driven iterative calibration levels will correct the aforementioned initial parameters.

[0038] 1.1) Regarding elastic parameters: When experimental data on the elastic modulus, Poisson's ratio, and density of ultra-high performance concrete are available, the experimental data can be directly used as the initial values ​​of the elastic parameters. Conversely, when the above experimental data are unavailable, such as when measured data on the elastic modulus is lacking, the initial value of the elastic modulus is generated based on the compressive strength, as follows: ,in This refers to the elastic modulus (in GPa). The compressive strength is given in MPa; when measured Poisson's ratio data is unavailable, the initial value of Poisson's ratio is taken as 0.20; when measured density data is unavailable, the initial value of density is taken as 2450~2550 kg / m³. 3 .

[0039] The fitting relationship between the elastic modulus and compressive strength of ultra-high performance concrete is as follows: Figure 5 As shown, the relevant data comes from the material test results published in references 5-1 to 5-27. The reason for selecting this type of data for fitting is that compressive strength is the most easily obtained basic parameter in the early stages of engineering, while elastic modulus is a key parameter in the elastic parameter set of the nonlinear constitutive model. By establishing an empirical relationship between elastic modulus and compressive strength, initial values ​​of elastic modulus can be generated when measured data of elastic modulus is lacking, thus ensuring the construction of a complete parameter set under low data conditions. Among them, references 5-1 to 5-27 are respectively: the impact resistance of cement-based materials against high-speed projectiles; and the research on a new type of RC structure using ultra-high strength fiber-reinforced concrete (UFC) - to achieve a 200 MPa... Challenges of applying UFC to earthquake-resistant building structures; Applicability of damage plastic constitutive models for ultra-high performance fiber-reinforced concrete under impact loads; Experimental study on the structural performance of steel tube-constrained ultra-high performance concrete columns; Influence of steel fiber content and aspect ratio on the uniaxial tensile and compressive properties of ultra-high performance concrete; Relationship between fiber orientation and tensile properties in ultra-high performance fiber-reinforced cementitious composites; Influence of fiber content on the mechanical and fracture properties of ultra-high performance fiber-reinforced cementitious composites; Structural performance of ultra-high performance concrete beams with different steel fibers; Influence of shrinkage-reducing agents considering fiber distribution characteristics on the tensile and flexural properties of ultra-high performance concrete; Study on direct tensile damage of ultra-high performance concrete based on acoustic emission technology; Push-out test of detachable stud connectors in steel composite structures; Axial compression performance of high-strength and ultra-high-strength steel tube concrete short columns; Influence of steel fiber content and type on the static mechanical properties of ultra-high performance concrete; Steel fiber The Influence of Size and Shape on the Mechanical Properties of Ultra-High Performance Concrete (UHPC); Experimental Study on the Mechanical Properties of UHPC; Material Properties of UHPC for the Michigan Bridges - Phase I Final Report; Material Property Characterization of UHPC; Evaluation of the Elastic Modulus of UHPC; Mix Design of UHPC and its Response to Projectile Impact; Benefits of Synthetic Fibers on the Residual Mechanical Properties of UHPC after Exposure to ISO Standard Fire; Influence of Different Fiber Types on the Microstructure and Mechanical Properties of UHPC; Mechanical Properties of Steel Fiber Reinforced UHPC Blends Exposed to High Temperatures: Effects of Exposure Duration and Fiber Content; Study on the Mechanical Properties of Ultra-High Performance Fiber Reinforced Concrete (UHPFRC); Tensile and Compressive Creep of UHPC: Effects of Heat Treatment; Direct Tensile Properties of Reinforced UHPC: Effects of Steel Fibers and Reinforcing Steel; Engineered / Strain Hardening Cement-Based Composites with Ultra-High Compressive Strength Above 210 MPa; Tensile Response of Ultra-High Performance PE Fiber Reinforced Concrete (PE-UHPFRC) under Applied Shrinkage Deformation.

[0040] 1.2) Regarding the yield criterion parameter: When measured tensile strength data is lacking, an initial value for tensile strength is generated based on the compressive strength, as follows: ;in For tensile strength, Both are in MPa, representing compressive strength.

[0041] The fitting relationship between the tensile strength and compressive strength of ultra-high performance concrete is as follows: Figure 6As shown, the relevant data comes from the direct tensile, splitting tensile, or equivalent tensile test results disclosed in references 6-1 to 6-29. The reason for selecting such data for fitting is that tensile strength is an important input for yield criterion parameters and tensile damage parameters. However, direct tensile test data is not always available in the early stages of engineering. By establishing an empirical relationship between tensile strength and compressive strength, an initial value of tensile strength can be generated when only compressive strength is available, and it can be further used for the initial determination of tensile strength threshold and tensile damage-related parameters. References 6-1 to 6-29 are, in order: Research on direct tensile damage of ultra-high performance concrete based on acoustic emission technology; Push-out test of detachable stud connectors in steel composite structures; Test method for determining the uniaxial tensile and compressive properties of ultra-high performance fiber-reinforced concrete; Influence of steel fiber content and aspect ratio on the uniaxial tensile and compressive properties of ultra-high performance concrete; Experimental study on the mechanical properties of ultra-high performance concrete; Evolution of mechanical damage in ultra-high performance concrete: experimental and numerical studies; Influence of steel fiber content and type on the static mechanical properties of ultra-high performance concrete; Influence of steel fiber size and shape on the mechanical properties of ultra-high performance concrete; Influence of shrinkage reducing agents considering fiber distribution characteristics on the tensile and flexural properties of ultra-high performance concrete; Mix design of ultra-high performance concrete and its response to projectile impact; Optimization of ultra-high performance fiber-reinforced concrete; Effect of synthetic fibers on ultra-high performance concrete after exposure to ISO standard fire. Benefits of residual mechanical properties of high-performance concrete; Study on mechanical properties of ultra-high performance fiber-reinforced concrete (UHPFRC); Tensile response of low-clinker UHPFRC under fully constrained shrinkage; Tensile and compressive creep of UHPC: Effect of heat treatment; Strengthening reinforced concrete beams with UHPFRC; Performance evaluation of UHPFRC based on sustainability; Part 1 experiments on UHPFRC under high-velocity projectile impact; Part 3 of development and mechanical properties: uniaxial tensile response and other mechanical properties; Direct tensile properties of reinforced UHPFRC: Effect of steel fibers and reinforcing bars; Material property characterization of UHPFRC; Development of direct tensile testing methods for UHPFRC; Comprehensive performance of high-strength and high-ductility concrete; Structural response of "UHPFRC-concrete" composite members under bending conditions; With 210 Engineering / strain-hardening cement-based composites with ultra-high compressive strength above MPa; the development of impact-resistant high-strength strain-hardening cement-based composites (HS-SHCC) outperforms reactive powder concrete (RPC) in terms of bending performance; tensile response of ultra-high performance PE fiber-reinforced concrete (PE-UHPFRC) under applied shrinkage deformation; experimental and numerical study on the ultimate bearing capacity of ultra-high performance prestressed concrete composite beams; bending response of high-strength steel ultra-high performance fiber-reinforced concrete beams based on a mesoscopic constitutive model: experimental and theoretical.

[0042] When measured data on biaxial compressive strength are lacking, such as Figure 7 As shown, the initial value of the biaxial compressive strength is generated based on the compressive strength, as follows: ;in Biaxial compressive strength, This refers to compressive strength.

[0043] Furthermore, based on the aforementioned compressive strength, tensile strength, and biaxial compressive strength, the initial value of the eccentricity parameter can be calculated as follows: ; ; in, For the eccentricity parameter, For intermediate parameters, For compressive strength, For tensile strength, It represents biaxial compressive strength.

[0044] like Figure 8 As shown, the initial values ​​of the friction parameters can be calculated based on the compressive strength, tensile strength, and eccentricity parameters, as follows: ; in, For friction parameters, For the eccentricity parameter, For compressive strength, For tensile strength. Preferably, when triaxial compression test response data is available, the friction parameters can be corrected based on the triaxial compression test response data.

[0045] in, Figure 8 The triaxial compression data in this paper are derived from the confining pressure test results of ultra-high performance concrete published in references 8-1 to 8-8. The reason for selecting this type of data for fault surface parameter correction is that compressive strength and tensile strength mainly reflect uniaxial stress characteristics and are insufficient to fully constrain the deviatoric stress response of materials under different hydrostatic pressure conditions. Triaxial compression tests can provide peak stress and stress difference responses under different confining pressures, which can be used to correct the fault surface parameters, making the calibrated fault surface closer to the actual strength variation law of ultra-high performance concrete under confining pressure conditions. References 8-1 to 8-8, in order, cover: laboratory characteristics of concrete with and without steel fibers; triaxial compression test study of ultra-high strength concrete; performance of slurry-permeable fiber concrete (SIFCON) under triaxial compression; triaxial compression test study and multi-scale simulation of reactive powder cement paste; triaxial compression test study of ultra-high performance concrete; calibration of concrete model low-velocity impact test; triaxial compressive strength of ultra-high performance concrete; and laboratory characteristics of the coral baseline and UHPC-S·ERDC / GSL TR-21-7.

[0046] 1.3) Regarding flow rule parameters: such as Figure 9 As shown, the flow law parameters can be corrected based on triaxial compressive stress and strain response; when relevant experimental data are lacking, the initial value of the flow law parameters is taken as 0.55.

[0047] 1.4) Regarding hardening parameters: the initial value of the hardening modulus can be taken as 0.01; the initial hardening parameters can be generated based on the confining pressure or hydrostatic pressure, as follows: ; ; or: ; ; in, These are the initial hardening parameters. For effective hydrostatic pressure, For confining pressure. When using the expression for confining pressure, the confining pressure is substituted according to the convention of negative sign for compression.

[0048] The hardening ductility parameter includes a first hardening ductility parameter. Second hardening ductility parameter Third hardening ductility parameter and the fourth hardening ductility parameter Among them, the first hardening ductility parameter Used to control the initial segment shape of the hardening curve, its initial value can be 0.12; for example Figure 10 As shown, the second hardening ductility parameter This is used to characterize the effect of the axial plastic strain corresponding to the peak stress on the hardening response, and to generate initial values ​​based on the axial plastic strain corresponding to the peak stress, which can be expressed as: ; in, This is the second hardening ductility parameter. The axial plastic strain corresponding to the peak stress is expressed in units of 1 / 2 Ω·cm. When relevant experimental data is lacking, Take 0.0016.

[0049] in, Figure 10The peak stress-corresponding axial plastic strain data are derived from the uniaxial or triaxial compressive stress-strain curves of ultra-high performance concrete disclosed in references 10-1 and 10-2. The reason for selecting this type of data for fitting is that the second hardening ductility parameter is related to the nonlinear segment before the material peak and the position of the peak strain, while the axial plastic strain corresponding to the peak stress can reflect the nonlinear hardening characteristics of ultra-high performance concrete before reaching its peak strength. By establishing the relationship between the second hardening ductility parameter and the axial plastic strain corresponding to the peak stress, initial values ​​for the hardening parameters can be provided when complete hardening curve calibration data are lacking. References 10-1 and 10-2 respectively describe the research on the impact resistance of cement-based materials against high-speed projectiles and the study of a novel RC structure using ultra-high strength fiber-reinforced concrete (UFC).

[0050] Third hardening ductility parameter To characterize the effect of confining pressure or hydrostatic pressure on hardening ductility, initial values ​​can be generated based on the confining pressure or hydrostatic pressure, and can be expressed as: ; or: ; in, This is the third hardening ductility parameter. For effective hydrostatic pressure, For confining pressure, This represents the compressive strength. When using the expression for confining pressure, the confining pressure is substituted according to the convention that compression is negative.

[0051] In addition, the fourth hardening ductility parameter Used to control the ductile response of the tail or residual section of the hardening curve, its initial value can be taken as 1×10. 6 .

[0052] 1.5) Regarding damage parameters: the initial value of the inelastic strain threshold can be taken as follows: ,in The inelastic strain threshold; the second compressive damage ductility parameter The initial value can be 1.0; for example... Figure 11 As shown in (a), under uniaxial compression, the first compressive damage ductility parameter Initial values ​​can be generated based on the uniaxial compression softening segment data, as follows: ; in, This is the first compressive damage ductility parameter.

[0053] like Figure 11 As shown in (b), under triaxial compression conditions, the initial value of the first compressive damage ductility parameter, combined with the confining pressure or hydrostatic pressure, is: ; ; or: ; ; When using the confining pressure expression, the confining pressure is substituted according to the convention of negative sign for compression.

[0054] Tensile damage is assessed using a bilinear criterion, and the tensile strength threshold is initially generated based on the tensile strength, as follows: ; in, The tensile strength threshold, This refers to tensile strength.

[0055] When the steel fiber length is available, the initial value of the ultimate crack opening displacement is generated based on the steel fiber length, as follows: ; in, This represents the ultimate crack opening displacement. This represents the length of the steel fiber.

[0056] When steel fiber length is missing Determined by preset default values ​​or material design values.

[0057] The crack opening displacement threshold is initially generated based on the ultimate crack opening displacement, and is as follows: ; in, The crack opening displacement threshold. This represents the ultimate crack opening displacement.

[0058] The initial parameter vector under low data conditions can be calculated through the above steps. This initial parameter vector can serve as the complete parameter set for initial calibration under low data conditions, or as input for subsequent grouping correction and iterative calibration.

[0059] 2) In the partial data correction level, using the existing measured basic parameters, one or more of the elastic parameters, yield criterion parameters, flow rule parameters, hardening parameters, and damage parameters in the initially calibrated complete parameter set are grouped and corrected accordingly to obtain the corrected complete parameter set.

[0060] Specifically, while the empirical formula method based on a small number of basic parameters (i.e., the calibration method in the low-data parameter generation level mentioned above) can quickly generate some model parameters and construct a complete model parameter set with a small amount of data, the applicability of the parameters obtained above may be insufficient under different loading conditions. Therefore, this embodiment designs a partial data correction level. In this level, the model parameters are grouped and corrected using existing measured basic parameters, so that the parameter set is updated from the empirically generated parameter set under low data conditions to a corrected parameter set consistent with the existing measured data, thereby improving its applicability.

[0061] As one implementation method, when measured elastic modulus, Poisson's ratio, or density exists, the measured values ​​are used to replace the initial values ​​of the corresponding elastic parameters; when measured tensile strength exists, the measured tensile strength is used to correct the tensile strength parameters, tensile strength threshold, and tensile damage parameters; when steel fiber length, steel fiber diameter, or steel fiber volume fraction exists, the crack opening displacement related parameters are corrected.

[0062] 3) In the error-driven iterative calibration level, based on the initial complete parameter set, the current parameter set is formed after correction using existing measured basic parameters. Material parameter files are generated based on the current parameter set, and the nonlinear constitutive model in the finite element software is called to perform numerical simulation at the element level to obtain numerical simulation response data. Then, the error value corresponding to the current parameter set is calculated in conjunction with the experimental response data to update the parameter set. Through continuous iterative updates, the optimized complete parameter set is obtained.

[0063] Specifically, the process begins with an initial, fully calibrated parameter set generated at a low-data-parameter generation level. This set is then corrected using existing measured parameters (i.e., by implementing correction strategies from a partial data correction level) to form the current parameter set. Based on this set, a nonlinear constitutive model material parameter file is automatically generated. The nonlinear constitutive model in the finite element software is then used to perform element-level numerical simulations for the corresponding working conditions. After the numerical simulation is complete, the numerical stress-strain curves and corresponding characteristic indices are extracted to obtain the numerical simulation response data. In this embodiment, the established finite element-level numerical model includes one or more of the following: a uniaxial compression element model, a uniaxial tension element model, a uniaxial compression cyclic element model, and a triaxial compression element model.

[0064] Secondly, a comprehensive error objective function is constructed based on experimental and numerical simulation response data. In this embodiment, the objective function includes one or more of the following: uniaxial compression error term, uniaxial tensile error term, uniaxial cyclic compression error term, and triaxial compression error term. Each error term includes one or more of the following: peak strength error, peak strain error, elastic segment slope error, post-peak softening segment error, unloading stiffness error, residual deformation error, and confining pressure response error. By constructing the error objective function, the deviation between the numerical simulation results and experimental results corresponding to the current parameter set can be evaluated, which serves as the basis for parameter iterative updates.

[0065] like Figure 3 As shown, when there are multiple types of experimental response data, the designed comprehensive error objective function is: ; in, The objective function is the comprehensive error. For the current parameter vector, This is a uniaxial compression error term. This is the uniaxial tensile error term. This is the uniaxial compression cycle error term. This is the triaxial compression error term. , , and For the corresponding weights.

[0066] 3.1) The uniaxial compression error term, including the elastic segment slope error, peak strength error, peak strain error, and post-peak softening segment error, can be expressed as: ; in, This is a uniaxial compression error term. and The uniaxial compressive strengths obtained from numerical simulation and experiments are respectively. and The peak compressive strains obtained from numerical simulation and experiments are respectively. and The elastic modulus is obtained from numerical simulation and experiment, respectively. For the normalized error of the uniaxial compression curve, , , and These are the weighting coefficients.

[0067] 3.2) For the uniaxial tensile error term, including peak tensile strength error and tensile softening segment error, it can be expressed as: ; in, This is the uniaxial tensile error term. and The tensile strengths obtained from numerical simulation and experiments are respectively. For the normalized error of the uniaxial stretch curve, and These are the weighting coefficients.

[0068] 3.3) The uniaxial compression cycle error term, including unloading stiffness error and residual deformation error, can be expressed as: ; in, This is the uniaxial compression cycle error term. and The unloading stiffness is obtained from numerical simulation and experiment, respectively. and The residual strains obtained from numerical simulation and experiments are respectively. This is the normalized error of the uniaxial compression cycle curve. , and These are the weighting coefficients.

[0069] 3.4) The triaxial compression error term, including peak stress error, peak strain error, and residual response error under different confining pressure conditions, can be expressed as: ; in, This is the triaxial compression error term. The number of confining pressure conditions. and The first The peak stress obtained from numerical simulation and experiment under confining pressure. and The first The peak strain obtained from numerical simulation and experiment under confining pressure. For the first Normalized error of triaxial compression curve under confining pressure , and These are the weighting coefficients.

[0070] The normalization error of the above curve can be expressed as: ; In the above formula, For curve normalization error, This represents the number of curve sampling points. For the first The strain corresponding to each sampling point For the first Numerical simulation stress at each sampling point For the first Test stress at each sampling point.

[0071] Preferably, before performing the above calculations, the numerical simulation curves and experimental curves are interpolated to the same strain sampling points. As one implementation, when material-level calibration is the primary focus, the weights of uniaxial compression, uniaxial tension, and triaxial compression error terms are increased; when component response prediction is the primary focus, the weights of the response error terms for bending components or composite columns are increased.

[0072] Next, based on the error objective function, the error value corresponding to the current parameter set is calculated according to the numerical simulation response data and the experimental response data. If the error value is greater than the preset error threshold, the current parameter set is updated under the constraints of the preset parameter value range and parameter update rules, and then the numerical simulation and error calculation are performed again based on the updated parameter set.

[0073] In this embodiment, the parameter vector can be updated in the following way: ; in, For the first During the nth iteration The possible values ​​of each parameter For the first During the nth iteration The possible values ​​of each parameter For the first The update step size for each parameter; This is a parametric projection function used to limit the updated parameters to their minimum value. and maximum value between.

[0074] As another implementation, when updating the current parameter set, a parameter vector can be constructed from the parameter set, and one or more combined algorithms such as grid search, genetic algorithm, particle swarm optimization, Bayesian optimization, and differential evolution can also be used to update the parameter vector.

[0075] As a further implementation method, during the iterative update process, value ranges and constraints are set for each parameter to avoid the parameters exceeding the physically reasonable range of the corresponding nonlinear constitutive model and to prevent the finite element calculation from failing to converge after parameter updates. When the updated parameters exceed the corresponding value range or do not meet the corresponding constraints, the updated parameters are truncated, rolled back, or regenerated.

[0076] Furthermore, this embodiment also includes parameter update rule constraints, which can iteratively correct and update the current parameter set based on parameter sensitivity or a preset parameter update order, including: 1) Calculate the parameter sensitivity of each parameter, sort them according to their sensitivity, and perform updates sequentially. The parameter sensitivity can be calculated using the following formula: ; in, For the first Sensitivity of each parameter For the first One parameter to be updated. For the first The disturbance of each parameter, The objective function is the comprehensive error. This is the current parameter vector.

[0077] 2) Update parameters according to a preset parameter update order to reduce parameter tuning errors caused by parameter coupling. In this embodiment, the preset parameter update order is as follows: first update the yield criterion parameter and flow rule parameter to reduce peak strength error and confining pressure response error; then update the hardening parameter to reduce peak strain error and pre-peak nonlinear segment error; then update the compression damage parameter to reduce post-peak softening segment error, unloading stiffness error and residual response error; finally update the tensile damage parameter to reduce uniaxial tensile response error or bending response error.

[0078] Finally, the parameter update, numerical simulation and error calculation are repeated iteratively until the error value is no greater than the preset error threshold or the preset maximum number of iterations is reached, and the final calibrated complete parameter set and corresponding material parameter file are output.

[0079] In this embodiment, the iteration termination condition is: or ,in To preset the error threshold, This sets the maximum number of iterations. When the iteration termination condition is met, the iteration stops, and the final nonlinear constitutive model parameter set and material parameter file, which can be used by finite element software, are output.

[0080] Step S4: Based on the parameters in the constructed model parameter system, output the final calibrated complete parameter set and generate a material parameter file that can be called by finite element software.

[0081] Specifically, when the highest parameter construction level is the low data parameter generation level, a complete initial parameter set and material parameter file are output; when the highest parameter construction level is the partial data correction level, a corrected parameter set and material parameter file are output; when the highest parameter construction level is the error-driven iterative calibration level, numerical simulation, error calculation, and parameter updates are repeatedly executed until the error objective function value is no greater than a preset error threshold or the preset maximum number of iterations is reached, at which point the final calibration parameter set is output, and a material parameter file that can be used by finite element software is generated. In this embodiment, the material parameter file includes elastic parameters, yield criterion parameters, flow rule parameters, hardening parameters, damage parameters, and corresponding parameter descriptions.

[0082] The above-described method proposed in this embodiment will be described in more detail through the following examples.

[0083] Example 1: A set of reinforced ultra-high performance concrete beams was selected as the verification object under the condition of incomplete experimental data to illustrate the effect of parameter classification construction and component response prediction of this method when complete material test response curves are lacking. The available material parameters of the selected reinforced ultra-high performance concrete beams include: compressive strength of 194.0 MPa, elastic modulus of 46.4 GPa, straight steel fibers with a length of 13 mm, a diameter of 0.2 mm, a volume fraction of 2.0%, and a maximum aggregate particle size of 0.5 mm silica sand. This example does not provide complete uniaxial tensile test curves, uniaxial compression cycle test curves, and triaxial compression test curves. Therefore, it belongs to the parameter construction and verification condition under the condition of measured basic parameters. Its basic parameters are shown in Table 1 below.

[0084] Table 1 Verification parameters for reinforced ultra-high performance concrete beams in Example 1

[0085] Based on the materials shown in Table 1 above, the process first enters the low-data parameter generation level. Using compressive strength as the primary input, a complete parameter set for the initial calibration of the nonlinear constitutive model is generated according to preset empirical relationships and default constraints. Tensile strength, biaxial compressive strength, eccentricity parameters, friction parameters, hardening parameters, and damage parameters are generated according to preset empirical relationships or default constraints. Subsequently, the process enters the partial data correction level. Based on existing measured elastic modulus, steel fiber parameters, and maximum aggregate particle size, elastic parameters and tensile damage-related parameters are grouped and corrected to form a material parameter set suitable for this reinforced ultra-high performance concrete beam.

[0086] Based on this, the obtained parameters were input into a four-point bending finite element model of a reinforced ultra-high performance concrete beam. In the model, the ultra-high performance concrete beam adopts a nonlinear constitutive model, the support axis and loading axis adopt rigid body material models, and the reinforcement adopts a piecewise linear plastic material model. The ultra-high performance concrete beam, support axis, and loading axis all use eight-node solid elements, while the reinforcement uses beam elements. The material parameters for the support axis and loading axis are a density of 7800 kg / m³. 3 The elastic modulus is 200 GPa, and Poisson's ratio is 0.30. The material parameters of the reinforcing steel are a density of 7800 kg / m³. 3 The ultra-high performance concrete beam has an elastic modulus of 200 GPa, a Poisson's ratio of 0.30, and a yield strength of 615 MPa. The ultra-high performance concrete beam and its supporting and loading axes utilize automatic surface-to-surface contact, with a friction coefficient of 0.30. Reinforcing steel bars are embedded within the ultra-high performance concrete beam.

[0087] Depend on Figure 12 It can be seen that, even without complete material test response curves, the nonlinear constitutive model parameters generated and corrected using this method can still predict the four-point bending load and displacement response of reinforced ultra-high performance concrete beams relatively well. This result demonstrates that this method can generate a set of material parameters suitable for numerical analysis of components even with incomplete experimental data, and the applicability of the parameters can be verified based on existing component test responses.

[0088] Example 2: A group of ultra-high performance concretes was selected as the implementation object. The parameter construction method proposed in this embodiment was used to determine its nonlinear constitutive model parameters, and numerical analysis was performed under uniaxial compression, uniaxial tension, and uniaxial compression cyclic conditions. The basic parameters of the selected ultra-high performance concretes are shown in Table 2 below. This group of materials possesses compressive strength, tensile strength, elastic modulus, steel fiber parameters, and uniaxial compression, tensile, and cyclic compression test results, which can be used to verify the method at the material level.

[0089] Table 2 Parameters of Ultra-High Performance Concrete Foundation Used in Example 2

[0090] Based on the materials shown in Table 2 above (including basic parameters and corresponding test curves), since this group of materials possesses compressive strength, one or more other measured basic parameters, and uniaxial compression, uniaxial tension, and uniaxial compression cyclic test curves, it can enter the error-driven iterative calibration level. Specifically, firstly, an initial complete parameter set for calibration is generated based on the basic parameters and preset empirical relationships. Then, the corresponding parameter groups are grouped and corrected according to the measured elastic modulus, tensile strength, and steel fiber parameters, forming a corrected complete parameter set. Finally, the corrected parameter set is used as the current parameter set, and error-driven iterative calibration is performed based on the uniaxial compression, uniaxial tension, and uniaxial compression cyclic test curves.

[0091] Typical parameters in the aforementioned parameter set include compressive strength, tensile strength, elastic modulus, Poisson's ratio, density, flow law parameters, initial hardening parameters, hardening modulus, hardening ductility parameters, inelastic strain threshold, compressive damage ductility parameters, tensile strength threshold, ultimate crack opening displacement, and crack opening displacement threshold. Specifically, the biaxial compressive strength is initialized based on the compressive strength; the tensile damage uses a bilinear criterion, and the tensile strength threshold is initialized based on the tensile strength; the steel fiber length is 13 mm, and the ultimate crack opening displacement is initialized based on the steel fiber length; the crack opening displacement threshold is initialized based on the ultimate crack opening displacement; the remaining parameters are initialized according to preset empirical relationships or recommended values, and used as the initial input for error-driven iterative calibration.

[0092] Table 3. Parameter Construction Results of the Nonlinear Constitutive Model in Example 2

[0093] Input the parameters shown in Table 3 above into the nonlinear constitutive model in the finite element software to establish an element-level finite element model. The element feature size is taken as 10 mm. Perform cyclic numerical simulations of uniaxial compression, uniaxial tension, and uniaxial compression respectively, and compare the numerical simulation results with the experimental curves.

[0094] Depend on Figure 13 It is evident that the numerical simulation curves and experimental curves generally agree well, reflecting the initial elastic stage, peak strength, and post-peak softening characteristics of the material under uniaxial compression conditions. Figure 14 As can be seen, after using the tensile damage parameters determined by this method, numerical simulation can reflect the peak tensile strength and post-peak softening characteristics of the material. Figure 15 It is evident that the numerical simulation results can reflect the characteristics of material stiffness degradation and residual deformation accumulation during cyclic loading and unloading.

[0095] The above results demonstrate that the nonlinear constitutive model parameters determined by this method can be used for mechanical response analysis of ultra-high performance concrete under uniaxial compression, uniaxial tension, and uniaxial compression cyclic conditions.

[0096] Example 3: Triaxial compression data of ultra-high performance concrete was selected as the verification object to illustrate the effect of parameter construction and correction of this method under confining pressure conditions.

[0097] First, a set of triaxial compression data under medium and low confining pressures was selected for verification. The selected ultra-high performance concrete has a compressive strength of 155.7 MPa, uses straight steel fibers with a length of 10 mm, a diameter of 0.12 mm, a volume fraction of 2.0%, and a maximum aggregate size of 4.75 mm. Confining pressures of 5 MPa, 10 MPa, 20 MPa, and 60 MPa were applied during the triaxial compression verification. Its basic parameters are shown in Table 4 below.

[0098] Table 4. Triaxial Compression Verification Parameters under Low Confining Pressure in Example 3

[0099] Based on the materials shown in Table 4 above, triaxial compression test curves were imported according to this method. Combined with peak stress, peak strain, and post-peak softening response under different confining pressures, the yield criterion parameters, flow rule parameters, hardening parameters, and compression damage parameters were grouped, corrected, and calibrated using error-driven iteration. In the numerical simulation, confining pressure was applied first, followed by axial displacement load, to obtain stress differences and strain curves under different confining pressures.

[0100] Depend on Figure 16 As shown in (a), the parameters determined by this method can reflect the triaxial compressive response of ultra-high performance concrete under confining pressures of 5MPa, 10MPa, 20MPa, and 60MPa, indicating that this method is applicable to parameter construction and numerical analysis under medium and low confining pressure conditions.

[0101] Furthermore, to demonstrate the applicability of this method under high confining pressure conditions, a set of triaxial compression test data under high confining pressure was selected as the verification object. This set of data includes the triaxial compressive stress difference and strain response of ultra-high performance concrete under confining pressure conditions of 0MPa, 25MPa, 50MPa, 100MPa, 200MPa, and 400MPa.

[0102] For the aforementioned high confining pressure conditions, an initial complete parameter set is first obtained based on a low-data parameter generation strategy. Then, a corrected complete parameter set is formed by combining existing measured parameters. Simultaneously, based on the peak stress, peak strain, post-peak response, and lateral deformation response under different confining pressure conditions, the yield criterion parameters, flow rule parameters, hardening parameters, and compression damage parameters are grouped and corrected. Numerical simulations are then performed, and error values ​​are calculated. When the error value exceeds a preset error threshold, the parameter set is iteratively corrected according to parameter sensitivity or a preset parameter update order. During the numerical simulation, the corresponding confining pressure is first applied to the element model, followed by an axial displacement load, to obtain stress difference and strain curves under different confining pressure conditions.

[0103] Depend on Figure 16 As shown in (b), the parameters determined by this method can well reflect the triaxial compressive stress difference and strain response of ultra-high performance concrete under high confining pressure. This indicates that this method is not only suitable for parameter construction under medium and low confining pressure, but also for the correction and verification of nonlinear constitutive model parameters under high confining pressure.

[0104] Example 4: A set of plain ultra-high performance concrete beams was selected as the verification object. The nonlinear constitutive model parameters determined according to this method were input into a four-point bending finite element model to analyze the component response. The selected plain ultra-high performance concrete beams have a cross-sectional dimension of 50mm × 100mm and a length of 500mm. The material has a compressive strength of 164.0MPa, a tensile strength of 12.0MPa, an elastic modulus of 57.5GPa, straight steel fibers with a length of 13mm, a diameter of 0.16mm, a volume fraction of 3.0%, and a maximum aggregate size of 0.50mm. Its basic parameters are shown in Table 5.

[0105] Table 5 Verification parameters for Example 4 ultra-high performance concrete beams

[0106] Based on the materials shown in Table 5, the material level parameters were first constructed and the error-driven iterative calibration was completed according to this method. Then, the obtained parameters were input into the four-point bending finite element model of the ultra-high performance concrete beam to verify the component response.

[0107] Depend on Figure 17 It can be seen that the load-displacement curves obtained from the numerical simulation are in good agreement with the experimental curves, indicating that the parameters determined by this method can be used for the bending response analysis of pure ultra-high performance concrete beams.

[0108] Example 5: Three sets of ultra-high performance concrete-filled steel pipe columns were selected as verification objects. The nonlinear constitutive model parameters determined by this method were input into the composite column finite element model to analyze the component response under uniaxial compression.

[0109] All three sets of steel pipes are filled with plain ultra-high performance concrete. The compressive strength of the ultra-high performance concrete is 152.3 MPa, the elastic modulus is 62.0 GPa, the maximum aggregate size is 4.75 mm, and the aggregate type is bauxite sand. The parameters of the three sets of steel pipes are shown in Table 6, and the parameters of the ultra-high performance concrete filling material are shown in Table 7.

[0110] Table 6 Verification parameters for ultra-high performance concrete-filled steel pipe columns in Example 5

[0111] Table 7. Parameters of Ultra-High Performance Concrete Filled in Example 5

[0112] Based on the component and material parameters shown in Tables 6 and 7 above, the parameters for the ultra-high performance concrete (UHVPC) filling material were first constructed using this method, and then the obtained parameters were input into the finite element model of the UHVPC-filled steel pipe column. In the model, the UHVPC adopted a nonlinear constitutive model, the steel pipe adopted a piecewise linear plastic material model, and both the loading plate and the support plate adopted solid elements. The UHVPC, steel pipe, loading plate, and support plate all adopted eight-node solid elements. Automatic surface-to-surface contact was used between the UHVPC and the steel pipe, with the friction coefficient set to 0.30.

[0113] Depend on Figure 18 It can be seen that for the three steel pipes with different wall thicknesses, the load and axial displacement curves obtained by numerical simulation are in good agreement with the experimental curves. They can reflect the bearing capacity and deformation law of ultra-high performance concrete-filled steel pipe columns under uniaxial compressive load, indicating that the nonlinear constitutive model parameters determined by this method can be used for the compressive response analysis of ultra-high performance concrete-filled steel pipe columns.

[0114] Example 2 This embodiment provides a parameter construction system for a nonlinear constitutive model of ultra-high performance concrete, such as... Figure 2 As shown, it specifically includes: The model parameter system construction module is used to build the parameter system of the nonlinear constitutive model of ultra-high performance concrete, including elastic parameters, yield criterion parameters, flow law parameters, hardening parameters, and damage parameters. The data acquisition module is used to acquire the ultra-high performance concrete foundation parameters and test response data obtained through actual testing; the foundation parameters include at least the compressive strength in the yield criterion parameters, and the other foundation parameters and test response data are selectively acquired according to the actual test conditions. The model parameter construction module is used to determine the highest executable parameter construction level based on the completeness of the acquired data and execute parameter construction according to the preset logic of that level. During the construction process, the parameter set calculated by the previous lower level is used as the input for solving the parameters of the current level, and the construction of each parameter in the model parameter system is completed step by step. The parameter construction levels include the low data parameter generation level from low to high, the partial data correction level, and the error-driven iterative calibration level. The results output module is used to output the final calibrated complete parameter set based on each parameter in the constructed model parameter system, and generate a material parameter file that can be called by finite element software.

[0115] As one implementation method, the model parameter construction module can be further divided into: The data completeness identification module is configured to determine the highest executable parameter construction level based on the completeness of the acquired data. The low-data parameter generation level is configured to use compressive strength as the main control input and rely on the preset empirical relationship of ultra-high performance concrete to generate the initial calibration complete parameter set; Some data correction levels are configured to use existing measured basic parameters to perform corresponding group corrections on one or more of the elastic parameters, yield criterion parameters, flow rule parameters, hardening parameters, and damage parameters in the initially calibrated complete parameter set, so as to obtain the corrected complete parameter set; The error-driven iterative calibration hierarchy is configured to take the initial complete parameter set as the basis, correct it using existing measured basic parameters to form the current parameter set, generate a material parameter file based on the current parameter set, call the nonlinear constitutive model in the finite element software to perform numerical simulation at the element level, obtain numerical simulation response data, and then calculate the error value corresponding to the current parameter set in conjunction with the experimental response data to update the parameter set; through continuous iterative updates, the optimized complete parameter set is obtained.

[0116] Example 3 This embodiment provides an electronic device, including: a memory for storing executable instructions; and a processor for executing the executable instructions stored in the memory to implement the method provided in this embodiment.

[0117] Example 4 This embodiment also provides a computer-readable storage medium storing executable instructions, which, when executed by a processor, will cause the processor to execute the method described above in this embodiment.

[0118] The steps and methods involved in Embodiments 2 to 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0119] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0120] The above description is only a preferred embodiment of the present invention. Although the specific implementation of the present invention has been described in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that, based on the technical solution of the present invention, various modifications or variations that can be made by those skilled in the art without creative effort are still within the scope of protection of the present invention.

Claims

1. A method for constructing parameters of a nonlinear constitutive model for ultra-high performance concrete, characterized in that, include: A parameter system for the nonlinear constitutive model of ultra-high performance concrete was established, including elastic parameters, yield criterion parameters, flow rule parameters, hardening parameters, and damage parameters. Obtain the ultra-high performance concrete foundation parameters and test response data obtained through actual testing; the foundation parameters include at least the compressive strength in the yield criterion parameters, and the other foundation parameters and test response data are selectively obtained according to the actual test conditions. Based on the completeness of the acquired data, the highest executable parameter construction level is determined, and parameter construction is performed according to the preset logic of that level. During the construction process, the parameter set calculated by the previous lower level is used as the input for the parameter solution of the current level, and the construction of each parameter in the model parameter system is completed step by step. Among them, the parameter construction levels include the low data parameter generation level from low to high, the partial data correction level, and the error-driven iterative calibration level. Based on the parameters in the constructed model parameter system, the final calibrated complete parameter set is output, and a material parameter file that can be called by finite element software is generated; Based on the completeness of the acquired data, the highest executable parameter construction level is determined, including: When the acquired data only contains compressive strength and not test response data, the highest parameter construction level that can be executed is determined to be the low data parameter generation level. When the acquired data includes compressive strength and one or more other basic parameters, but lacks test response data, the highest parameter construction level that can be executed is determined to be the partial data correction level. When the acquired data includes compressive strength, one or more other basic parameters, and at least one test response data, the highest parameter construction level that can be executed is determined to be the error-driven iterative calibration level. The preset parameter construction logic in each parameter construction level is as follows: In the low data parameter generation level, compressive strength is the main control input, and the initial calibration complete parameter set is generated based on the preset empirical relationship of ultra-high performance concrete. In some data correction levels, using existing measured basic parameters, one or more of the elastic parameters, yield criterion parameters, flow rule parameters, hardening parameters, and damage parameters in the initially calibrated complete parameter set are grouped and corrected accordingly to obtain the corrected complete parameter set; In the error-driven iterative calibration hierarchy, the initial complete parameter set is used as the basis. The current parameter set is formed by correcting the existing measured basic parameters. A material parameter file is generated based on the current parameter set. The nonlinear constitutive model in the finite element software is called to perform numerical simulation at the element level to obtain numerical simulation response data. Then, the error value corresponding to the current parameter set is calculated by combining the experimental response data to update the parameter set. Through continuous iterative updates, the optimized complete parameter set is obtained. The iterative update process in the error-driven iterative calibration hierarchy is as follows: An error objective function is constructed; the error objective function includes one or more of the following: uniaxial compression error term, uniaxial tensile error term, uniaxial cyclic compression error term, and triaxial compression error term. Each error term includes one or more of the following: peak strength error, peak strain error, elastic segment slope error, post-peak softening segment error, unloading stiffness error, residual deformation error, and confining pressure response error. Based on the error objective function, the error value corresponding to the current parameter set is calculated according to the numerical simulation response data and the experimental response data. If the error value is greater than the preset error threshold, the current parameter set is updated under the constraints of the preset parameter value range and parameter update rules, and the numerical simulation and error calculation are performed again according to the updated parameter set. Repeatedly iterate through parameter updates, numerical simulations, and error calculations until the error value is no greater than the preset error threshold or the preset maximum number of iterations is reached, and output the final calibrated complete parameter set and the corresponding material parameter file. When updating the current parameter set, construct a multidimensional parameter vector from the parameter set. The update of the parameter vector is represented as: ； In the above formula, For the first The possible values ​​of each parameter For the first During the nth iteration The possible values ​​of each parameter The objective function is the comprehensive error. For the first During the nth iteration The possible values ​​of each parameter For the first The update step size of each parameter, This is a parametric projection function used to limit the updated parameters to their minimum value. and maximum value between; The parameter update rule constraint is as follows: parameters in the current parameter set are updated step by step according to parameter sensitivity or according to a preset parameter update order to reduce parameter tuning errors caused by parameter coupling; wherein, the parameter sensitivity of each parameter is calculated, and the parameters are sorted according to their sensitivity and updated sequentially; the formula for calculating the parameter sensitivity is: ； In the above formula, For the first Sensitivity of each parameter For the first The disturbance of each parameter; The preset parameter update order is as follows: first update the yield criterion parameters and flow law parameters to reduce peak strength error and confining pressure response error; then update the hardening parameters to reduce peak strain error and pre-peak nonlinear segment error; then update the compression damage parameters to reduce post-peak softening segment error, unloading stiffness error and residual response error; finally update the tensile damage parameters to reduce uniaxial tensile response error or bending response error.

2. The method for constructing parameters of the nonlinear constitutive model of ultra-high performance concrete as described in claim 1, characterized in that, The basic parameters, excluding compressive strength, include one or more of the following: tensile strength, elastic modulus, Poisson's ratio, density, steel fiber length, steel fiber diameter, steel fiber volume fraction, and maximum aggregate particle size; the test response data include one or more of the following: uniaxial compression test curve, uniaxial compression cycle test curve, triaxial compression test curve, and uniaxial tensile test curve.

3. The method for constructing parameters of the nonlinear constitutive model of ultra-high performance concrete as described in claim 1, characterized in that, The elastic parameters include elastic modulus, Poisson's ratio, and density; the yield criterion parameters include compressive strength, tensile strength, biaxial compressive strength, eccentricity parameter, and friction parameter; the flow rule parameters are parameters that control the direction of plastic flow; the hardening parameters include initial hardening parameter, hardening modulus, and hardening ductility parameter; the damage parameters include inelastic strain threshold, compressive damage ductility parameter, tensile strength threshold, ultimate crack opening displacement, and crack opening displacement threshold.

4. A parameter construction system for a nonlinear constitutive model of ultra-high performance concrete, characterized in that, The method for constructing parameters of the nonlinear constitutive model of ultra-high performance concrete as described in any one of claims 1-3 includes: The model parameter system construction module is used to build the parameter system of the nonlinear constitutive model of ultra-high performance concrete, including elastic parameters, yield criterion parameters, flow law parameters, hardening parameters, and damage parameters. The data acquisition module is used to acquire ultra-high performance concrete foundation parameters and test response data obtained through actual testing; the foundation parameters include at least the compressive strength in the yield criterion parameters, and the other foundation parameters and test response data are selectively acquired according to the actual test conditions; The model parameter construction module is used to determine the highest executable parameter construction level based on the completeness of the acquired data and execute parameter construction according to the preset logic of that level. During the construction process, the parameter set calculated by the previous lower level is used as the input for solving the parameters of the current level, and the construction of each parameter in the model parameter system is completed step by step. The parameter construction levels include the low data parameter generation level from low to high, the partial data correction level, and the error-driven iterative calibration level. The results output module is used to output the final calibrated complete parameter set based on each parameter in the constructed model parameter system, and generate a material parameter file that can be called by finite element software.

5. An electronic device, characterized in that, include: Memory, used to store executable instructions; The processor, when executing executable instructions stored in the memory, implements the method for constructing parameters of the nonlinear constitutive model of ultra-high performance concrete as described in any one of claims 1-3.

6. A computer-readable storage medium, characterized in that, The device stores executable instructions that, when executed by a processor, implement the method for constructing parameters of the nonlinear constitutive model of ultra-high performance concrete as described in any one of claims 1-3.

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