Multi-axial concrete damage plasticity constitutive model implementation for beam elements

Abstract

The application discloses a method for implementing a multi-axial concrete damage plastic constitutive model suitable for a beam element. The method comprises the following steps: obtaining a three-dimensional strain increment tensor by performing dimension upgrading on the strain increment of a target beam element in a current increment step based on a transverse elastic constraint relationship; calculating a three-dimensional trial stress based on a three-dimensional elastic constitutive relationship; determining a flow direction based on a plastic potential function, coupling a yield condition and the transverse elastic constraint relationship at the three-dimensional trial stress, and solving a solution result of a to-be-solved unknown quantity and a plastic multiplier increment by using a single-step back mapping; updating three-dimensional state variables of a previous increment step based on the solution result, the flow direction and the plastic multiplier increment, and obtaining a constitutive implementation result from a target stress component extracted from the three-dimensional state variables. By the technical scheme, the damage softening history of concrete under a three-dimensional stress state can be completely retained while the original three degrees of freedom of the beam element are used, so that the technical effect of consistent nonlinear analysis precision with a solid element is achieved.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation technology for structural engineering, and in particular to a method for implementing a multiaxial concrete damage plastic constitutive model applicable to beam elements. Background Technology

[0002] With the gradual development of numerical simulation technology in structural engineering, nonlinear finite element analysis has been increasingly applied to the seismic performance evaluation of reinforced concrete beams, columns, and joint components. It is used to reveal the yielding sequence, damage distribution, and residual deformation characteristics of components under complex stresses, providing a quantitative basis for performance-based seismic design.

[0003] In existing technologies, finite element software typically employs a built-in multiaxial plastic damage model based on solid or shell elements, or a uniaxial constitutive model based on fiber beam elements using user-defined subroutines, to apply the concrete constitutive model.

[0004] However, the built-in multiaxial plastic damage model based on solid or shell elements is only developed for solid or shell strain formats at the underlying interface, making it incompatible with the strain output and stress return logic of beam elements. Forcing the beam-column members to undergo 3D solid meshing to use this model would result in an order-of-magnitude increase in the number of degrees of freedom, a sharp decrease in computational efficiency, and difficulty in meeting the timeliness requirements of engineering designs. While the uniaxial constitutive scheme of fiber beam elements based on user-defined subroutines solves the beam element adaptation problem, forcibly degenerating the 3D stress state at the beam element integration points into uniaxial strain input leads to the loss of multiaxial physical mechanisms.

[0005] Therefore, how to directly perform the return mapping of multiaxial damage plastic constitutive model at the integration point level of beam element, so as to maintain the low degree of freedom efficiency of beam element while maintaining the multiaxial accuracy comparable to that of solid element, is an urgent problem to be solved. Summary of the Invention

[0006] This invention provides a method for implementing a multiaxial concrete damage plastic constitutive model applicable to beam elements, which can solve the problem of the trade-off between computational efficiency and multiaxial accuracy in the nonlinear analysis of reinforced concrete, beams, columns and joint components in existing technologies.

[0007] According to one aspect of the present invention, a method for implementing a multiaxial concrete damage plastic constitutive model suitable for beam elements is provided. This method is applied to the nonlinear finite element analysis of concrete beam-column members in structural engineering numerical simulation. The method includes: Obtain the strain increment corresponding to the target beam element in the current increment step and the three-dimensional state variables corresponding to the target beam element saved at the end of the previous increment step; The strain increment is subjected to dimensionality-upgrading processing based on a preset transverse elastic constraint relationship to obtain a three-dimensional strain increment tensor; wherein, the three-dimensional strain increment tensor contains at least the transverse normal strain increment as an unknown quantity to be determined. The three-dimensional strain increment tensor is calculated based on a preset three-dimensional elastic constitutive relation to obtain the three-dimensional test stress; The flow direction of the stress corresponding to the target beam element is determined by the plastic potential energy function based on the preset concrete damage plasticity model. The yield condition of the preset concrete damage plasticity model and the preset transverse elastic constraint relationship are coupled at the three-dimensional test stress and solved by the single-step regression algorithm to obtain the solution result of the unknown quantity to be solved and the plastic multiplier increment. Based on the solution results, the flow direction, and the plastic multiplier increment, the three-dimensional state variables of the target beam element are updated, and the target stress component of the target beam element is extracted from the updated three-dimensional state variables to obtain the constitutive realization result of the target beam element.

[0008] According to another aspect of the present invention, a device for realizing a multiaxial concrete damage plastic constitutive model suitable for beam elements is provided. This device is applied to the nonlinear finite element analysis of concrete beam-column members in structural engineering numerical simulation. The device includes: The data acquisition module is used to acquire the strain increment corresponding to the target beam element in the current increment step and the three-dimensional state variables corresponding to the target beam element saved at the end of the previous increment step. The strain dimension-up module is used to perform dimension-up processing on the strain increment based on a preset transverse elastic constraint relationship to obtain a three-dimensional strain increment tensor; wherein, the three-dimensional strain increment tensor contains at least the transverse normal strain increment as an unknown quantity to be determined. The test stress calculation module is used to calculate the three-dimensional strain increment tensor based on a preset three-dimensional elastic constitutive relation to obtain the three-dimensional test stress. The coupled solution module is used to determine the flow direction of the stress corresponding to the target beam element based on the plastic potential energy function of the preset concrete damage plasticity model. It couples the yield condition of the preset concrete damage plasticity model with the preset transverse elastic constraint relationship at the three-dimensional test stress and solves it through a single-step regression algorithm to obtain the solution results of the unknown quantity to be solved and the plastic multiplier increment. The result generation module is used to update the three-dimensional state variables of the target beam element based on the solution results, the flow direction, and the plastic multiplier increment, and to extract the target stress component of the target beam element from the updated three-dimensional state variables to obtain the constitutive realization result of the target beam element.

[0009] According to another aspect of the present invention, an electronic device is provided, the electronic device comprising: At least one processor; and A memory communicatively connected to the at least one processor; wherein, The memory stores a computer program that can be executed by the at least one processor, which enables the at least one processor to perform the method for implementing a multiaxial concrete damage plastic constitutive model for beam elements as described in any embodiment of the present invention.

[0010] According to another aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium storing computer instructions for causing a processor to execute and implement the method for implementing a multiaxial concrete damage plastic constitutive model applicable to beam elements as described in any embodiment of the present invention.

[0011] The technical solution of this invention involves obtaining the strain increment corresponding to the target beam element in the current increment step and the three-dimensional state variables corresponding to the target beam element saved at the end of the previous increment step. Then, based on a preset transverse elastic constraint relationship, the strain increment is upgraded to obtain a three-dimensional strain increment tensor; wherein the three-dimensional strain increment tensor contains at least the transverse normal strain increment as an unknown quantity. Further, based on a preset three-dimensional elastic constitutive relationship, the three-dimensional strain increment tensor is calculated to obtain the three-dimensional test stress. Further, based on the plastic potential energy function of a preset concrete damage plasticity model, the flow direction of the stress corresponding to the target beam element is determined. The yield condition of the preset concrete damage plasticity model is coupled with the preset transverse elastic constraint relationship at the three-dimensional test stress and solved using a single-step regression algorithm to obtain the solution result of the unknown quantity and the plastic multiplier increment. Finally, based on the solution result, flow direction, and plastic multiplier increment, the three-dimensional state variables of the target beam element are updated, and the target stress component of the target beam element is extracted from the updated three-dimensional state variables to obtain the constitutive realization result corresponding to the target beam element. By introducing the assumption of transverse elastic constraints within the material constitutive model to establish a physical mapping relationship between transverse strain and transverse stress in beam elements, and using a novel single-step regression algorithm, the yield condition of the Concrete Damaged Plasticity (CDP) model is coupled with the transverse elastic constraints at the stress test point in a first-order linearization manner. This directly constructs and solves a closed system of linear algebraic equations, obtaining the corrections for transverse strain and plasticity multipliers in a single step. This solves the problem of the trade-off between computational efficiency and multiaxial accuracy faced by existing technologies in nonlinear analysis of reinforced concrete, beams, columns, and joint components. It enables beam elements to realistically reflect the multiaxial stress behavior of three-dimensional beam elements under different transverse constraints while maintaining the original strain input format. In other words, it allows beam elements to retain and characterize the stiffness degradation and damage evolution history of concrete under three-dimensional stress states while maintaining the original three degrees of freedom, thus achieving the same technical effect in nonlinear analysis accuracy as solid elements.

[0012] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of the present invention, nor is it intended to limit the scope of the invention. Other features of the invention will become readily apparent from the following description. Attached Figure Description

[0013] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1 This is a flowchart of a method for implementing a multiaxial concrete damage plastic constitutive model applicable to beam elements according to Embodiment 1 of the present invention; Figure 2 This is a flowchart of a method for implementing a multiaxial concrete damage plastic constitutive model applicable to beam elements according to Embodiment 2 of the present invention; Figure 3 This is a schematic diagram of a device for realizing a multiaxial concrete damage plastic constitutive model for beam elements, according to Embodiment 3 of the present invention. Figure 4 This is a schematic diagram of the structure of an electronic device that implements the method for realizing a multiaxial concrete damage plastic constitutive model applicable to beam elements according to embodiments of the present invention. Detailed Implementation

[0015] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0016] It should be noted that the terms "first," "second," "target," etc., used in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0017] Example 1 Figure 1This is a flowchart illustrating a method for implementing a multiaxial concrete damage plastic constitutive model for beam elements, as provided in Embodiment 1 of the present invention. This embodiment is applicable to nonlinear finite element analysis of concrete beam-column members in structural engineering numerical simulation. The method can be executed by a device for implementing a multiaxial concrete damage plastic constitutive model for beam elements. This device can be implemented in hardware and / or software, and can rely on a system with a fully autonomous Computer-Aided Engineering (CAE) software platform, which can be configured in an electronic device. Figure 1 As shown, the method includes: S110. Obtain the strain increment corresponding to the target beam element in the current increment step and the three-dimensional state variable corresponding to the target beam element saved at the end of the previous increment step.

[0018] In this context, "incremental step" refers to a series of sequentially loaded segments obtained by discretizing the total load or displacement history during finite element nonlinear solution. "Current increment step" refers to the increment step corresponding to the current material constitutive invocation. "Beam element" refers to a finite element based on beam theory, with nodal degrees of freedom typically including axial displacement, lateral displacement, and torsional angle, and internal integration points that only transmit axial normal strain and two engineering shear strains. "Target beam element" refers to the beam element instance being processed in the current increment step. "Strain increment" refers to the change in strain in the current increment step relative to the end of the previous increment step. "Three-dimensional state variables" refers to the complete set of variables used to describe the internal state of the integration point at the current moment. For example, three-dimensional state variables may include stress, strain, and damage.

[0019] S120. The strain increment is subjected to dimensionality-upgrading processing based on the preset transverse elastic constraint relationship to obtain a three-dimensional strain increment tensor; wherein, the three-dimensional strain increment tensor contains at least the transverse normal strain increment as an unknown quantity to be determined.

[0020] Here, the preset transverse elastic constraint relationship can refer to a pre-defined assumption used to describe the linear relationship between transverse stress and strain in the beam section. The three-dimensional strain increment tensor can refer to a complete tensor composed of the low-dimensional strain increment of the beam element and the transverse strain increment to be determined. The unknown quantity to be determined can refer to the variable vector that was unknown before the coupled solution and obtained after the solution. The transverse normal strain increment can refer to the change in normal strain in the transverse direction of the beam section.

[0021] S130. The three-dimensional strain increment tensor is calculated based on the preset three-dimensional elastic constitutive relation to obtain the three-dimensional test stress.

[0022] The preset three-dimensional elastic constitutive relation can refer to the pre-defined linear elastic stress-strain relationship. The three-dimensional test stress can refer to the predicted stress value calculated according to the elastic constitutive relation when the current increment step is entirely elastic deformation.

[0023] S140. Based on the plastic potential energy function of the preset concrete damage plasticity model, determine the flow direction of the stress corresponding to the target beam element. Couple the yield condition of the preset concrete damage plasticity model with the preset transverse elastic constraint relationship at the three-dimensional test stress and solve it through a single-step regression algorithm to obtain the solution result of the unknown quantity to be solved and the plastic multiplier increment.

[0024] The pre-defined concrete damage plasticity model can refer to a multiaxial constitutive model of concrete based on continuum mechanics, including tensile or compressive dual damage variables, yield, and correction. The plastic potential energy function can refer to the potential energy function used to determine the direction of plastic flow. The flow direction can refer to the direction vector of the plastic strain increment. The yield criterion can refer to a scalar function used to determine whether the material has entered the plastic phase. The single-step regression algorithm refers to a hybrid algorithm that provides analytical values ​​for a subset of variables at the current stress point based on assumptions, and solves all unknowns step-by-step through coupling relationships during the solution process. The solution result can refer to the updated values ​​of unknowns obtained from the coupled linear equation system. The plastic multiplier increment can refer to the scalar increment used to control the magnitude of plastic flow.

[0025] S150. Based on the solution results, the flow direction, and the plastic multiplier increment, update the three-dimensional state variables of the target beam element, and extract the target stress component of the target beam element from the updated three-dimensional state variables to obtain the constitutive realization result corresponding to the target beam element.

[0026] Here, stress components can refer to independent components in a three-dimensional stress tensor. Typically, a single three-dimensional stress tensor contains six stress components. Target stress components can refer to the components extracted from the three-dimensional stress tensor according to the degrees of freedom of the beam elements. Constitutive realization results can refer to the minimum output package of the current analysis process.

[0027] In an optional implementation, after extracting the target stress component of the target beam element from the updated three-dimensional state variables to obtain the constitutive realization result corresponding to the target beam element, the method further includes: Step a1: Determine the three-dimensional uniform tangent stiffness matrix corresponding to the target beam element based on the plastic multiplier increment and the flow direction.

[0028] The three-dimensional uniform tangent stiffness matrix can be defined as the constitutive Jacobian matrix derived from the total differential of stress with respect to strain increment, guaranteeing quadratic convergence of global Newton and Raphson iterations. Typically, the three-dimensional uniform tangent stiffness matrix can be calculated using a constitutive integral engine.

[0029] Step a2: Based on the preset beam element degree of freedom mapping relationship, project the three-dimensional consistent tangent stiffness matrix onto the beam element stress and strain space to obtain the three-dimensional beam element tangent stiffness matrix, and return the three-dimensional beam element tangent stiffness matrix.

[0030] The preset beam element degree-of-freedom mapping relationship can refer to a predefined linear mapping matrix used to convert between the stress-strain space of the beam element and the stress-strain space of the three-dimensional continuous medium. The stress-strain space of the beam element can refer to the stress vector space and strain vector space used by the beam element itself. The three-dimensional beam element tangent stiffness matrix can refer to the projected Jacobian matrix. For example, the three-dimensional consistent tangent stiffness matrix is... Taking a beam element stress-strain space as a 3-dimensional space and a presupposed beam element degree-of-freedom mapping relationship of P as an example, the tangent stiffness matrix of the 3D beam element can be expressed as: P is a 6×3 mapping matrix, and the tangent stiffness matrix of the three-dimensional beam element is a 3×3 Jacobian matrix.

[0031] Specifically, after the stress and state variables of the concrete constitutive model of the beam element are updated, a three-dimensional consistent tangent stiffness matrix is ​​constructed based on the plastic multiplier increment and the frozen flow direction obtained from this incremental step, according to the consistent linearization format of the CDP model. This matrix is ​​then projected onto the stress and strain space of the beam element itself through the beam element degree-of-freedom mapping relationship, resulting in a directly returnable three-dimensional beam element tangent stiffness matrix. Thus, this three-dimensional beam element tangent stiffness matrix ensures that the global Newton and Raphson iterations still possess quadratic convergence characteristics when using the multiaxial constitutive model of the beam element of this invention. This avoids the slowed convergence or oscillations caused by only returning stress and using numerical difference stiffness. Furthermore, since the projection uses the same set of preset mapping relationships as the dimensionality increase or decrease, the entire constitutive interface is self-consistently closed-loop within the architecture. This allows the invention to achieve CDP accuracy equivalence for solid elements without disrupting the stiffness assembly logic of the original beam element solver on the autonomous CAE platform, simultaneously controlling engineering iteration efficiency and numerical stability.

[0032] The technical solution of this invention involves obtaining the strain increment corresponding to the target beam element in the current increment step and the three-dimensional state variables corresponding to the target beam element saved at the end of the previous increment step. Then, based on a preset transverse elastic constraint relationship, the strain increment is upgraded to obtain a three-dimensional strain increment tensor; wherein the three-dimensional strain increment tensor contains at least the transverse normal strain increment as an unknown quantity. Further, based on a preset three-dimensional elastic constitutive relationship, the three-dimensional strain increment tensor is calculated to obtain the three-dimensional test stress. Further, based on the plastic potential energy function of a preset concrete damage plasticity model, the flow direction of the stress corresponding to the target beam element is determined. The yield condition of the preset concrete damage plasticity model is coupled with the preset transverse elastic constraint relationship at the three-dimensional test stress and solved using a single-step regression algorithm to obtain the solution result of the unknown quantity and the plastic multiplier increment. Finally, based on the solution result, flow direction, and plastic multiplier increment, the three-dimensional state variables of the target beam element are updated, and the target stress component of the target beam element is extracted from the updated three-dimensional state variables to obtain the constitutive realization result corresponding to the target beam element. Within the material constitutive model, a physical mapping relationship between the transverse strain and transverse stress of the beam element is established by introducing the assumption of transverse elastic constraints. A single-step regression algorithm is then used to couple the yield condition of the concrete damage plasticity model with the transverse elastic constraints at the stress test point in a first-order linearized manner. This directly constructs and solves a closed system of linear algebraic equations, obtaining the corrections for transverse strain and plasticity multipliers in a single step. This solves the problem of the trade-off between computational efficiency and multiaxial accuracy faced by existing technologies in nonlinear analysis of reinforced concrete, beams, columns, and joint components. It enables the beam element to realistically reflect the multiaxial stress behavior of the three-dimensional beam element under different transverse constraints while maintaining the original strain input format. In other words, it allows the beam element to retain and characterize the stiffness degradation and damage evolution history of concrete under three-dimensional stress while maintaining the original three degrees of freedom, thus achieving the same technical effect in nonlinear analysis accuracy as solid elements.

[0033] Example 2 Figure 2This is a flowchart of a method for implementing a multiaxial concrete damage plastic constitutive model applicable to beam elements, provided in Embodiment 2 of the present invention. This embodiment is a refinement based on the above embodiment. Specifically, this embodiment refines the step of "coupling and solving the yield condition of the preset concrete damage plastic model with the preset transverse elastic constraint relationship at the three-dimensional test stress to obtain the solution result of the unknown quantity to be solved and the plastic multiplier increment". Specifically, it may include: performing a first-order Taylor expansion of the preset transverse elastic constraint relationship at the three-dimensional test stress to obtain a first residual equation and a second residual equation; wherein, the first residual equation and the second residual equation are used to characterize two... The stress and strain constraints in the transverse direction are balanced; the yield condition of the preset concrete damage plasticity model is expanded using a first-order Taylor series at the three-dimensional test stress to obtain the third residual equation; wherein, the third residual equation is used to characterize the convergence condition of the yield function; a three-dimensional residual vector is constructed based on the first residual equation, the second residual equation, and the third residual equation, and the partial derivative of the three-dimensional residual vector is obtained with respect to the unknown quantity and the plasticity multiplier increment to obtain the Jacobian matrix; a system of linear algebraic equations is obtained based on the Jacobian matrix and the three-dimensional residual vector, and the solution result of the corrected unknown quantity and the plasticity multiplier increment are obtained based on the system of linear algebraic equations. Figure 2 As shown, the method includes: S210. Obtain the strain increment corresponding to the target beam element in the current increment step and the three-dimensional state variable corresponding to the target beam element saved at the end of the previous increment step.

[0034] S220. The strain increment is subjected to dimensionality-upgrading processing based on the preset transverse elastic constraint relationship to obtain a three-dimensional strain increment tensor; wherein, the three-dimensional strain increment tensor contains at least the transverse normal strain increment as an unknown quantity to be determined.

[0035] Specifically, the three-dimensional strain increment array of the target beam element in the current increment step is used as... For example, among which, It can represent the axial normal strain increment. and This can represent the increments of engineering shear strain in two orthogonal directions, corresponding to the two transverse shear deformations of the beam element. First, the engineering shear strain is converted into tensor shear strain, i.e. , This forms the initial framework for constructing the three-dimensional strain increment tensor. Subsequently, a pre-defined lateral elastic constraint relationship is introduced: .in, , and The preset transverse elastic constraint stiffness coefficient can be taken from zero to infinity depending on the degree of constraint on the beam section. This is due to the transverse normal strain at the integration point of the beam element. and Since it is not directly input to the solver, and cannot be forcibly zeroed using the plane stress assumption, its corresponding increment is used instead. , Let this be the unknown variable to be solved, and the related variables will be reversed. According to Timoshenko beam theory, it will not be treated as an iteration variable for the time being, thus filling the initial framework with a complete three-dimensional strain increment tensor: This tensor not only preserves the axial and shear deformation information of the original input beam element, but also provides complete strain input conditions for the subsequent return mapping of concrete damage plastic constitutive model in three-dimensional stress space by introducing the unknown transverse normal strain increment.

[0036] S230. The three-dimensional strain increment tensor is calculated based on the preset three-dimensional elastic constitutive relation to obtain the three-dimensional test stress.

[0037] Specifically, after completing the dimensionality-upgrading construction of the three-dimensional strain increment tensor, the three-dimensional state variables saved after the convergence of the previous increment step are retrieved. These three-dimensional state variables contain the full three-dimensional stress tensor. With full three-dimensional strain tensor Based on the pre-defined three-dimensional elastic constitutive relation, namely the generalized Hooke's law derived from the isotropic linear elastic model. Elastic prediction is performed on the strain increment of the current increment step. Among them, This is a 6×6 elastic stiffness matrix constructed based on the user-input elastic modulus E and Poisson's ratio ν. For example, the three-dimensional strain increment tensor... Substituting into the elastic stress update formula The three-dimensional test stress tensor was calculated. This tensor represents the tentative stress state at the current strain increment if the material does not undergo plastic yielding, and its components are in the form of... This three-dimensional stress test will serve as the core benchmark for subsequent determination of whether the plastic state has been entered, calculation of the plastic potential energy gradient, and first-order Taylor expansion of the relationship between the yield condition and the transverse elastic constraint at the stress test point, thereby anchoring the starting point of the constitutive integral to the elastic prediction solution under the framework of continuum mechanics.

[0038] S240. Determine the deviatoric stress tensor corresponding to the target beam element based on the three-dimensional test stress.

[0039] The deviatoric stress tensor refers to the deviatoric portion remaining after subtracting the hydrostatic pressure component from the total stress tensor. For example, the deviatoric stress tensor can be expressed by the formula: The calculation yielded the result. For effective hydrostatic pressure, It is a unit tensor.

[0040] S250. Based on the deviatoric stress tensor and the three-dimensional test stress, the partial derivative of the plastic potential energy function of the preset concrete damage plasticity model is obtained to obtain the plastic flow direction vector.

[0041] Here, the plastic flow direction vector can refer to the form of the plastic potential energy function before the gradient normalization of the corresponding force. For example, the plastic potential energy function of a pre-defined concrete damage plasticity model is used as... For example, It can represent the tensile strength of a shaft. It can represent the shear dilatation angle. It can represent the sharp angle offset of the potential function. It can represent the effective Mises equivalent stress. Taking the partial derivative of the plastic potential energy function, we can obtain the plastic flow direction vector: .

[0042] S260. Based on the single-step reflection algorithm, the plastic flow direction vector is frozen at the three-dimensional test stress point, and the frozen plastic flow direction vector is used as the flow direction of the corresponding stress of the target beam element.

[0043] Freezing can refer to the operation of forcing a variable to retain its value calculated at the first stress point during multiple local iterations within an incremental step.

[0044] Specifically, after calculating the three-dimensional test stress of the current increment step, its trace is first obtained to acquire the hydrostatic pressure, and a deviatoric stress tensor is constructed. Then, this deviatoric stress tensor is substituted into the hyperbolic plastic potential energy function of the preset CDP model to obtain the plastic flow direction vector. Subsequently, the single-step regression algorithm is activated, stipulating that in the subsequent coupled solutions of the entire current increment step, this plastic flow direction vector will not be recalculated with the stress update after plastic correction; that is, it is frozen at the three-dimensional test stress point, and this frozen plastic flow direction vector is used as the flow direction output for the corresponding stress of the target beam element, for use in constructing the plastic correction term and updating the stress and equivalent plastic strain. Thus, by decomposing the deviatoric stress tensor from the three-dimensional test stress, the Mises deviatoric term and the hydrostatic pressure term in the plastic potential energy function are explicitly separated. Furthermore, by taking the partial derivative with respect to the potential energy, the resulting flow direction vector possesses both the physical meaning of shear flow determined by the deviatoric stress and the volumetric expansion determined by the expansion angle. Based on this, a single-step back mapping algorithm is used to freeze the flow direction vector at the test stress point, so that subsequent coupled solutions do not need to recalculate the yield or potential energy gradient in each iteration. The Jacobian matrix can be directly constructed using the constant vector yield gradient and the constant vector flow direction, reducing the traditional fully implicit back mapping nested loop to a single linear algebra solution or a very small number of updates. While preserving the physical rationality of non-associated flow, it significantly reduces the computational cost of constitutive integrals at the integration point of beam elements.

[0045] S270. Perform a first-order Taylor expansion on the preset transverse elastic constraint relationship at the three-dimensional test stress to obtain a first residual equation and a second residual equation; wherein, the first residual equation and the second residual equation are used to characterize the stress and strain constraint balance in two transverse directions, respectively.

[0046] The first residual equation can refer to the equation relating the transverse elastic constraint relationship. At the stress test point After the first-order Taylor expansion, the stress components are compared with those of the test stress. Plasticity correction term and historical strain The resulting equilibrium residuals. For example, the first residual equation can be expressed as: The second residual equation can be used to express the relationship between the lateral elastic constraints. At the stress test point After the first-order Taylor expansion, the stress components are compared with those of the test stress. Plasticity correction term and historical strain The resulting equilibrium residuals. For example, the second residual equation can be expressed as: .

[0047] S280. The yield condition of the preset concrete damage plasticity model is expanded by a first-order Taylor series at the three-dimensional test stress to obtain the third residual equation; wherein, the third residual equation is used to characterize the convergence condition of the yield function.

[0048] The third residual equation can refer to the scalar residual obtained by expanding the yield function to the first order at the test stress point and substituting the plastic correction.

[0049] It is worth noting that, in this embodiment of the invention, the yield condition can be expressed as: .in, , and It can represent effective tensile stress and effective compressive stress. According to the test results, the concrete... The value range is from 1.10 to 1.16; therefore, in this embodiment of the invention, The value can range from 0.08 to 0.12. , The typical value of concrete is... , .

[0050] In an optional implementation, the yield condition of the preset concrete damage plasticity model is subjected to a first-order Taylor expansion at the three-dimensional test stress to obtain a third residual equation, including: Step b1: Determine the plasticity correction term corresponding to the target beam element based on the flow direction and the three-dimensional test stress.

[0051] The plasticity correction term can refer to the stress change that occurs when plastic flow takes place along the flow direction, assuming the stress originates from the test stress state. For example, the plasticity correction term can be expressed as: .

[0052] Step b2: The plasticity correction term is introduced as a stress increment into the yield condition of the preset concrete damage plasticity model in the first-order Taylor expansion at the three-dimensional test stress to obtain the third residual equation.

[0053] The stress increment can refer to the stress perturbation substituted into the first-order Taylor expansion.

[0054] Specifically, in initiating coupled solution and already in three-dimensional stress testing Calculate and freeze the flow direction. Under this premise, firstly, a plasticity correction term is constructed by combining the three-dimensional elastic stiffness: Subsequently, the CDP yield function is retrieved. ,exist A first-order Taylor expansion is performed at the stress point, and the plasticity correction term is introduced as the stress increment into the first-order Taylor expansion at the three-dimensional stress test, resulting in the third residual equation: .

[0055] S290. Construct a three-dimensional residual vector based on the first residual equation, the second residual equation, and the third residual equation, and obtain the Jacobian matrix by taking the partial derivative of the three-dimensional residual vector with respect to the unknown quantity to be solved and the plastic multiplier increment.

[0056] Here, the three-dimensional residual vector can refer to a column vector formed by arranging the first, second, and third residual equations in sequence. For example, continuing the previous example, let the first residual equation be... The second residual equation is The third residual equation is For example, the three-dimensional residual vector can be represented as: .

[0057] Here, the Jacobian matrix can refer to the partial derivative matrix of the residual vector with respect to the unknown. In this embodiment of the invention, the unknown can be expressed as: , This represents the increment of the plastic multipliers. For example, consider the above residual equation system. Taking the partial derivative with respect to the unknown vector X yields the Jacobian matrix J. The Jacobian matrix contains elements corresponding to... The first line can be specifically represented as: Corresponding to The second line can be specifically represented as: Corresponding to The third line can be specifically represented as: Because, within the framework of the single-step regression algorithm, the true stress after plastic correction can be expressed as: .therefore, Finally, the elements of the third row of the Jacobian matrix can be represented as: .

[0058] S2100. Based on the Jacobian matrix and the three-dimensional residual vector, a system of linear algebraic equations is obtained, and based on the system of linear algebraic equations, the solution results of the corrected unknown quantity and the plastic multiplier increment are obtained.

[0059] Here, the system of linear algebraic equations can refer to Newtonian linearized equations generated from the combination of the Jacobian matrix and the three-dimensional residual vector. For example, in the form of linear equations... For example, the system of linear algebraic equations can be expressed as: After solving this system of linear algebraic equations, the corrected vector can be obtained: ( , , By superimposing the correction vector onto the initial value of the unknown, the updated solution for the unknown can be obtained. and plastic multiplier increment .

[0060] Specifically, when entering the coupled solution process, firstly, the pre-calculated three-dimensional test stress, flow direction, and preset transverse elastic constraint relationship are obtained. Then, the transverse constraint equation in the preset transverse elastic constraint relationship is expanded using a first-order Taylor expansion at the three-dimensional test stress, and the plasticity correction term is substituted to obtain the first and second residual equations. Simultaneously, the CDP yield function is expanded at the three-dimensional test stress to obtain the third residual equation. Further, these three equations are arranged into a three-dimensional residual vector, and partial derivatives are calculated with respect to the unknowns to construct the Jacobian matrix. Finally, a system of linear algebraic equations is constructed based on the Jacobian matrix and the three-dimensional residual vector, and solving this system yields a correction vector. This correction vector is then superimposed on the initial values ​​of the unknowns to obtain the updated solution results for the unknowns and the plasticity multiplier increment. Thus, by transforming the two problems—the plasticity return mapping and the lack of transverse degrees of freedom in the beam element (originally performed separately in the solid element CDP)—into a closed-loop solution by uniformly expanding the transverse elastic constraint equation and the CDP yield equation at the test stress point using a first-order Taylor expansion and simultaneously establishing a 3×3 residual system. This allows the transverse normal strain increment to no longer be assumed to be zero or given, but instead to be solved as an unknown along with the plasticity multiplier. This preserves the coupling of shear stress and normal stress while avoiding the drawbacks of uniaxial degradation or solid element subdivision in traditional fiber beams. Furthermore, by employing explicit construction of the Jacobian matrix instead of numerical difference, coupled with single-step back mapping to freeze the flow direction, the constitutive integral is reduced from a fully implicit nested iteration to a single-step or very few-step linear algebra solution. The computational cost at a single integration point of the beam element is close to that of an explicit algorithm, while the accuracy is equivalent to the three-dimensional CDP return mapping. This directly supports the dual goals of efficiency and accuracy in performing multiaxial constitutive modeling within the beam element framework.

[0061] S2110. Based on the transverse normal strain increment correction in the solution result, update the full three-dimensional strain tensor corresponding to the current increment step to obtain the updated three-dimensional strain tensor.

[0062] Among them, the transverse normal strain increment correction can correct the first two components of the unknown correction vector. and The final value of the transverse normal strain increment is obtained by superimposing it onto the initial value. For example, the transverse normal strain increment correction can be expressed as... and The three-dimensional strain tensor can refer to a tensor used to describe the three-dimensional strain state at the current moment of the material's integration point.

[0063] S2120. Based on the flow direction and the plastic multiplier increment, the three-dimensional test stress is plastically corrected to obtain the updated three-dimensional stress tensor.

[0064] Here, the three-dimensional stress tensor can refer to a tensor used to describe the three-dimensional stress state at the material's integration point. For example, continuing the example above, the three-dimensional stress tensor can be expressed as: .

[0065] S2130. Calculate the equivalent plastic strain increment based on the plastic multiplier increment and the flow direction, and update the equivalent tensile plastic strain and equivalent compressive plastic strain corresponding to the current increment step based on the equivalent plastic strain increment, to obtain the updated equivalent tensile plastic strain and the updated equivalent compressive plastic strain.

[0066] The equivalent plastic strain increment can refer to a scalar increment defined by the plastic multiplier and the modulus of flow direction. For example, following the above example, the equivalent plastic strain increment can be expressed as: Equivalent tensile plastic strain can refer to the cumulative equivalent plastic strain scalar value attributable to the tensile mechanism. For example, equivalent tensile plastic strain can be expressed as: Typically, if the maximum principal stress is greater than zero, the increment of the equivalent plastic strain is added to the equivalent tensile plastic strain. The equivalent compressive plastic strain can refer to the cumulative equivalent plastic strain scalar attributable to the compression mechanism. For example, the equivalent compressive plastic strain can be expressed as: Typically, if the maximum principal stress is less than zero, the equivalent plastic strain increment is added to the equivalent compressive plastic strain.

[0067] S2140. Based on the preset damage evolution equation, the updated equivalent tensile plastic strain and the updated equivalent compressive plastic strain are calculated to obtain the updated tensile damage variable and the updated compressive damage variable.

[0068] The preset damage evolution equation can refer to a pre-defined constitutive relation for calculating damage variables from equivalent plastic strain. Tensile damage variables can refer to variables used to characterize the degree of tensile stiffness degradation. For example, continuing the above example, the tensile damage variables can be expressed as: Compression damage variables can refer to variables used to characterize the degree of stiffness degradation on the compressed side. For example, continuing the example above, compression damage variables can be expressed as: .

[0069] S2150. The updated three-dimensional stress tensor, three-dimensional strain tensor, tensile damage variable, compressive damage variable, equivalent tensile plastic strain, and equivalent compressive plastic strain are used as the updated three-dimensional state variables.

[0070] Specifically, after obtaining the corrected solution results for the unknowns and the plasticity multiplier increment, the full three-dimensional strain tensor of the previous increment step is taken, and the transverse normal strain increment correction from the solution results is added to obtain the updated full three-dimensional strain tensor. Then, the plasticity correction term is subtracted from the three-dimensional test stress to obtain the updated full three-dimensional stress tensor. Next, the equivalent plastic strain increment is calculated using the plasticity multiplier increment and the flow direction, and a portion of it is accumulated to the equivalent tensile plastic strain and equivalent compressive plastic strain of the previous increment step according to the sign of the current principal stress direction, resulting in the updated equivalent tensile plastic strain and the updated equivalent compressive plastic strain. Subsequently, the preset damage evolution equation is called, substituting the updated two equivalent plastic strains respectively, to calculate the updated tensile damage variables and compressive damage variables. Finally, the six types of quantities—three-dimensional stress tensor, three-dimensional strain tensor, tensile damage variable, compressive damage variable, equivalent tensile plastic strain, and equivalent compressive plastic strain—are written back to the state array as updated three-dimensional state variables for use in extracting the target stress and initial values ​​for the next increment step. Therefore, by updating the transverse strain correction obtained from the coupled solution with the plastic multiplier and the frozen flow direction in a closed loop according to the sequence of continuum mechanics, the result is a complete three-dimensional state variable that includes full three-dimensional stress, full three-dimensional strain, equivalent plastic strain under tension and compression, and tensile and compressive damage variables. This ensures that the beam element integration point transmits a multiaxial damage plastic state that is completely isomorphic to the solid CDP between incremental steps, rather than a uniaxial degradation state like that of a fiber beam.

[0071] S2160. Based on the preset beam element degree-of-freedom mapping relationship, extract the axial normal stress component and the shear stress components in two orthogonal directions from the updated three-dimensional stress tensor, and use them as the target stress components of the target beam element.

[0072] The preset beam element degree-of-freedom mapping relationship can refer to a predefined linear correspondence used to extract or fill the stress space of the three-dimensional continuous medium with the stress space recognized by the beam element solver. The axial normal stress component can refer to the first component in the three-dimensional stress tensor. For example, the axial normal stress component can be expressed as: Shear stress components can refer to the components in the three-dimensional stress tensor corresponding to the two transverse shear degrees of freedom of the beam section. For example, shear stress components can be expressed as: and . , .

[0073] S2170. Summarize and process the target stress components and the updated three-dimensional state variables to obtain the constitutive realization result corresponding to the target beam element.

[0074] Specifically, after updating the 3D state variables, the preset beam element degree-of-freedom mapping relationship is first retrieved. Then, the axial normal stress component and the shear stress components in two orthogonal directions are taken from the updated 3D stress tensor according to the preset beam element degree-of-freedom mapping relationship as the target stress components of the target beam element. Subsequently, the target stress vector and the updated 3D state variables are aggregated and processed according to the solver subroutine interface format, assembled into the constitutive implementation result for this constitutive step, and returned to the solver main program. The main program uses the target stress as the nodal force residual and saves the state variables for the initial values ​​of the next incremental step. The material layer task for this incremental step ends, achieving zero-intrusion integration between the constitutive module and the structural solver.

[0075] The technical solution of this invention involves obtaining the strain increment corresponding to the target beam element in the current increment step and the three-dimensional state variables corresponding to the target beam element saved at the end of the previous increment step. Then, based on a preset transverse elastic constraint relationship, the strain increment is upgraded to obtain a three-dimensional strain increment tensor; wherein the three-dimensional strain increment tensor contains at least the transverse normal strain increment as an unknown quantity. Further, based on a preset three-dimensional elastic constitutive relationship, the three-dimensional strain increment tensor is calculated to obtain the three-dimensional test stress. Further, based on the three-dimensional test stress, the deviatoric stress tensor corresponding to the target beam element is determined. Based on the deviatoric stress tensor and the three-dimensional test stress, the partial derivative of the plastic potential energy function of the preset concrete damage plasticity model is obtained to obtain the plastic flow direction vector. Based on a single-step regression algorithm, the plastic flow direction vector is frozen at the three-dimensional test stress point, and the frozen plastic flow direction vector is used as the flow direction corresponding to the target beam element. The preset transverse elastic constraint relationship is expanded using a first-order Taylor series at the three-dimensional test stress to obtain the first and second residual equations. The yield condition of the preset concrete damage plasticity model is expanded using a first-order Taylor series at the three-dimensional test stress to obtain the third residual equation. A three-dimensional residual vector is constructed based on the first, second, and third residual equations. Partial derivatives of the three-dimensional residual vector with respect to the unknowns and the plastic multiplier increment are obtained to yield the Jacobian matrix. A system of linear algebraic equations is derived from the Jacobian matrix and the three-dimensional residual vector. Based on this system, the corrected solutions for the unknowns and the plastic multiplier increment are obtained. Finally, the full three-dimensional strain tensor corresponding to the current increment step is updated based on the transverse normal strain increment correction in the solution results, resulting in the updated three-dimensional strain tensor. Plastic correction is applied to the three-dimensional test stress based on the flow direction and the plastic multiplier increment, resulting in the updated three-dimensional stress tensor. The equivalent plastic strain increment is calculated based on the plastic multiplier increment and the flow direction. The equivalent tensile plastic strain and equivalent compressive plastic strain corresponding to the current increment step are updated based on this equivalent plastic strain increment, resulting in the updated equivalent tensile plastic strain and the updated equivalent compressive plastic strain. Based on the preset damage evolution equation, the updated equivalent tensile plastic strain and the updated equivalent compressive plastic strain are calculated to obtain the updated tensile damage variables and the updated compressive damage variables. The updated three-dimensional stress tensor, three-dimensional strain tensor, tensile damage variables, compressive damage variables, equivalent tensile plastic strain, and equivalent compressive plastic strain are used as the updated three-dimensional state variables. Based on the preset beam element degree-of-freedom mapping relationship, the axial normal stress component and the shear stress components in two orthogonal directions are extracted from the updated three-dimensional stress tensor as the target stress components of the target beam element. The target stress components and the updated three-dimensional state variables are summarized and processed to obtain the constitutive realization result of the target beam element.Within the material constitutive model, a physical mapping relationship between the transverse strain and transverse stress of the beam element is established by introducing the assumption of transverse elastic constraints. A single-step regression algorithm is then used to couple the yield condition of the concrete damage plasticity model with the transverse elastic constraints at the stress test point in a first-order linearized manner. This directly constructs and solves a closed system of linear algebraic equations, obtaining the corrections for transverse strain and plasticity multipliers in a single step. This solves the problem of the trade-off between computational efficiency and multiaxial accuracy faced by existing technologies in nonlinear analysis of reinforced concrete, beams, columns, and joint components. It enables the beam element to realistically reflect the multiaxial stress behavior of the three-dimensional beam element under different transverse constraints while maintaining the original strain input format. In other words, it allows the beam element to retain and characterize the stiffness degradation and damage evolution history of concrete under three-dimensional stress while maintaining the original three degrees of freedom, thus achieving the same technical effect in nonlinear analysis accuracy as solid elements.

[0076] It is worth noting that the technical solution described in the embodiments of the present invention can be integrated into a fully independent CAE software platform and a material model intelligent scheduling system based on automatic element type perception. This system encapsulates the above-mentioned improved beam element constitutive method into an independently callable material model module. Its overall architecture includes: a user parameter input module that provides a standard CDP parameter input interface; a scheduling module that automatically identifies element types and adapts to appropriate constitutive algorithms; a constitutive integration engine module that encapsulates core logic such as strain dimensionality enhancement, single-step retrospective coupled solution, and damage update; a module responsible for stress return and tangent stiffness update; and a state variable full-dimensional management module. In the intelligent scheduling system for the material model, users only need to select the model of this invention in the material property definition and input a set of standardized parameters that are completely consistent with the solid or shell element CDP and can be obtained through standard tests or specifications, such as density, elastic modulus, Poisson's ratio, expansion angle and biaxial strength ratio. The system can then automatically complete all calculations from strain dimensionality increase, multiaxial coupling solution to state update. Unlike the existing uniaxial constitutive method for fiber beams, there is no need for tedious empirical fitting and calibration of hysteresis rule parameters. This achieves the unification of constitutive theory system under multiple element types and facilitates engineering applications.

[0077] Example 3 Figure 3 This is a structural schematic diagram of a device for realizing a multiaxial concrete damage plastic constitutive model suitable for beam elements, provided in Embodiment 3 of the present invention. Figure 3 As shown, the device includes: a data acquisition module 310, a strain dimensionality enhancement module 320, a test stress calculation module 330, a coupled solution module 340, and a result generation module 350; The data acquisition module 310 is used to acquire the strain increment corresponding to the target beam element in the current increment step and the three-dimensional state variable corresponding to the target beam element saved at the end of the previous increment step. The strain dimension-upgrading module 320 is used to perform dimension-upgrading processing on the strain increment based on a preset transverse elastic constraint relationship to obtain a three-dimensional strain increment tensor; wherein, the three-dimensional strain increment tensor contains at least the transverse normal strain increment as an unknown quantity to be determined. The test stress calculation module 330 is used to calculate the three-dimensional strain increment tensor based on a preset three-dimensional elastic constitutive relation to obtain the three-dimensional test stress; The coupled solution module 340 is used to determine the flow direction of the stress corresponding to the target beam element based on the plastic potential energy function of the preset concrete damage plasticity model, and to couple the yield condition of the preset concrete damage plasticity model with the preset transverse elastic constraint relationship at the three-dimensional test stress and solve it through a single-step regression algorithm to obtain the solution result of the unknown quantity to be solved and the plastic multiplier increment. The result generation module 350 is used to update the three-dimensional state variables of the target beam element based on the solution results, the flow direction and the plastic multiplier increment, and extract the target stress component of the target beam element from the updated three-dimensional state variables to obtain the constitutive realization result of the target beam element.

[0078] The technical solution of this invention involves obtaining the strain increment corresponding to the target beam element in the current increment step and the three-dimensional state variables corresponding to the target beam element saved at the end of the previous increment step. Then, based on a preset transverse elastic constraint relationship, the strain increment is upgraded to obtain a three-dimensional strain increment tensor; wherein the three-dimensional strain increment tensor contains at least the transverse normal strain increment as an unknown quantity. Further, based on a preset three-dimensional elastic constitutive relationship, the three-dimensional strain increment tensor is calculated to obtain the three-dimensional test stress. Further, based on the plastic potential energy function of a preset concrete damage plasticity model, the flow direction of the stress corresponding to the target beam element is determined. The yield condition of the preset concrete damage plasticity model is coupled with the preset transverse elastic constraint relationship at the three-dimensional test stress and solved using a single-step regression algorithm to obtain the solution result of the unknown quantity and the plastic multiplier increment. Finally, based on the solution result, flow direction, and plastic multiplier increment, the three-dimensional state variables of the target beam element are updated, and the target stress component of the target beam element is extracted from the updated three-dimensional state variables to obtain the constitutive realization result corresponding to the target beam element. Within the material constitutive model, a physical mapping relationship between the transverse strain and transverse stress of the beam element is established by introducing the assumption of transverse elastic constraints. A single-step regression algorithm is then used to couple the yield condition of the concrete damage plasticity model with the transverse elastic constraints at the stress test point in a first-order linearized manner. This directly constructs and solves a closed system of linear algebraic equations, obtaining the corrections for transverse strain and plasticity multipliers in a single step. This solves the problem of the trade-off between computational efficiency and multiaxial accuracy faced by existing technologies in nonlinear analysis of reinforced concrete, beams, columns, and joint components. It enables the beam element to realistically reflect the multiaxial stress behavior of the three-dimensional beam element under different transverse constraints while maintaining the original strain input format. In other words, it allows the beam element to retain and characterize the stiffness degradation and damage evolution history of concrete under three-dimensional stress while maintaining the original three degrees of freedom, thus achieving the same technical effect in nonlinear analysis accuracy as solid elements.

[0079] Optionally, the coupled solution module 340 can be specifically used to: perform a first-order Taylor expansion of the preset transverse elastic constraint relationship at the three-dimensional test stress to obtain a first residual equation and a second residual equation; wherein the first residual equation and the second residual equation are used to characterize the stress and strain constraint balance in two transverse directions, respectively; perform a first-order Taylor expansion of the yield condition of the preset concrete damage plasticity model at the three-dimensional test stress to obtain a third residual equation; wherein the third residual equation is used to characterize the convergence condition of the yield function; construct a three-dimensional residual vector based on the first residual equation, the second residual equation, and the third residual equation, and obtain a Jacobian matrix by taking the partial derivative of the three-dimensional residual vector with respect to the unknown quantity and the plasticity multiplier increment; obtain a system of linear algebraic equations based on the Jacobian matrix and the three-dimensional residual vector, and obtain the solution result of the corrected unknown quantity and the plasticity multiplier increment based on the system of linear algebraic equations.

[0080] Optionally, the coupled solution module 340 can be used to: determine the plasticity correction term corresponding to the target beam element based on the flow direction and the three-dimensional test stress; introduce the plasticity correction term as a stress increment into the first-order Taylor expansion of the yield condition of the preset concrete damage plasticity model at the three-dimensional test stress to obtain the third residual equation.

[0081] Optionally, the coupled solution module 340 can be used to: determine the deviatoric stress tensor corresponding to the target beam element based on the three-dimensional test stress; obtain the plastic flow direction vector by taking the partial derivative of the plastic potential energy function of the preset concrete damage plasticity model based on the deviatoric stress tensor and the three-dimensional test stress; freeze the plastic flow direction vector at the three-dimensional test stress point based on the single-step regression algorithm, and use the frozen plastic flow direction vector as the flow direction of the stress corresponding to the target beam element.

[0082] Optionally, the result generation module 350 can be specifically used to: update the full three-dimensional strain tensor corresponding to the current increment step based on the transverse normal strain increment correction in the solution result, to obtain the updated three-dimensional strain tensor; perform plastic correction on the three-dimensional test stress based on the flow direction and the plastic multiplier increment, to obtain the updated three-dimensional stress tensor; calculate the equivalent plastic strain increment based on the plastic multiplier increment and the flow direction, and update the equivalent tensile plastic strain and equivalent compressive plastic strain corresponding to the current increment step based on the equivalent plastic strain increment, to obtain the updated equivalent tensile plastic strain and the updated equivalent compressive plastic strain; calculate the updated equivalent tensile plastic strain and the updated equivalent compressive plastic strain based on the preset damage evolution equation, to obtain the updated tensile damage variable and the updated compressive damage variable; and use the updated three-dimensional stress tensor, three-dimensional strain tensor, tensile damage variable, compressive damage variable, equivalent tensile plastic strain, and equivalent compressive plastic strain as the updated three-dimensional state variables.

[0083] Optionally, the result generation module 350 can be used to: extract the axial normal stress component and the shear stress components in two orthogonal directions from the updated three-dimensional stress tensor based on the preset beam element degree-of-freedom mapping relationship, as the target stress component of the target beam element; summarize and process the target stress component and the updated three-dimensional state variables to obtain the constitutive realization result corresponding to the target beam element.

[0084] Optionally, the device for realizing a multiaxial concrete damage plastic constitutive model for beam elements may further include: a dimension reduction projection module, used to: after extracting the target stress component of the target beam element from the updated three-dimensional state variables and obtaining the constitutive realization result corresponding to the target beam element, determine the three-dimensional consistent tangent stiffness matrix corresponding to the target beam element based on the plastic multiplier increment and the flow direction; project the three-dimensional consistent tangent stiffness matrix onto the stress and strain space of the beam element based on a preset beam element degree of freedom mapping relationship to obtain the three-dimensional beam element tangent stiffness matrix, and return the three-dimensional beam element tangent stiffness matrix.

[0085] The apparatus for implementing a multiaxial concrete damage plastic constitutive model for beam elements provided in the embodiments of the present invention can execute the method for implementing a multiaxial concrete damage plastic constitutive model for beam elements provided in any embodiment of the present invention, and has the corresponding functional modules and beneficial effects of the method.

[0086] Example 4 Figure 4A schematic diagram of an electronic device 410 that can be used to implement embodiments of the present invention is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices (e.g., helmets, glasses, watches, etc.), and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the invention described and / or claimed herein.

[0087] like Figure 4 As shown, the electronic device 410 includes at least one processor 420 and a memory, such as a read-only memory (ROM) 430 or a random access memory (RAM) 440, communicatively connected to the at least one processor 420. The memory stores computer programs executable by the at least one processor. The processor 420 can perform various appropriate actions and processes based on the computer program stored in the ROM 430 or loaded into the RAM 440 from storage unit 490. The RAM 440 may also store various programs and data required for the operation of the electronic device 410. The processor 420, ROM 430, and RAM 440 are interconnected via a bus 450. An input / output (I / O) interface 460 is also connected to the bus 450.

[0088] Multiple components in electronic device 410 are connected to I / O interface 460, including: input unit 470, such as keyboard, mouse, etc.; output unit 480, such as various types of monitors, speakers, etc.; storage unit 490, such as disk, optical disk, etc.; and communication unit 4100, such as network card, modem, wireless transceiver, etc. Communication unit 4100 allows electronic device 410 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0089] Processor 420 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of processor 420 include, but are not limited to, central processing unit (CPU), graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various processors running machine learning model algorithms, digital signal processors (DSPs), and any suitable processor, controller, microcontroller, etc. Processor 420 performs the various methods and processes described above, such as the implementation method of multiaxial concrete damage plastic constitutive model applicable to beam elements.

[0090] The method includes: Obtain the strain increment corresponding to the target beam element in the current increment step and the three-dimensional state variables corresponding to the target beam element saved at the end of the previous increment step; The strain increment is subjected to dimensionality-upgrading processing based on a preset transverse elastic constraint relationship to obtain a three-dimensional strain increment tensor; wherein, the three-dimensional strain increment tensor contains at least the transverse normal strain increment as an unknown quantity to be determined. The three-dimensional strain increment tensor is calculated based on a preset three-dimensional elastic constitutive relation to obtain the three-dimensional test stress; The flow direction of the stress corresponding to the target beam element is determined by the plastic potential energy function based on the preset concrete damage plasticity model. The yield condition of the preset concrete damage plasticity model and the preset transverse elastic constraint relationship are coupled at the three-dimensional test stress and solved by the single-step regression algorithm to obtain the solution result of the unknown quantity to be solved and the plastic multiplier increment. Based on the solution results, the flow direction, and the plastic multiplier increment, the three-dimensional state variables of the target beam element are updated, and the target stress component of the target beam element is extracted from the updated three-dimensional state variables to obtain the constitutive realization result of the target beam element.

[0091] In some embodiments, the method for implementing a multiaxial concrete damage plastic constitutive model for beam elements can be implemented as a computer program tangibly contained in a computer-readable storage medium, such as storage unit 490. In some embodiments, part or all of the computer program can be loaded and / or installed on electronic device 410 via ROM 430 and / or communication unit 4100. When the computer program is loaded into RAM 440 and executed by processor 420, one or more steps of the method for implementing a multiaxial concrete damage plastic constitutive model for beam elements described above can be performed. Alternatively, in other embodiments, processor 420 can be configured to execute the method for implementing a multiaxial concrete damage plastic constitutive model for beam elements by any other suitable means (e.g., by means of firmware).

[0092] Various embodiments of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SoCs), payload-programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0093] Computer programs used to implement the methods of the present invention may be written in any combination of one or more programming languages. These computer programs may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the processor, the computer programs cause the functions / operations specified in the flowcharts and / or block diagrams to be performed. The computer programs may be executed entirely on a machine, partially on a machine, or as a standalone software package, partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0094] In the context of this invention, a computer-readable storage medium can be a tangible medium that may contain or store a computer program for use by or in conjunction with an instruction execution system, apparatus, or device. A computer-readable storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination thereof. Alternatively, a computer-readable storage medium may be a machine-readable signal medium. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0095] To provide interaction with a user, the systems and techniques described herein can be implemented on an electronic device having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the electronic device. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0096] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as data servers), or middleware components (e.g., application servers), or frontend components (e.g., user computers with graphical user interfaces or web browsers through which users can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., communication networks). Examples of communication networks include local area networks (LANs), wide area networks (WANs), blockchain networks, and the Internet.

[0097] A computing system can include clients and servers. Clients and servers are generally located far apart and typically interact through a communication network. The client-server relationship is created by computer programs running on the respective computers and having a client-server relationship with each other. The server can be a cloud server, also known as a cloud computing server or cloud host, which is a hosting product within the cloud computing service system to address the shortcomings of traditional physical hosts and VPS services, such as high management difficulty and weak business scalability.

[0098] It should be understood that the various forms of processes shown above can be used, with steps reordered, added, or deleted. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this invention can be achieved, and this is not limited herein.

[0099] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for implementing a multiaxial concrete damage plastic constitutive model suitable for beam elements, characterized in that, The method is applied to the nonlinear finite element analysis of concrete beam-column members in structural engineering numerical simulation. The method includes: Obtain the strain increment corresponding to the target beam element in the current increment step and the three-dimensional state variables corresponding to the target beam element saved at the end of the previous increment step; The strain increment is subjected to dimensionality-upgrading processing based on a preset transverse elastic constraint relationship to obtain a three-dimensional strain increment tensor; wherein, the three-dimensional strain increment tensor contains at least the transverse normal strain increment as an unknown quantity to be determined. The three-dimensional strain increment tensor is calculated based on a preset three-dimensional elastic constitutive relation to obtain the three-dimensional test stress; The flow direction of the stress corresponding to the target beam element is determined by the plastic potential energy function based on the preset concrete damage plasticity model. The yield condition of the preset concrete damage plasticity model and the preset transverse elastic constraint relationship are coupled at the three-dimensional test stress and solved by the single-step regression algorithm to obtain the solution result of the unknown quantity to be solved and the plastic multiplier increment. Based on the solution results, the flow direction, and the plastic multiplier increment, the three-dimensional state variables of the target beam element are updated, and the target stress component of the target beam element is extracted from the updated three-dimensional state variables to obtain the constitutive realization result of the target beam element.

2. The method according to claim 1, characterized in that, The process of coupling the yield condition of the preset concrete damage plasticity model with the preset transverse elastic constraint relationship at the three-dimensional test stress and solving it using a single-step regression algorithm to obtain the solution results of the unknown quantities and the plasticity multiplier increment includes: The preset transverse elastic constraint relationship is expanded by a first-order Taylor series at the three-dimensional test stress to obtain the first residual equation and the second residual equation; wherein, the first residual equation and the second residual equation are used to characterize the stress and strain constraint balance in the two transverse directions, respectively. The yield condition of the preset concrete damage plasticity model is expanded by a first-order Taylor series at the three-dimensional test stress to obtain the third residual equation; wherein, the third residual equation is used to characterize the convergence condition of the yield function. A three-dimensional residual vector is constructed based on the first residual equation, the second residual equation, and the third residual equation. The Jacobian matrix is ​​obtained by taking the partial derivative of the three-dimensional residual vector with respect to the unknown quantity and the plastic multiplier increment. Based on the Jacobian matrix and the three-dimensional residual vector, a system of linear algebraic equations is obtained, and based on the system of linear algebraic equations, the solution results of the corrected unknown quantity and the plastic multiplier increment are obtained.

3. The method according to claim 2, characterized in that, The yield condition of the preset concrete damage plasticity model is subjected to a first-order Taylor expansion at the three-dimensional test stress to obtain the third residual equation, including: The plasticity correction term corresponding to the target beam element is determined based on the flow direction and the three-dimensional test stress. The plasticity correction term is introduced as a stress increment into the yield condition of the preset concrete damage plasticity model in the first-order Taylor expansion at the three-dimensional test stress, resulting in the third residual equation.

4. The method according to claim 1, characterized in that, The determination of the flow direction of the stress corresponding to the target beam element by the plastic potential energy function based on the preset concrete damage plasticity model includes: The deviatoric stress tensor corresponding to the target beam element is determined based on the three-dimensional test stress. The plastic flow direction vector is obtained by taking the partial derivative of the plastic potential energy function of the pre-set concrete damage plasticity model based on the deviatoric stress tensor and the three-dimensional test stress. The plastic flow direction vector is frozen at the three-dimensional stress test point based on the single-step reflection algorithm, and the frozen plastic flow direction vector is used as the flow direction of the corresponding stress of the target beam element.

5. The method according to claim 1, characterized in that, The process of updating the three-dimensional state variables of the target beam element based on the solution results, the flow direction, and the plastic multiplier increment includes: Based on the transverse normal strain increment correction in the solution result, update the full three-dimensional strain tensor corresponding to the current increment step to obtain the updated three-dimensional strain tensor; The three-dimensional test stress is plastically corrected based on the flow direction and the plastic multiplier increment to obtain the updated three-dimensional stress tensor. The equivalent plastic strain increment is calculated based on the plastic multiplier increment and the flow direction, and the equivalent tensile plastic strain and equivalent compressive plastic strain corresponding to the current increment step are updated based on the equivalent plastic strain increment to obtain the updated equivalent tensile plastic strain and the updated equivalent compressive plastic strain. The updated equivalent tensile plastic strain and the updated equivalent compressive plastic strain are calculated based on the preset damage evolution equation to obtain the updated tensile damage variable and the updated compressive damage variable. The updated three-dimensional stress tensor, three-dimensional strain tensor, tensile damage variable, compressive damage variable, equivalent tensile plastic strain, and equivalent compressive plastic strain are used as the updated three-dimensional state variables.

6. The method according to claim 1, characterized in that, The step of extracting the target stress component of the target beam element from the updated three-dimensional state variables to obtain the constitutive realization result corresponding to the target beam element includes: Based on the preset beam element degree of freedom mapping relationship, the axial normal stress component and the shear stress components in two orthogonal directions are extracted from the updated three-dimensional stress tensor and used as the target stress components of the target beam element. By summarizing and processing the target stress components and the updated three-dimensional state variables, the constitutive realization result corresponding to the target beam element is obtained.

7. The method according to claim 1, characterized in that, After extracting the target stress components of the target beam element from the updated three-dimensional state variables to obtain the constitutive realization result corresponding to the target beam element, the method further includes: The three-dimensional uniform tangent stiffness matrix corresponding to the target beam element is determined based on the plastic multiplier increment and the flow direction. Based on the preset beam element degree-of-freedom mapping relationship, the three-dimensional consistent tangent stiffness matrix is ​​projected onto the stress and strain space of the beam element to obtain the three-dimensional beam element tangent stiffness matrix, and the three-dimensional beam element tangent stiffness matrix is ​​returned.

8. A device for realizing a multiaxial concrete damage plastic constitutive model suitable for beam elements, characterized in that, The device is used in the nonlinear finite element analysis of concrete beam-column members in structural engineering numerical simulation. The device includes: The data acquisition module is used to acquire the strain increment corresponding to the target beam element in the current increment step and the three-dimensional state variables corresponding to the target beam element saved at the end of the previous increment step. The strain dimension-up module is used to perform dimension-up processing on the strain increment based on a preset transverse elastic constraint relationship to obtain a three-dimensional strain increment tensor; wherein, the three-dimensional strain increment tensor contains at least the transverse normal strain increment as an unknown quantity to be determined. The test stress calculation module is used to calculate the three-dimensional strain increment tensor based on a preset three-dimensional elastic constitutive relation to obtain the three-dimensional test stress. The coupled solution module is used to determine the flow direction of the stress corresponding to the target beam element based on the plastic potential energy function of the preset concrete damage plasticity model. It couples the yield condition of the preset concrete damage plasticity model with the preset transverse elastic constraint relationship at the three-dimensional test stress and solves it through a single-step regression algorithm to obtain the solution results of the unknown quantity to be solved and the plastic multiplier increment. The result generation module is used to update the three-dimensional state variables of the target beam element based on the solution results, the flow direction, and the plastic multiplier increment, and to extract the target stress component of the target beam element from the updated three-dimensional state variables to obtain the constitutive realization result of the target beam element.

9. An electronic device, characterized in that, The electronic device includes: At least one processor; and A memory communicatively connected to the at least one processor; wherein, The memory stores a computer program that can be executed by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to perform the method for implementing a multiaxial concrete damage plastic constitutive model for beam elements as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that cause a processor to execute the method for implementing the multiaxial concrete damage plastic constitutive model applicable to beam elements as described in any one of claims 1-7.

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