A concrete damage plasticity constitutive calculation method based on crack band and variable strain ratio

Abstract

The application discloses a kind of concrete damage plastic constitutive calculation method based on crack zone and variable strain ratio.The calculation method includes the following steps: obtaining the characteristic length of material basic physical information and finite element grid;Introduce crack zone theory, convert cracking strain into crack opening displacement based on characteristic length, execute displacement type damage conversion;Tension and compression parallel calculation obtains tension damage variable and compression damage variable;Reconstruct nonlinear unloading-reloading stiffness degradation trajectory, deduce tension-compression asymmetric residual plastic strain and dynamically give loading and unloading pinch coefficient;Data is cleaned and truncated, and numerical interface is formatted output.This method eliminates the grid dependence caused by softening localization in nonlinear finite element analysis, improves the calculation stability and solving convergence rate of large complex components under extreme damage working condition simulation;And the method improves the mechanical response prediction accuracy of RC structure under reciprocating load such as earthquake.

Description

Technical Field

[0001] This invention relates to the field of data processing, and in particular to a method for calculating the plastic constitutive damage of concrete based on crack zones and variable strain ratios. Background Technology

[0002] In the field of civil engineering, with the development of numerical simulation technology, finite element analysis is widely used to evaluate the mechanical response of concrete and other material components or systems under complex stress states (such as seismic cyclic loads). Among them, the concrete damaged plasticity (CDP) model has become one of the most commonly used constitutive models for concrete in mainstream commercial finite element software (such as ABAQUS) because it can simultaneously consider the plastic yielding and stiffness degradation of materials.

[0003] To accurately apply the CDP model, a complete set of monotonic constitutive envelopes for the material and damage evolution parameters (including tensile and compressive damage variables) needs to be predefined. However, current techniques and data processing tools in the generation and preprocessing stages of CDP finite element parameters generally suffer from the following limitations:

[0004] First, existing parameter generation methods struggle to accurately track the unloading-reloading behavior of materials under cyclic loading, leading to inaccurate predictions of structural hysteretic energy dissipation. Existing methods for calculating damage variables (including recommended formulas from relevant standards and commonly used parameter calculation tools) generally assume that strain ratio factors are constant when describing material stiffness degradation. This assumption of constant coefficients ignores the nonlinear characteristics of damage development rates as crack propagation changes. When simulating cyclic loading conditions such as earthquakes, existing models often overestimate or underestimate the degree of stiffness degradation and fail to accurately characterize the pinching effect and asymmetric residual plastic deformation unique to quasi-brittle materials during tension-compression cyclic switching, ultimately affecting the reliability of overall structural energy dissipation analysis.

[0005] Second, existing strain softening models are prone to mesh sensitivity issues when simulating severe structural damage. Traditional parameter generation methods mostly output softened constitutive data based on cracking strain or inelastic strain. When nonlinear calculations enter the strain localization stage, this strain-based softening data causes the calculation results to heavily depend on the finite element mesh size (i.e., the denser the mesh, the smaller the energy dissipated during fracture). This can easily lead to singular solution matrices and computational non-convergence in simulations of tensile cracking or severe damage to large, complex components.

[0006] In summary, there is an urgent need for a computational method that can overcome grid sensitivity and accurately reconstruct the degradation path of cyclic hysteresis stiffness in order to meet the data preprocessing requirements of finite element simulation in modern complex civil engineering. Summary of the Invention

[0007] This invention provides a method for calculating the plastic constitutive damage of concrete based on crack zones and variable strain ratios to solve the above-mentioned problems.

[0008] The method for calculating the plastic constitutive damage of concrete based on crack zones and variable strain ratios includes the following steps:

[0009] S1. Obtain the basic physical information of the material and the characteristic length of the finite element mesh;

[0010] S2. Introduce the crack zone theory, convert the cracking strain into crack opening displacement based on the characteristic length, and combine the fracture energy to adaptively correct the softening coefficient to perform displacement-type damage conversion.

[0011] S3. Parallel calculation of tension and compression: Dynamically calculate the strain ratio coefficients of tension and compression using the underlying nonlinear equations to obtain the tensile damage variable and the compressive damage variable.

[0012] S4. Reconstruct the nonlinear unloading-reloading stiffness degradation trajectory, deduce the residual plastic strain of tension-compression asymmetry, and dynamically assign loading and unloading pinching coefficients.

[0013] S5. Clean, truncate, and format the data using the numerical interface for output.

[0014] According to the aforementioned method for calculating the plastic constitutive model of concrete damage based on crack bands and variable strain ratios, step S2 specifically includes the following steps:

[0015] S21. Using the equivalent relationship, the cracking strain ε ck Converted to crack opening displacement w:

[0016] ;

[0017] In the formula, h is the characteristic length of the finite element mesh;

[0018] S22. The system adaptively inverts and corrects the exponential softening coefficient c:

[0019] ;

[0020] In the formula, This represents the average axial tensile strength. This is the fracture energy;

[0021] S23. Establish the displacement attenuation equation for the tensile softening segment and calculate the nominal tensile stress σ. t :

[0022] .

[0023] According to the aforementioned method for calculating the plastic constitutive model of concrete damage based on crack bands and variable strain ratios, step S3 specifically includes tensile damage variables. and pressure damage variables The calculation process;

[0024] Among them, the tensile damage variable d t The calculation process is as follows:

[0025] S31. Solve for the tensile monotonic constitutive damped response using the equation Extract the equivalent crack opening displacement w, and extract the tensile non-destructive elastic strain. ;

[0026] S32. Extracting the maximum value of the independent variable in the process. And according to the formula Calculation of normalized crack strain Substituting into the underlying nonlinear polynomial equation, the tensile strain ratio coefficient k is dynamically calculated. t :

[0027] ;

[0028] S33. The dynamically obtained tensile strain ratio coefficient k t Substituting into the displacement-type damage evolution equation, calculate the tensile damage variable d. t :

[0029] .

[0030] Among them, the pressure damage variable d c The calculation process is as follows:

[0031] S31' Solve for the three-segment constitutive hardening-softening response under compression, and calculate the nominal compressive stress σ at each strain step. c The compressive inelastic strain ε is extracted according to the following formula. in :

[0032] ;

[0033] In the formula, ε c The total compressive strain is calculated; simultaneously, the compressive lossless elastic strain is extracted. ;

[0034] S32' Extracting the maximum value of the independent variable in the process And according to the formula Calculate normalized inelastic strain Substituting into the underlying nonlinear polynomial equation, the compressive strain ratio coefficient k is dynamically calculated. c :

[0035] ;

[0036] S33', The dynamically obtained compressive strain ratio coefficient k c Substituting into the strain-type damage evolution equation, calculate the compressive damage variable d. c :

[0037] .

[0038] According to the aforementioned method for calculating the plastic constitutive model of concrete damage based on crack bands and variable strain ratios, step S4 specifically includes the following steps:

[0039] S41. Calculate the asymmetric tensile residual plastic strain. and compressive residual plastic strain :

[0040] ;

[0041] ;

[0042] S42. Introduce the local loading history variable ξ:

[0043] ;

[0044] In the formula, ε is the total strain of the current loading step, ε res To unload residual strain, ε peak This represents the historical peak strain.

[0045] S43. Dynamically assign nonlinear loading / unloading pinch coefficients based on the strain loading process:

[0046] Tension-reload pinch coefficient The pinching coefficient under pressure and reloading ;

[0047] S44. Solve for the reconstructed nonlinear unloading-reloading stiffness degradation trajectory.

[0048] According to the aforementioned method for calculating the plastic constitutive model of concrete damage based on crack bands and variable strain ratios, step S5 specifically includes the following steps:

[0049] S51. Numerically truncate and constrain the independent and damage variable matrices obtained from the solution, explicitly forcing the retention of the zero damage initiation point at w=0 or ε. in At point =0, let d t =0, d c=0, and limit the damage cap to 0.999999;

[0050] S52. Execute the formatted interface output to generate the numerical text cards required for the Concrete Damaged Plasticity model in the finite element simulation software ABAQUS.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] (1) The calculation method of the present invention establishes a mapping between the strain softening behavior of the material and the finite element mesh size, and transforms the "strain space boundary" into the "displacement space boundary" from the underlying algorithm. This mechanism eliminates the mesh dependence caused by softening localization in nonlinear finite element analysis, and improves the calculation stability and solution convergence rate of large and complex components under extreme failure conditions.

[0053] (2) The calculation method of the present invention can more accurately characterize the nonlinear characteristics of the stiffness degradation of concrete materials in the early stage, the middle stage, and the later stage. The generated parameter matrix gives the finite element model the ability to accurately reconstruct the hysteretic energy dissipation characteristics of the structure, and improves the accuracy of mechanical response prediction of RC structure under cyclic loads such as earthquakes. Attached Figure Description

[0054] Figure 1 The flowchart shows the logic of the concrete damage plastic constitutive calculation method based on crack bands and variable strain ratio.

[0055] Figure 2 This is a monotonic physical damage feature map of an embodiment;

[0056] Figure 3 Simulation diagram of the stretching, pinching, and hysteresis path for an embodiment;

[0057] Figure 4 The simulation diagram of compression pinching and hysteresis path is shown in the example. Detailed Implementation

[0058] To make the technical problem to be solved, the technical solution and advantages of the present invention clearer, the following description will be provided in conjunction with the accompanying drawings. Figures 1 to 4 The technical solution of the present invention will be clearly and completely described in conjunction with specific embodiments.

[0059] The method for calculating the plastic constitutive damage of concrete based on crack zones and variable strain ratios includes the following steps:

[0060] S1. Obtain the basic physical information of the material and the characteristic length of the finite element mesh.

[0061] S2. Introducing the crack zone theory, based on the characteristic length, the cracking strain is converted into crack opening displacement, and the softening coefficient is adaptively corrected in conjunction with the fracture energy to perform displacement-type damage transformation. Step S2 specifically includes the following steps:

[0062] S21. Using the equivalent relationship, the cracking strain ε ck Converted to crack opening displacement w:

[0063] ;

[0064] In the formula, h is the characteristic length of the finite element mesh;

[0065] S22. The system adaptively inverts and corrects the exponential softening coefficient c:

[0066] ;

[0067] In the formula, This represents the average axial tensile strength. This is the fracture energy;

[0068] S23. Establish the displacement attenuation equation for the tensile softening segment and calculate the nominal tensile stress σ. t :

[0069]

[0070] S3. Parallel calculation of tension and compression: Dynamically calculate the strain ratio coefficients of tension and compression using the underlying nonlinear equations to obtain the tensile damage variable and the compressive damage variable.

[0071] Step S3 specifically includes tensile damage variables. and pressure damage variables The calculation process.

[0072] Among them, the tensile damage variable d t The calculation process is as follows:

[0073] S31. Solve for the tensile monotonic constitutive damped response using the equation Extract the equivalent crack opening displacement w, and extract the tensile non-destructive elastic strain. .

[0074] S32. Extracting the maximum value of the independent variable in the process. And according to the formula Calculation of normalized crack strain Substituting into the underlying nonlinear polynomial equation, the tensile strain ratio coefficient k is dynamically calculated. t :

[0075] .

[0076] S33. The dynamically obtained tensile strain ratio coefficient k t Substituting into the displacement-type damage evolution equation, calculate the tensile damage variable d. t :

[0077] .

[0078] Among them, the pressure damage variable d c The calculation process is as follows:

[0079] S31' Solve for the three-segment constitutive hardening-softening response under compression, and calculate the nominal compressive stress σ at each strain step. c The compressive inelastic strain ε is extracted according to the following formula. in :

[0080] ;

[0081] In the formula, ε c The total compressive strain is calculated; simultaneously, the compressive lossless elastic strain is extracted. .

[0082] S32' Extracting the maximum value of the independent variable in the process And according to the formula Calculate normalized inelastic strain Substituting into the underlying nonlinear polynomial equation, the compressive strain ratio coefficient k is dynamically calculated. c :

[0083] .

[0084] S33', The dynamically obtained compressive strain ratio coefficient k c Substituting into the strain-type damage evolution equation, calculate the compressive damage variable d. c :

[0085] .

[0086] S4. Reconstruct the nonlinear unloading-reloading stiffness degradation trajectory, deduce the residual plastic strain of tension-compression asymmetry, and dynamically assign a loading / unloading pinching coefficient. Step S4 specifically includes the following steps:

[0087] S41. Calculate the asymmetric tensile residual plastic strain. and compressive residual plastic strain :

[0088] ;

[0089] .

[0090] S42. Introduce the local loading history variable ξ:

[0091] ;

[0092] In the formula, ε is the total strain of the current loading step, ε res To unload residual strain, ε peak This represents the historical peak strain.

[0093] S43. Dynamically assign nonlinear loading and unloading pinch coefficients based on the strain loading process.

[0094] Tension-reload pinch coefficient The pinching coefficient under pressure and reloading .

[0095] S44. Solve for the reconstructed nonlinear unloading-reloading stiffness degradation trajectory.

[0096] S5. Clean, truncate, and format the data using the numerical interface for output. Step S5 specifically includes the following steps:

[0097] S51. Numerically truncate and constrain the independent and damage variable matrices obtained from the solution, explicitly forcing the retention of the zero damage initiation point at w=0 or ε. in At point =0, let d t =0, d c =0, and limit the damage cap to 0.999999;

[0098] S52. Execute the formatted interface output to generate the numerical text cards required for the Concrete Damaged Plasticity model in the finite element simulation software ABAQUS.

[0099] Compared with the prior art, the present invention has the following beneficial effects:

[0100] (1) This invention introduces a displacement-type damage conversion mechanism based on crack zone theory into the underlying data processing flow. The algorithm forcibly reads the characteristic length of the finite element mesh and uses the equivalent geometric mapping relationship to convert the cracking strain into crack opening displacement; at the same time, the system can adaptively back-calculate and correct the exponential softening coefficient. This logic establishes a mapping between the strain softening behavior of the material and the finite element mesh size, and transforms the "strain space boundary" into the "displacement space boundary" from the underlying algorithm. This mechanism eliminates the mesh dependence caused by softening localization in nonlinear finite element analysis, and improves the computational stability and solution convergence rate of large and complex components under extreme failure conditions.

[0101] (2) In the core parallel computing module, this invention abandons the constant coefficient assumption and adopts a nonlinear polynomial equation based on normalized crack inelastic strain to dynamically solve the tensile and compressive strain ratio coefficients, and then couples the calculation of the damage variable d.t d c Based on this, the system activates a dynamic hysteresis path reconstruction algorithm to rigorously deduce the residual plastic strain with tension-compression asymmetry characteristics, and assigns a nonlinear dynamic pinching coefficient according to the strain loading history, thereby reconstructing a nonlinear unloading-reloading stiffness degradation trajectory. This algorithm can more accurately characterize the nonlinear characteristics of stiffness degradation in concrete materials, which are slow in the initial stage, accelerated in the middle stage, and gradual in the later stage. The generated parameter matrix endows the finite element model with the ability to accurately reconstruct the hysteresis energy dissipation characteristics of the structure, improving the prediction accuracy of the mechanical response of RC structures under cyclic loads such as earthquakes.

[0102] To better illustrate the working principle and technical effects of this invention, the following uses a common ordinary concrete strength grade (C30 grade) in a conventional engineering project as an example to explain in detail how the underlying algorithm of this invention automatically calculates and generates a complete set of finite element numerical parameters for the CDP model based on a single macroscopic strength index, which can eliminate the problems of mesh sensitivity and hysteresis energy dissipation distortion.

[0103] Obtain basic material information and the characteristic length of the finite element mesh. Basic material information includes matrix type and initial elastic modulus. The user directly inputs the basic physical parameters as "C30 grade ordinary concrete". Simultaneously, set the characteristic length of the mesh elements for subsequent nonlinear finite element analysis to h=50mm, and set the initial elastic modulus E0=30000.0MPa.

[0104] The system's underlying algorithm begins executing the cascade generation of associated mechanical parameters for C30:

[0105] (1) Calculate the standard value of axial compressive strength: ;

[0106] (2) Calculate the average axial compressive strength: ;

[0107] (3) Calculate the average axial tensile strength: ;

[0108] (4) Estimate the fracture energy and crushing energy using macroscopic empirical formulas:

[0109] , .

[0110] Through this step, the system can automatically calculate and complete the full set of basic mechanical property data required to establish a finite element monotonic constitutive model using only the single scalar "C30".

[0111] In traditional ABAQUS input, the tensile softening section of C30 concrete typically outputs "stress-cracking strain" directly. "Data. If the characteristic length is not introduced, when the finite element mesh h is reduced from 50mm to 25mm, the fracture energy that the element can dissipate will decrease proportionally with the mesh size, causing the structure to exhibit pseudo-brittleness at the numerical level. This not only seriously underestimates the deformation capacity of the component, leading to distorted results, but also easily causes serious localization problems, ultimately resulting in singular and non-convergent solution matrices."

[0112] In this example, the system enables "displacement-based damage transformation," and the algorithm forces the mesh size to be read as h=50.0mm.

[0113] (1) Converting cracking strain into crack opening displacement: ;

[0114] (2) Adaptive back-calculation correction of softening coefficient: to ensure that the thermodynamic dissipation energy is equal to the fracture energy G F The system does not use traditional empirical formulas, but calculates directly. ;

[0115] (3) Establish the tensile displacement attenuation equation: .

[0116] The generated stress-displacement "The constitutive model directly binds to the element size, fundamentally eliminating the mesh dependency in the nonlinear tensile cracking analysis of C30 components."

[0117] In traditional methods, the strain ratio coefficient of C30 concrete is usually preset to a constant (e.g., k). t =0.1, k c =0.7), which fails to reflect the nonlinear characteristics of material damage development.

[0118] In this example, the system extracts the maximum crack strain during the evolution of the constitutive curve. With the maximum value of inelastic strain In each calculation step, the normalized strain (e.g., ...) is calculated. ), and substitute into the underlying polynomial equation to dynamically solve for the variable strain ratio coefficient. At a certain step in the middle of the tensile softening process (assuming normalized strain...), (At time), the system dynamically solves to obtain:

[0119]

[0120] The dynamic will then be Substituting into the displacement-type damage evolution equation, the tensile damage variable d corresponding to this step is calculated using coupled methods. t Similarly, under compression, k can be dynamically solved. c and d c .

[0121] To accurately simulate the energy dissipation performance of the C30 concrete component under cyclic loading such as earthquakes, the system activates the hysteretic reconstruction algorithm:

[0122] (1) The system abandons the empirical proportionality constant method and strictly bases itself on the real damage-plastic coupling equation, using the dynamic damage variable d obtained in step 4. t and d c The residual plastic strain ε due to tension-compression asymmetry is derived. pl This inference algorithm can accurately capture the true material properties of concrete, namely, the residual deformation after tensile unloading is minimal, while the residual strain after compressive unloading increases nonlinearly with the degree of damage.

[0123] (2) During the simulated cyclic reloading branch, the system calculates the dynamic pinching coefficient based on the local loading history variable ξ (for example, when the local loading history variable ξ is 0.5 at a certain point in the pressure reloading stage, the pressure reloading pinching coefficient Pinch is calculated). c (0.965). Using this pinching coefficient, the reloading stress is smoothly corrected, and a nonlinear unloading-reloading stiffness degradation trajectory that closely approximates the real physical experiment is reconstructed.

[0124] Finally, the system safely truncates the matrix containing the "monotonically displaced envelope" and "dynamic hysteresis evolution data," automatically formats it, and outputs CDP parameters suitable for ABAQUS, as follows: Figures 2 to 4 As shown in Table 1, the complete data generated by the system can be copied to ABAQUS. Table 2 shows the data that can be copied to ABAQUS.

[0125] Table 1. Full Data Matrix Data Table of the Example

[0126]

[0127] Table 2 Data table for CAE solver mapping

[0128]

[0129] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit them. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the scope of the technology disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention.

Claims

1. A method for calculating the plastic constitutive damage of concrete based on crack zones and variable strain ratios, characterized in that, Includes the following steps: S1. Obtain the basic physical information of the material and the characteristic length of the finite element mesh; S2. Introduce the crack zone theory, convert the cracking strain into crack opening displacement based on the characteristic length, and combine the fracture energy to adaptively correct the softening coefficient to perform displacement-type damage conversion. S3. Parallel calculation of tension and compression: Dynamically calculate the strain ratio coefficients of tension and compression using the underlying nonlinear equations to obtain the tensile damage variable and the compressive damage variable. S4. Reconstruct the nonlinear unloading-reloading stiffness degradation trajectory, deduce the residual plastic strain of tension-compression asymmetry, and dynamically assign loading and unloading pinching coefficients. S5. Clean, truncate, and format the data using the numerical interface for output.

2. The method for calculating the plastic constitutive structure of concrete damage based on crack bands and variable strain ratios according to claim 1, characterized in that, Step S2 specifically includes the following steps: S21. Using the equivalent relationship, the cracking strain ε ck Converted to crack opening displacement w: ； In the formula, h is the characteristic length of the finite element mesh; S22. The system adaptively inverts and corrects the exponential softening coefficient c: ； In the formula, This represents the average axial tensile strength. This is the fracture energy; S23. Establish the displacement attenuation equation for the tensile softening segment and calculate the nominal tensile stress σ. t : 。 3. The method for calculating the plastic constitutive structure of concrete damage based on crack bands and variable strain ratios according to claim 1, characterized in that, Step S3 specifically includes tensile damage variables. and pressure damage variables The calculation process; Among them, the tensile damage variable d t The calculation process is as follows: S31. Solve for the tensile monotonic constitutive damped response using the equation Extract the equivalent crack opening displacement w, and extract the tensile non-destructive elastic strain. ; S32. Extracting the maximum value of the independent variable in the process. And according to the formula Calculation of normalized crack strain Substituting into the underlying nonlinear polynomial equation, the tensile strain ratio coefficient k is dynamically calculated. t : ； S33. The dynamically obtained tensile strain ratio coefficient k t Substituting into the displacement-type damage evolution equation, calculate the tensile damage variable d. t : ； Among them, the pressure damage variable d c The calculation process is as follows: S31' Solve for the three-segment constitutive hardening-softening response under compression, and calculate the nominal compressive stress σ at each strain step. c The compressive inelastic strain ε is extracted according to the following formula. in : ； In the formula, ε c The total compressive strain is calculated; simultaneously, the compressive lossless elastic strain is extracted. ; S32' Extracting the maximum value of the independent variable in the process And according to the formula Calculate normalized inelastic strain Substituting into the underlying nonlinear polynomial equation, the compressive strain ratio coefficient k is dynamically calculated. c : ； S33', The dynamically obtained compressive strain ratio coefficient k c Substituting into the strain-type damage evolution equation, calculate the compressive damage variable d. c : 。 4. The method for calculating the plastic constitutive structure of concrete damage based on crack bands and variable strain ratios according to claim 1, characterized in that, Step S4 specifically includes the following steps: S41. Calculate the asymmetric tensile residual plastic strain. and compressive residual plastic strain : ； ； S42. Introduce the local loading history variable ξ: ； In the formula, ε is the total strain of the current loading step, ε res To unload residual strain, ε peak This represents the historical peak strain. S43. Dynamically assign nonlinear loading / unloading pinch coefficients based on the strain loading process: Tension-reload pinch coefficient The pinching coefficient under pressure and reloading ; S44. Solve for the reconstructed nonlinear unloading-reloading stiffness degradation trajectory.

5. The method for calculating the plastic constitutive structure of concrete damage based on crack bands and variable strain ratios according to claim 1, characterized in that, Step S5 specifically includes the following steps: S51. Numerically truncate and constrain the independent and damage variable matrices obtained from the solution, explicitly forcing the retention of the zero damage initiation point at w=0 or ε. in At point =0, let d t =0, d c =0, and limit the damage cap to 0.999999; S52. Execute the formatted interface output to generate the numerical text cards required for the Concrete Damaged Plasticity model in the finite element simulation software ABAQUS.

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