Concrete elastic-plastic damage constitutive model construction method and system

Abstract

The invention provides a concrete elastic-plastic damage constitutive model construction method and system, belongs to the field of computers, and solves the problems that in the prior art, an integral or gradient enhanced regularization method is adopted to establish a non-local constitutive model, but the two methods require relatively fine finite element grid division, and numerical value implementation is very difficult. Comprising the following steps: 1, determining a damage variable, nominal stress, effective stress and an elastic-plastic damage stress-strain relationship, and decomposing the effective stress according to tension and compression characteristics; 2, in the effective stress space, a concrete elastic-plastic damage constitutive model is established; and step 3, based on an energy regularization method, determining a tensile damage variable, a compression damage variable and a corresponding stress-strain relationship, and in combination with a plastic loading and unloading rule, constructing a concrete elastic-plastic damage constitutive model based on energy regularization. The invention provides the construction method of the PC box girder concrete elastic-plastic damage constitutive model under the non-uniform constraint, and the application range is wide.

Description

Technical Field

[0001] The present invention belongs to the field of computer technology, and in particular relates to a method and system for constructing an elastoplastic damage constitutive model of concrete. Background Art

[0002] In engineering practice, numerous PC box girder bridges have experienced varying degrees of cracking during construction and service, indicating that some concrete has entered a nonlinear stress stage. Existing research has shown that the nonlinear mechanical behavior of concrete under load is caused by irreversible deformation and stiffness degradation. Irreversible deformation is caused by plastic slip within the material, while stiffness degradation is caused by damage such as the growth, convergence, and interconnection of microcracks within the material, as well as the collapse of microvoids. Therefore, a reasonable constitutive model for concrete should be able to account for both plastic deformation and damage mechanisms. Elastoplastic damage models based on continuum plasticity and damage mechanics are particularly suitable for this purpose. They can describe key characteristics of concrete during nonlinear deformation, such as loading history and loading path dependence, strain softening, stiffness degradation, and irreversible deformation. Furthermore, these models account for certain mesoscopic mechanisms and are relatively easy to implement numerically. Therefore, compared to other constitutive models for concrete, elastoplastic damage models offer significant advantages both theoretically and practically.

[0003] The stress-strain relationship of concrete under uniaxial loading exhibits a softening phase, leading to strain localization. The ill-posed initial-boundary value problem caused by strain localization leads to ill-posed numerical analysis results, making the corresponding finite element analysis results dependent on the mesh size, i.e., mesh sensitivity. Although some scholars have adopted integral or gradient-enhanced regularization methods to establish nonlocalized constitutive models to address this issue, both methods require relatively fine finite element meshing and are difficult to implement numerically. Therefore, they are not suitable for the analysis of the nonlinear mechanical behavior of large concrete structures such as PC box girders. Summary of the Invention

[0004] In view of this, the present invention provides a method and system for constructing an elastoplastic damage constitutive model of concrete to solve the problem that in the prior art, a non-localized constitutive model is established by using an integral or gradient enhancement regularization method to solve the above-mentioned problem, but both methods require relatively fine finite element mesh division and are very difficult to implement numerically.

[0005] The technical solution adopted in the present invention is as follows:

[0006] A method for constructing an elastic-plastic damage constitutive model of concrete comprises the following steps:

[0007] Step 1: Based on the classical elastic-plastic principle and damage mechanics theory, combined with the damage and plastic behavior characteristics of concrete in PC box girders, the damage variable, nominal stress and effective stress, and elastic-plastic damage stress-strain relationship are determined, and the effective stress is decomposed according to the tension and compression characteristics;

[0008] Step 1.1: Determine the damage variable. In continuum damage mechanics, the micro-defect state inside concrete can be described by the damage variable d. Assuming that the damage is uniformly distributed in all directions, the concrete damage variable can be expressed as follows:

[0009]

[0010] Where: In continuum damage mechanics, d is the damage variable, which is used to describe the micro-defect state inside the concrete; A is the cross-sectional area of ​​the damaged configuration; A D is the damaged area of ​​the damaged configuration; is the cross-sectional area of ​​the lossless configuration;

[0011] Step 1.2, determine the nominal stress and effective stress;

[0012] Nominal stress:

[0013] Effective stress:

[0014] Where: T is the uniaxial pressure; σ is the nominal stress; is the effective stress;

[0015] The relationship between effective stress and nominal stress is:

[0016]

[0017] For the three-dimensional stress state, the fourth-order damage tensor D is also needed to describe it:

[0018]

[0019] M=ID

[0020] Where: M is the fourth-order damage influence tensor; D is the fourth-order damage tensor; I is the fourth-order unit tensor;

[0021] Step 1.3: Determine the elastic-plastic damage stress-strain relationship. Based on the principle of strain additive splitting, the elastic-plastic damage model divides the total strain into recoverable elastic strain and irrecoverable plastic strain:

[0022] ε=ε e +ε p

[0023] Where: ε is the total strain tensor; ε eis the elastic strain tensor; ε p is the plastic strain tensor;

[0024] According to the generalized Hooke's law, the effective stress-strain relationship of concrete is:

[0025]

[0026] The nominal stress-strain relationship of the concrete elastic-plastic damage model is:

[0027] σ=E:(ε-ε p )

[0028] Where: E0 is the undamaged fourth-order elastic stiffness tensor; E is the damaged fourth-order elastic stiffness tensor;

[0029] Based on the equivalence assumption, the damage variable can be introduced into the nominal stress-strain constitutive relation:

[0030]

[0031] Where: E0 is the undamaged elastic modulus of concrete material; ν is the Poisson's ratio of concrete material; Q is the shear modulus of concrete material; K is the bulk modulus of concrete material; δ ik , δ jl , δ ij , δ kl are all identity matrices;

[0032] According to the strain equivalence assumption, we can further obtain:

[0033] The relationship between the damaged elastic stiffness tensor and the undamaged elastic stiffness tensor is:

[0034] E=(ID):E0

[0035] Where: E is the damaged fourth-order elastic stiffness tensor; E0 is the undamaged elastic stiffness tensor; D is the fourth-order damage tensor; I is the fourth-order unit tensor;

[0036] The nominal stress-strain relationship of the concrete elastic-plastic damage model is:

[0037] σ=(ID):E0:(ε-ε p )

[0038] Where: σ is the nominal stress; E0 is the undamaged elastic stiffness tensor; D is the fourth-order damage tensor; I is the fourth-order unit tensor; ε is the total strain tensor; ε p is the plastic strain tensor;

[0039] Step 1.4: Based on the different damage characteristics of concrete under tension and compression, the effective stress can be decomposed into:

[0040]

[0041] Where: is the positive effective stress tensor of concrete tensile properties; is the negative effective stress tensor of the compressive properties of concrete;

[0042] After the effective stress is decomposed into positive and negative, the relationship between the nominal stress tensor and the positive and negative effective stress tensors is:

[0043]

[0044] Where: d + is the tensile damage variable, ranging from 0 (no damage) to 1 (complete damage); d - is the shear damage variable, ranging from 0 (no damage) to 1 (complete damage);

[0045] The fourth-order damage tensor D is:

[0046] D=d + P + +d - P -

[0047] Where: P + is the positive projection operator of effective stress; P - is the negative projection operator of effective stress;

[0048] Step 2: In the effective stress space, establish the elastic-plastic damage constitutive model of concrete by determining the plastic yield criterion, plastic hardening law, plastic flow law, and plastic loading and unloading law;

[0049] Step 2.1, determine the plastic yield criterion; use the Lubliner-MWFC yield criterion, and the tensile meridian and compression meridian of the MWFC are:

[0050]

[0051] Where: ρ t is the equivalent stress of the stretching meridian; ρ c is the equivalent stress of the compression meridian; f c 、k t 、k 2c is the concrete strength value; m w , e, and ξ are all model parameters;

[0052] In the effective stress space, after considering the evolution of the concrete yield surface, the original Lubliner-Lee yield criterion is:

[0053]

[0054] Where: and is the hardening function; (i=t or c) contains and is the tensile hardening parameter; is the compression hardening parameter; α is the model parameter; is the first invariant; is the second invariant; represents the maximum value among the principal stresses;

[0055] Step 2.2: Determine the plastic hardening law. Based on the Lubliner-Oller failure criterion, the original uniaxial compression hardening law can be extended to the concrete in the PC box girder with non-uniform restraint:

[0056]

[0057] Where: is the plastic hardening function; f is the uniaxial compressive strength of concrete; α and γ are model parameters; is the equivalent confining pressure of concrete under non-uniform confinement; is the first invariant; is the second invariant; is the equivalent stress of concrete; is the equivalent plastic strain of concrete;

[0058] For triaxial compression, we further have:

[0059]

[0060] Where: is the concrete stress under uniaxial compression;

[0061] Equivalent confining pressure of concrete under non-uniform confinement The following formula can be used for calculation:

[0062]

[0063] Where: f l is the original confining pressure; d c is the damage coefficient; f c is the uniaxial compressive strength of concrete; σ2, σ3 are stresses in different directions;

[0064] Step 2.3: Determine the plastic flow rule; in the effective stress space, the non-associative flow rule is:

[0065]

[0066] Where: is the plastic strain increment; dλ is a non-negative proportional coefficient, indicating the magnitude of the plastic strain; G is the plastic potential function; is the component of the stress tensor, which represents the stress state inside the material;

[0067] According to the non-orthogonal flow law, the plastic potential function G is:

[0068]

[0069] Where: ψ is the expansion angle of the concrete yield surface during the strengthening process; m is the eccentricity of the concrete plastic potential function, which is set to m = 0.1; ψ is the expansion angle of concrete, which ranges from 13° to 56°; f t is the concrete strength value;

[0070] Step 2.4: Determine the plastic loading and unloading rules:

[0071]

[0072] Where: is the plastic yield function, which is used to determine whether the material is in a plastic state; when F<0, the material is in the elastic stage; when F=0, the material begins to enter the plastic stage; is a non-negative proportional coefficient, which indicates the magnitude of plastic strain; is a complementary condition, ensuring the plasticity multiplier and yield function F, at least one of them is zero;

[0073] Step 3: Based on the energy regularization method, determine the tensile damage variable, compressive damage variable and the corresponding stress-strain relationship, and combine the plastic loading and unloading law to construct the concrete elastic-plastic damage constitutive model based on energy regularization. Specifically including:

[0074] Based on the local softening assumption, that is, assuming that the deformation of concrete is uniform before reaching the peak stress, and the deformation is localized after reaching the peak stress, the model is:

[0075]

[0076] Where: τ represents time; is the tensile damage loading function at the current moment n; Loading function for compression damage at the current moment n; is the axial tensile strain at the current moment n; is the axial compressive strain at the current moment n; is the axial damage driving variable at the current moment n;

[0077] Based on energy regularization, the tensile damage variable is:

[0078]

[0079] Where: d + is the tensile damage variable; a t 、b t are model parameters; is the cracking strain;

[0080] The relationship between tensile stress and cracking strain is:

[0081]

[0082] Where: σ t is the tensile stress; f t0 is the initial tensile strength of concrete; a t 、b t are model parameters; is the tensile cracking strain;

[0083] where a t 、b t for:

[0084]

[0085] Where: f tm is the tensile strength of concrete, which indicates the ultimate strength of the material under tension; f t0 is the initial tensile strength of concrete; l eq is the equivalent stress of concrete; G F is the fracture energy of the material;

[0086] Based on energy regularization, the compressive damage variable is:

[0087]

[0088] Where: d - is the compression damage variable; a c 、b c are model parameters; is the compressive cracking strain;

[0089] The relationship between compressive stress and cracking strain is:

[0090]

[0091] Where: σ c is the compressive stress; f c0 is the initial compressive strength of concrete; a c 、b c are model parameters; is the compressive cracking strain;

[0092] where a c 、b c for:

[0093]

[0094] Where: f cm is the compressive strength of concrete, which indicates the ultimate strength of the material under compression; f c0 is the initial compressive strength of concrete; l eq is the equivalent stress of concrete; G ch is the compression fracture energy dissipated per unit area of ​​concrete material;

[0095] According to the plastic loading and unloading law, combined with the damage variables and stress-strain relationship obtained by the energy regularization method, the loading and unloading process of non-uniform concrete is obtained:

[0096]

[0097] Where: is the tensile damage loading function at the current moment n; Loading function for compression damage at the current moment n; is the axial damage driving variable at the current moment n; when hour, and Indicates that the material is in an elastic unloading state and no new damage evolution occurs; when hour, and It indicates that the material is in the damage loading stage and new damage evolution occurs.

[0098] A system for constructing an elastic-plastic damage constitutive model of concrete, comprising:

[0099] Decomposition module: Based on the classical elastic-plastic principle and damage mechanics theory, combined with the damage and plastic behavior characteristics of concrete in PC box girders, the damage variable, nominal stress and effective stress, elastic-plastic damage stress-strain relationship are determined, and the effective stress is decomposed according to the tension and compression characteristics;

[0100] Concrete elastic-plastic damage constitutive model construction module: In the effective stress space, the concrete elastic-plastic damage constitutive model is established by determining the plastic yield criterion, plastic hardening law, plastic flow law, and plastic loading and unloading law;

[0101] Energy-regularized concrete elastic-plastic damage constitutive model construction module: Based on the energy regularization method, the tensile damage variables, compressive damage variables and the corresponding stress-strain relationship are determined. Combined with the plastic loading and unloading rules, an energy-regularized concrete elastic-plastic damage constitutive model is constructed.

[0102] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0103] 1. The present invention proposes a method for constructing an elastic-plastic damage constitutive model of PC box girder concrete under non-uniform constraints. The method is highly innovative and has a wide range of applications. The present invention combines loading and unloading rules with energy regularization for the first time, and can perform nonlinear mechanical behavior analysis on large concrete such as PC box girders, thus solving the grid sensitivity problem of the elastic-plastic damage constitutive model. The method is simple to implement and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0104] The present invention will now be described by way of example with reference to the accompanying drawings, in which:

[0105] Figure 1 is an overall flow chart of the method according to an embodiment of the present invention;

[0106] Figure 2 is the tensile damage evolution of the concrete constitutive model based on energy regularization, where a is the stress-strain relationship of concrete under uniaxial tension, and b is the total energy dissipated due to tensile damage;

[0107] Figure 3 is the compressive damage evolution of the concrete constitutive model based on energy regularization, where a is the stress-strain relationship of concrete under uniaxial compression, and b is the total energy dissipated due to compressive damage. DETAILED DESCRIPTION

[0108] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0109] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort are also within the scope of protection of the present invention.

[0110] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments of the present invention can be combined with each other.

[0111] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0112] In the present invention, unless otherwise expressly specified or limited, a first feature being "above" or "below" a second feature may include the first and second features being in direct contact, or may include the first and second features being in contact not directly but through another feature between them. Furthermore, a first feature being "above," "above," and "above" a second feature may include the first feature being directly above or obliquely above the second feature, or may simply mean that the first feature is higher in level than the second feature. A first feature being "below," "below," and "below" a second feature may include the first feature being directly below or obliquely below the second feature, or may simply mean that the first feature is lower in level than the second feature.

[0113] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments of the present invention can be combined with each other.

[0114] Example 1

[0115] The present invention discloses a method for constructing an elastic-plastic damage constitutive model of concrete, comprising the following steps:

[0116] Step 1: Based on the classical elastic-plastic principle and damage mechanics theory, combined with the damage and plastic behavior characteristics of concrete in PC box beams:

[0117] Step 1.1: Determine the damage variable. In continuum damage mechanics, the micro-defect state inside concrete can be described by the damage variable d. Assuming that the damage is uniformly distributed in all directions, the concrete damage variable can be expressed as follows:

[0118]

[0119] Where: In continuum damage mechanics, d is the damage variable, which is used to describe the micro-defect state inside the concrete; A is the cross-sectional area of ​​the damaged configuration; A D is the damaged area of ​​the damaged configuration; is the cross-sectional area of ​​the lossless configuration;

[0120] Step 1.2, determine the nominal stress and effective stress;

[0121] Nominal stress:

[0122] Effective stress:

[0123] Where: T is the uniaxial pressure;

[0124] The relationship between effective stress and nominal stress is:

[0125]

[0126] For the three-dimensional stress state, the fourth-order damage tensor D is also needed to describe it:

[0127]

[0128] M=ID

[0129] Where: M is the fourth-order damage influence tensor; D is the fourth-order damage tensor; I is the fourth-order unit tensor;

[0130] Step 1.3: Determine the elastic-plastic damage stress-strain relationship. Based on the principle of strain additive splitting, the elastic-plastic damage model divides the total strain into recoverable elastic strain and irrecoverable plastic strain:

[0131] ε=ε e +ε p

[0132] Where: ε is the total strain tensor; ε e is the elastic strain tensor; ε p is the plastic strain tensor;

[0133] According to the generalized Hooke's law, the effective stress-strain relationship of concrete is:

[0134]

[0135] The nominal stress-strain relationship of the concrete elastic-plastic damage model is:

[0136] σ=E:(ε-ε p )

[0137] Where: E0 is the undamaged fourth-order elastic stiffness tensor; E is the damaged fourth-order elastic stiffness tensor;

[0138] Based on the equivalence assumption, the damage variable can be introduced into the nominal stress-strain constitutive relation:

[0139]

[0140] Where: E0 is the undamaged elastic modulus of concrete material; ν is the Poisson's ratio of concrete material;

[0141] According to the strain equivalence assumption, we can further obtain:

[0142] The relationship between the damaged elastic stiffness tensor and the undamaged elastic stiffness tensor is:

[0143] E=(ID):E0

[0144] The nominal stress-strain relationship of the concrete elastic-plastic damage model is:

[0145] σ=(ID):E0:(ε-εp )

[0146] Step 1.4: Based on the different damage characteristics of concrete under tension and compression, the effective stress can be decomposed into:

[0147]

[0148] Where: is the positive effective stress tensor of concrete tensile properties; is the negative effective stress tensor of the compressive properties of concrete;

[0149] After the effective stress is decomposed into positive and negative, the relationship between the nominal stress tensor and the positive and negative effective stress tensors is:

[0150]

[0151] Where: d + is the tensile damage variable, ranging from 0 (no damage) to 1 (complete damage); d - is the shear damage variable, ranging from 0 (no damage) to 1 (complete damage);

[0152] The fourth-order damage tensor D is:

[0153] D=d + P + +d - P -

[0154] Where: P + is the positive projection operator of effective stress; P - is the negative projection operator of the effective stress; step 2, establishing a concrete elastic-plastic damage constitutive model in the effective stress space, characterized in that the model is:

[0155]

[0156] Where: is the stress increment; E0 is the undamaged elastic stiffness tensor; d ε is the total strain increment; dε p is the plastic strain increment, which can be expressed as the product of magnitude and direction;

[0157] In the effective stress space, the method for constructing the classic elastic-plastic damage constitutive model of concrete is characterized in that the model establishment process includes the following steps:

[0158] Step 2.1, determine the plastic yield criterion; use the Lubliner-MWFC yield criterion, and the tensile meridian and compression meridian of the MWFC are:

[0159]

[0160] Where: ρ t is the equivalent stress of the stretching meridian; ρ c is the equivalent stress of the compression meridian; f c 、k t 、k 2c is the concrete strength value; m w , e, and ξ are all model parameters;

[0161] In the effective stress space, after considering the evolution of the concrete yield surface, the original Lubliner-Lee yield criterion is:

[0162]

[0163] Where: and is the hardening function; (i=t or c) contains and is the tensile hardening parameter; is the compression hardening parameter; α is the model parameter; is the first invariant; is the second invariant; represents the maximum value among the principal stresses;

[0164] Step 2.2: Determine the plastic hardening law. Based on the Lubliner-Oller failure criterion, the original uniaxial compression hardening law can be extended to the concrete in the PC box girder with non-uniform restraint:

[0165]

[0166] Where: is the plastic hardening function; f is the uniaxial compressive strength of concrete; α and γ are model parameters; is the equivalent confining pressure of concrete under non-uniform confinement; is the first invariant; is the second invariant; is the equivalent stress of concrete; is the equivalent plastic strain of concrete;

[0167] For triaxial compression, we further have:

[0168]

[0169] Where: is the concrete stress under uniaxial compression;

[0170] Equivalent confining pressure of concrete under non-uniform confinement The following formula can be used for calculation:

[0171]

[0172] Where: f l is the original confining pressure; d c is the damage coefficient; f c is the uniaxial compressive strength of concrete; σ2, σ3 are stresses in different directions;

[0173] Step 2.3: Determine the plastic flow rule; in the effective stress space, the non-associative flow rule is:

[0174]

[0175] Where: is the plastic strain increment; dλ is a non-negative proportional coefficient, indicating the magnitude of the plastic strain; G is the plastic potential function; is the component of the stress tensor, which represents the stress state inside the material;

[0176] According to the non-orthogonal flow law, the plastic potential function G is:

[0177]

[0178] Where: ψ is the expansion angle of the concrete yield surface during the strengthening process; m is the eccentricity of the concrete plastic potential function, which is set to m = 0.1; ψ is the expansion angle of concrete, which ranges from 13° to 56°; f t is the concrete strength value;

[0179] Step 2.4: Determine the plastic loading and unloading rules:

[0180]

[0181] Where: is the plastic yield function, which is used to determine whether the material is in a plastic state; when F<0, the material is in the elastic stage; when F=0, the material begins to enter the plastic stage; is a non-negative proportional coefficient, which indicates the magnitude of plastic strain; is a complementary condition, ensuring the plasticity multiplier and yield function F, at least one of them is zero;

[0182] Step 3: Establish an energy regularized elastic-plastic damage constitutive model for concrete based on the local softening assumption, i.e., assuming that the deformation of concrete is uniform before reaching the peak stress, and that the deformation is localized after reaching the peak stress. The model is:

[0183]

[0184] Where: is the tensile damage loading function at the current moment n; Loading function for compression damage at the current moment n; is the axial tensile strain at the current moment n; is the axial compressive strain at the current moment n; is the axial damage driving variable at the current moment n;

[0185] Based on energy regularization, the tensile damage variable is:

[0186]

[0187] Where: d + is the tensile damage variable; a t 、b t are model parameters; is the cracking strain;

[0188] The relationship between tensile stress and cracking strain is:

[0189]

[0190] Where: σ t is the tensile stress; f t0 is the initial tensile strength of concrete; a t 、b t are model parameters; is the tensile cracking strain;

[0191] where a t 、b t for:

[0192]

[0193] Where: f tm is the tensile strength of concrete, which indicates the ultimate strength of the material under tension; f t0 is the initial tensile strength of concrete; l eq is the equivalent stress of concrete; G F is the fracture energy of the material;

[0194] Based on energy regularization, the compressive damage variable is:

[0195]

[0196] Where: d - is the compression damage variable; a c 、b c are model parameters; is the compressive cracking strain;

[0197] The relationship between compressive stress and cracking strain is:

[0198]

[0199] Where: σ c is the compressive stress; f c0 is the initial compressive strength of concrete; a c 、b c are model parameters; is the compressive cracking strain;

[0200] where a c 、b c for:

[0201]

[0202] Where: f cm is the compressive strength of concrete, which indicates the ultimate strength of the material under compression; f c0 is the initial compressive strength of concrete; l eq is the equivalent stress of concrete; G ch is the compression fracture energy dissipated per unit area of ​​concrete material;

[0203] According to the plastic loading and unloading law, combined with the damage variables and stress-strain relationship obtained by the energy regularization method, the loading and unloading process of non-uniform concrete is obtained:

[0204]

[0205] Where: is the tensile damage loading function at the current moment n; Loading function for compression damage at the current moment n; is the axial damage driving variable at the current moment n; when hour, and Indicates that the material is in an elastic unloading state and no new damage evolution occurs; when hour, and It indicates that the material is in the damage loading stage and new damage evolution occurs.

[0206] According to the tensile damage evolution of PC box girder concrete, the uniaxial tensile stress-strain relationship of concrete and the total energy dissipated due to tensile damage are obtained, as shown in Figure 2 As shown; According to the compressive damage evolution of PC box girder concrete, the uniaxial compressive stress-strain relationship of concrete and the total energy dissipated due to compressive damage are obtained, as shown in Figure 3 shown.

[0207] Example 2

[0208] This embodiment proposes a system for constructing an elastic-plastic damage constitutive model of concrete, including:

[0209] Decomposition module: Based on the classical elastic-plastic principle and damage mechanics theory, combined with the damage and plastic behavior characteristics of concrete in PC box girders, the damage variable, nominal stress and effective stress, elastic-plastic damage stress-strain relationship are determined, and the effective stress is decomposed according to the tension and compression characteristics;

[0210] Concrete elastic-plastic damage constitutive model construction module: In the effective stress space, the concrete elastic-plastic damage constitutive model is established by determining the plastic yield criterion, plastic hardening law, plastic flow law, and plastic loading and unloading law;

[0211] Energy-regularized concrete elastic-plastic damage constitutive model construction module: Based on the energy regularization method, the tensile damage variables, compressive damage variables and the corresponding stress-strain relationship are determined. Combined with the plastic loading and unloading rules, an energy-regularized concrete elastic-plastic damage constitutive model is constructed.

[0212] It should be understood that parts not elaborated in detail in this specification belong to the prior art.

[0213] It should be understood that the above description of the preferred embodiment is relatively detailed and cannot be regarded as limiting the scope of protection of the patent of the present invention. Under the guidance of the present invention, ordinary technicians in this field can also make substitutions or modifications without departing from the scope of protection of the claims of the present invention, which all fall within the scope of protection of the present invention. The scope of protection requested by the present invention shall be based on the attached claims.

[0214] The circuits, electronic components and modules involved are all existing technologies and can be fully implemented by those skilled in the art. Needless to say, the content protected by the present invention does not involve improvements to software and methods.

[0215] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0216] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for constructing an elastic-plastic damage constitutive model of concrete, characterized in that: The following steps are involved: Step 1: Based on the classical elastic-plastic principle and damage mechanics theory, combined with the damage and plastic behavior characteristics of concrete in PC box girders, the damage variable, nominal stress and effective stress, and elastic-plastic damage stress-strain relationship are determined, and the effective stress is decomposed according to the tension and compression characteristics; Step 2: In the effective stress space, establish the elastic-plastic damage constitutive model of concrete by determining the plastic yield criterion, plastic hardening law, plastic flow law, and plastic loading and unloading law; Step 3: Based on the energy regularization method, the tensile damage variables, compressive damage variables and the corresponding stress-strain relationship are determined. Combined with the plastic loading and unloading law, an elastoplastic damage constitutive model of concrete based on energy regularization is constructed.

2. The method for constructing a concrete elastic-plastic damage constitutive model according to claim 1, characterized in that: In step 1, the damage variables, nominal stress and effective stress, and elastic-plastic damage stress-strain relationships are determined, specifically including: The micro-defect state of concrete is described by the cross-sectional area ratio of the damaged configuration to the non-damaged configuration to determine the damage variable, as shown in the following formula: Where: d is the damage variable, which is used to describe the micro-defect state inside the concrete, A is the cross-sectional area of ​​the damaged configuration, and A D is the damage area of ​​the lossy configuration, is the cross-sectional area of ​​the lossless configuration; The nominal stress and effective stress are determined based on uniaxial pressure as shown below: Where: T is the uniaxial pressure, σ is the nominal stress, is the effective stress, D is the fourth-order damage tensor; Determine the elastic-plastic damage stress-strain relationship, including: The effective stress-strain relationship of concrete elastoplastic damage is determined based on the undamaged fourth-order elastic stiffness tensor and the damaged fourth-order elastic stiffness tensor, as shown in the following formula: Where: E0 is the undamaged fourth-order elastic stiffness tensor; E is the damaged fourth-order elastic stiffness tensor; The nominal stress-strain relationship of the concrete elastic-plastic damage model is determined based on the plastic strain tensor, as shown in the following formula: σ=(ID):E0:(e-e p ) Where: σ is the nominal stress, E0 is the undamaged elastic stiffness tensor, D is the fourth-order damage tensor, I is the fourth-order unit tensor, ε is the total strain tensor, and ε p is the plastic strain tensor.

3. The method for constructing a concrete elastic-plastic damage constitutive model according to claim 1, characterized in that: In step 1, decomposing the effective stress according to the tensile and compressive characteristics specifically includes: According to the different damage characteristics of concrete under tension and compression, the effective stress is decomposed as shown in the following formula: Where: is the positive effective stress tensor of concrete tensile properties, is the negative effective stress tensor of the compressive properties of concrete; After decomposing the effective stress into positive and negative values, the relationship between the nominal stress tensor and the positive and negative effective stress tensors is determined as follows: Where: d + is the tensile damage variable, ranging from 0 to 1, where 0 indicates no damage and 1 indicates complete damage. - is the shear damage variable, ranging from 0 to 1; Determine the fourth-order damage tensor D as: D = d + P + +d - P - Where: P + is the positive projection operator of effective stress, P - is the negative projection operator of the effective stress.

4. The method for constructing a concrete elastic-plastic damage constitutive model according to claim 1, characterized in that: In step 2, determining the plastic yield criterion specifically includes: In the effective stress space, after considering the evolution of the concrete yield surface, the plastic yield criterion is determined as shown in the following formula: Where: and is the hardening function, (i=t or c) contains and is the tensile hardening parameter, is the compression hardening parameter, α is the model parameter, is the first invariant, is the second invariant, Represents the maximum value among the principal stresses.

5. The method for constructing a concrete elastic-plastic damage constitutive model according to claim 1, characterized in that: In step 2, determining the plastic hardening law specifically includes: Based on the Lubliner-Oller failure criterion, the original uniaxial compression hardening law can be extended to the concrete with non-uniform confinement in PC box beams: Where: is the plastic hardening function, f is the uniaxial compressive strength of concrete, α and γ are model parameters, is the equivalent confining pressure of concrete under non-uniform confinement, is the first invariant, is the second invariant, is the equivalent stress of concrete, is the equivalent plastic strain of concrete.

6. The method for constructing a concrete elastic-plastic damage constitutive model according to claim 1, characterized in that: In step 2, the plastic flow law and plastic loading and unloading law are determined, including: In the effective stress space, the non-associative flow gauge is established as: Where: is the plastic strain increment, dλ is a non-negative proportional coefficient, which indicates the size of the plastic strain, G is the plastic potential function, is the component of the stress tensor, which represents the stress state inside the material; According to the non-orthogonal flow law, the plastic potential function G is established as: Where: ψ is the expansion angle of the concrete yield surface during the strengthening process, m is the eccentricity of the concrete plastic potential function, m = 0.1, ψ is the expansion angle of concrete, the value range is between 13° and 56°, f t is the concrete strength value.

7. The method for constructing a concrete elastic-plastic damage constitutive model according to claim 1, characterized in that: In step 2, the plastic loading and unloading law is determined as follows: Where: is the plastic yield function, which is used to determine whether the material is in a plastic state. When F<0, the material is in the elastic stage. When F=0, the material begins to enter the plastic stage. is a non-negative proportional coefficient, which indicates the magnitude of the plastic strain. is a complementary condition, ensuring the plasticity multiplier At least one of the and yield functions F is zero.

8. The method for constructing a concrete elastic-plastic damage constitutive model according to claim 1, characterized in that: In step 2, the concrete elastic-plastic damage constitutive model is shown as follows: Where: is the stress increment; E0 is the undamaged elastic stiffness tensor; dε is the total strain increment; dε p is the plastic strain increment, which can be expressed as the product of magnitude and direction.

9. The method for constructing a concrete elastic-plastic damage constitutive model according to claim 1, characterized in that: Step 3 specifically includes: Based on energy regularization, the tensile damage variable is determined as: Where: d + is the tensile damage variable, a t 、b t are model parameters, is the cracking strain; The relationship between tensile stress and cracking strain is determined based on tensile stress: Where: σ t is the tensile stress, f t0 is the initial tensile strength of concrete, a t 、b t are model parameters, is the tensile cracking strain; Based on energy regularization, the compressive damage variable is determined as: Where, d - is the compressive damage variable, a c 、b c are model parameters, is the compressive cracking strain; The relationship between compressive stress and cracking strain is determined as: Where: σ c is the compressive stress, f c0 is the initial compressive strength of concrete, a c 、b c are model parameters, is the compressive cracking strain; According to the plastic loading and unloading law, combined with the damage variable and stress-strain relationship obtained by the energy regularization method, the non-uniform concrete loading and unloading process is obtained as shown in the following formula: Where: is the tensile damage loading function at the current moment n, Loading function for compression damage at the current moment n; is the axial damage driving variable at the current moment n, when hour, and Indicates that the material is in an elastic unloading state and no new damage evolution occurs. hour, and It indicates that the material is in the damage loading stage and new damage evolution occurs.

10. A system for constructing a concrete elastic-plastic damage constitutive model, for implementing the method for constructing a concrete elastic-plastic damage constitutive model according to claims 1 to 9, characterized in that: include: Decomposition module: Based on the classical elastic-plastic principle and damage mechanics theory, combined with the damage and plastic behavior characteristics of concrete in PC box girders, the damage variable, nominal stress and effective stress, elastic-plastic damage stress-strain relationship are determined, and the effective stress is decomposed according to the tension and compression characteristics; Concrete elastic-plastic damage constitutive model construction module: In the effective stress space, the concrete elastic-plastic damage constitutive model is established by determining the plastic yield criterion, plastic hardening law, plastic flow law, and plastic loading and unloading law; Energy-regularized concrete elastic-plastic damage constitutive model construction module: Based on the energy regularization method, the tensile damage variables, compressive damage variables and the corresponding stress-strain relationship are determined. Combined with the plastic loading and unloading rules, an energy-regularized concrete elastic-plastic damage constitutive model is constructed.

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