Search

This paper develops a modeling method with an incremental stress–strain–environment constitutive model to predict the change in the plastic mechanical behavior of concrete caused by environmental action. The model regards the environmental factor as a constitutive variable, similar to stress and strain. The yield condition of the model is a function of stress, the plastic internal variable, and the environmental variable. The loading–unloading criterion is established in the space constructed by the strain and the environmental variable to determine the contribution of mechanical loads and environmental factors to plastic deformation. By considering the strain rate as an environmental factor and applying the proposed method, a stress–strain–strain rate constitutive model of concrete is developed to describe the plastic flow caused by the combined action of stress and strain rate. In addition, constant- and variable-strain rate loading tests are performed to evaluate the performance of the established model. In particular, the model's capabilities are further highlighted by comparing the simulation results of the dynamic stress–strain model and the proposed model under loading conditions with rapidly decreasing strain rates. [ABSTRACT FROM AUTHOR]

The accuracy of a constitutive model for confined concrete largely relies on its capability to capture concrete's dilatancy behavior. In this paper, a non-orthogonal flow rule (NFR) is used to reasonably characterize the concrete's volume change law in relation to the stress state without the necessity for a plastic potential function. Then, the non-orthogonal plastic model is implemented in the finite element (FE) software ABAQUS using the implicit stress update algorithm, which employs the line search method and the numerical consistent tangent stiffness matrix to ensure the robustness and computational efficiency of FE analysis. Finally, FE simulations are performed to evaluate the constitutive model's capabilities in actively and passively confined concrete. In the latter case, steel tubes restrict the concrete's lateral deformation. An analysis and discussion are conducted regarding the impact of dilatancy behavior on concrete-filled steel tube (CFST) columns. The consistency between experimental data and simulation results demonstrates that the FE modeling with a non-orthogonal constitutive model provides an effective tool to describe the behavior of confined concrete. • Non-orthogonal model of concrete is developed considering plastic flow related to stress states. • Constitutive model is numerically implemented by the robust implicit stress update algorithm. • Model performance describing properties of actively and passively confined concrete is explored. • Effect of dilatancy behavior on ultimate load of concrete-filled steel tube columns is analyzed. [ABSTRACT FROM AUTHOR]

A framework of the plastic-damage model with double scalar variables is established in nominal stress space under the small deformation assumption. In the damaged part, a damage tensor composed of double scalar variables is presented to comprehensively characterize the isotropic damage behavior in three-dimensional (3D) conditions. The damage laws of Young's modulus and shear modulus are proposed to capture their different damage characteristic observed in the test. For one-dimensional (1D) and 3D conditions, the applicability of single scalar and double scalar damage variables is discussed. The macroscopic damage difference between these two damage variables when describing damage under 3D conditions is analyzed. In the plastic part, the plastic strain increment is determined by two parts of magnitude and direction. The magnitude is obtained by the consistency condition, and the flow direction is defined by the nonorthogonal flow rule that can satisfactorily reproduce the dilatancy behavior of concrete. The proposed model is implemented by the explicit Runge–Kutta (RK) method with the fifth-order accuracy and the Pegasus method. The performance of the model is assessed by the comparison results between the model and the cyclic loading and unloading test data under different stress paths. [ABSTRACT FROM AUTHOR]

The physical mechanism of the static–dynamic combined (S–DC) multiaxial strength of concrete is investigated considering cohesive and frictional strength. It is determined that the strain rate effects and stress state effects on the shear strength of concrete can be decoupled. An effective initial static stress is defined to distinguish the part of the cohesive strength that is dependent on the strain rate; the other part is consumed by the initial static stress. Furthermore, the strength parameter, which reflects the coupled effects of the initial static stress and the strain rate on the strength, is obtained based on the effective initial static stress and dynamic increase factor (DIF). Combining the proposed strength parameter and nonlinear dynamic multiaxial strength criterion, a new S–DC multiaxial strength criterion for concrete is presented. The proposed strength criterion is applied to analyze the S–DC strength rules of concrete under multiaxial stress conditions and is further verified using five groups of test results. [ABSTRACT FROM AUTHOR]

• A total of 25 triaxial cyclic tests are used to analyze the damage of concrete. • Multiaxial damage rule is normalized by equivalent plastic shear strain. • A stress-path-independent damage variable is proposed by characteristic boundaries of damage gradient. • The proposed damage variable can reasonably capture multiaxial damage behavior of concrete. The damage rule of concrete is theoretically analyzed and discussed from the aspects of the stiffness degradation and the cohesive strength degradation. Further, the multiaxial damage rules of concrete are studied by 25 groups of tests under true triaxial and conventional triaxial compressive cyclic conditions. The analysis of the test results shows that the relationship between the damage variable and the axial plastic strain depends on the loading path. This dependence of the damage variable on the stress paths can be normalized by the equivalent plastic shear strain. A partial differential equation of the damage variable, driven by the equivalent plastic shear strain, is constructed based on two characteristic boundary conditions of the damage gradient. Then, a stress-path-independent isotropic damage variable is proposed by the integral of the partial differential equation. The proposed damage variable can reasonably capture the multiaxial damage behavior of the concrete. The stress path independence of the proposed damage variable is analyzed and further verified by the test results under multiaxial stress conditions. [ABSTRACT FROM AUTHOR]

In this paper, the proposed yield function is the function of stress, hardening parameter, and strain rate. To fully describe the stress state and strain rate condition of material during dynamic loading, a new coordinate system, which is composed of a stress axis and strain rate axis, is employed to present the proposed rate-dependent yield surface. The strain rate is regarded as a variable in applying the consistency condition. The rate-dependent consistency is satisfied strictly during the whole dynamic loading. The nonassociated flow rule is employed to describe the dilatancy behavior of concrete. The loading–unloading criterion based on Ilyushin's postulate is developed into the rate-dependent loading–unloading criterion that can consider reasonably the change of elastic domain caused by strain rate. Furthermore, a three-dimensional (3D) dynamic elastoplastic model of concrete is established within the framework of the rate-dependent consistency condition. Under the dynamic uniaxial compression loading condition, the model characteristics related to rate-dependent consistency condition are discussed and analyzed. Five sets of dynamic experiment results of concrete are employed to evaluate the performance of the model. [ABSTRACT FROM AUTHOR]

Abstract The core mission to establish elastoplastic constitutive model is how to determine the magnitude and direction of plastic strain increment for material under the given load. Fractional derivative provides a powerful tool for determining the nonorthogonal direction of a certain differentiable function. A three-dimensional (3D) fractional plastic flow rule suitable for concrete material is presented for the first time utilizing fractional derivative. The direction of plastic strain increment is determined by the proposed fractional plastic flow rule. A closed form yield function is developed in the transformed stress (TS) space based on the nonlinear unified strength criterion, and further used to describe the plastic strain induced by hydrostatic loading. A united hardening/softening function proposed by the authors in previous works is adopted to describe the pre-peak hardening and post-peak softening behaviour of concrete. Furthermore, a 3D fractional elastoplastic constitutive model for concrete material is presented. Only nine material parameters with the clear physical meaning are need for the proposed model, and the determination method of each material parameter is given. A series of test results of concrete with different strength under biaxial and triaxial stress conditions are used to assess the performance of proposed model. [ABSTRACT FROM AUTHOR]

The numerical implementation of advanced plastic damage models has been challenging due to the diverse computational difficulties caused by material nonlinearity. In this study, firstly, a plastic damage model is developed by a nonsmoothed Mohr–Coulomb yield criterion. The nonorthogonal flow rule without plastic potential function is employed to describe the dilatancy behavior of concrete. The stiffness degradation is considered through two tensile and compressive damage variables. Subsequently, an implicit stress update algorithm incorporating several advanced numerical methods is proposed to tackle difficulties arising in the numerical calculation of the plastic damage model. In the model implementation, the Mohr–Coulomb yield function with corners is replaced by a single smooth expression to ensure the stability of the numerical calculation. A line search method is used to solve nonlinear systems of integral stress equations to obtain better convergence than Newton method. The complex step derivative approximation is used to evaluate the consistent tangent operator to provide quadratic convergence speed of the global equilibrium iterations, thus avoiding tedious analytical derivative operations. The integral nonlocal method is also used to regularize the finite element solution. At the material point scale, the ability of the proposed model to describe the complex mechanical behavior of concrete is verified by utilizing nine sets of monotonic and cyclic loading and unloading tests. Finally, the algorithm and model's performance is well tested by the failure analysis of five numerical examples. The code of this work will be freely available at https://github.com/zhouxin615/PD_model. • A robust numerical implementation of plastic nonlocal damage model. • Integral nonlocal method is used to regularize the finite element solution. • Line search method is used for the solution of nonlinear equations. • Consistent tangent operator is determined by complex step derivative approximation. [ABSTRACT FROM AUTHOR]

The majority of existing studies on the strain rate effect of concrete have concentrated on the dynamic uniaxial strength or a narrow range of strain rates. However, concrete material always works under a multiaxial stress state and suffers from loads with different strain rates. This paper presents a method to describe the dynamic multiaxial strength of concrete at all strain rates. The advantages of the nonlinear unified strength criterion (NUSC) are that this factor can reasonably describe the static strength behavior of concrete under a multiaxial stress state. In addition, the dynamic uniaxial S criterion can express the actual dynamic uniaxial strength at all strain rates. A nonlinear dynamic multiaxial strength criterion is developed based on the strain rate–dependent strength parameters of the NUSC, in which the strain rate–dependent strength parameters are derived from the S criterion. The obtained strength criterion consists of a series of continuous smooth convex surfaces in the principal stress space, which extends outward with increasing strain rate. In addition, the strength curve gradually changes from a curved triangle to a von Mises circle with increasing strain rate in the deviatoric plane. The proposed criterion is verified via its application to extensive experimental data from multiaxial dynamic tests in the literature, and the results demonstrate that the proposed criterion can reasonably describe the multiaxial strength and reflect the ultimate dynamic strength of concrete. [ABSTRACT FROM AUTHOR]

The existing test results and semi-empirical equations of the rate-dependent concrete strength have overestimated the actual dynamic strength because they do not distinguish between the actual dynamic strength related to the strain rate effects and the additional resistance caused by inertial effects. However, an ultimate strength of concrete exists at a strain rate exceeding a certain value. This paper proposes a nonlinear dynamic uniaxial strength criterion for concrete based on an analysis of the physical mechanisms governing the strain-rate-dependent behavior of concrete strength. The proposed criterion is able to describe the actual dynamic strength and to reflect the ultimate strength at a high strain rate of concrete. The results from two groups of dynamic uniaxial compressive tests and two groups of dynamic uniaxial tensile tests are used to verify the criterion. Moreover, the recommended physical parameters in the criterion are obtained by analyzing the statistical test results of dynamic uniaxial compression and tension. The recommended parameters can be used in the criterion to study the dynamic strength of concrete when dynamic tests are not feasible, and to predict the dynamic strength at high strain rates when tests are performed at lower strain rates. [ABSTRACT FROM AUTHOR]

• The viscoelastic peridynamic method is applied to simulate the impact fracture of the concrete beam. • The strain rate evolution law of the concrete beam during loading is visualized intuitively. • The cracking mechanism of the concrete beam with initial crack is revealed. • The coupling influence law of impact velocity and initial crack on the fracture mode of the concrete beam is obtained. Based on viscoelastic peridynamic method, a numerical model of a three-point bending concrete beam with an initial crack is established in this work, whose accuracy and rationality are verified by comparing the fracture modes calculated by this model with the experimental results. The paper analyzed the angle of crack propagation and the evolution of energy, displacement, strain, and strain rate in the beam by the verified numerical model, while a total of 24 numerical examples with different initial crack positions and loading velocities are simulated, based on which the coupling influence law of the initial crack and loading velocity on the fracture mode of the beam is obtained. This paper reveals the dynamic fracture mechanism of the three-point bending concrete beam with an initial crack, and further assesses the features and superiorities of the viscoelastic peridynamic method by the agency of numerical experiments. Thus far, it has been certified that the developed viscoelastic peridynamic mothed can fairly consider the impact of the initial crack and loading velocity on the bearing capacity, deformation, and fracture properties of the concrete structure. [ABSTRACT FROM AUTHOR]

The nonlinear unified strength criterion proposed by authors in 2010 is adopted as the yield function and the plastic potential function for concrete. Four original material parameters of the nonlinear unified strength criterion are derived as functions of four conventional strength indexes of concrete. A three-dimensional elastoplastic constitutive model for concrete is then developed by using hardening and softening functions that are determined from the uniaxial compressive stress–strain relationship. The performance of the constitutive model is evaluated by comparing prediction and experimental data from literatures. The comparison shows the model is able to reasonably describe the three-dimensional strength characteristics, strain softening behavior after the peak stress and the dilatancy of various concretes. Moreover, the proposed model is integrated in the general finite element package ABAQUS via UMAT to simulate the deformation process of reinforced concrete columns under eccentric compression. The simulations show that the proposed constitutive model is able to describe the nonlinear mechanical behavior under complex stress states with high computational efficiency. [ABSTRACT FROM AUTHOR]

• A method to determine cohesion-friction combined hardening law using M−C yield criterion and multiaxial test data is presented. • Plastic flow direction is determined directly by the non-orthogonal gradient of yield function without the need for the plastic potential function. • Integral-type nonlocal method is used to regularize the finite element solution. • Proposed model has been implemented in ABAQUS based on the implicit return mapping algorithm. A cohesion-friction combined hardening model of concrete was developed. Combined with the Mohr-Coulomb strength criterion, the yield curve is determined directly by the test data of concrete. Then, a method to determine the hardening law from the evolutionary process of the yield curve is elaborated. To consider the influence of the multiaxial stress state on the ductility of concrete, a stress dependent plastic internal variable is proposed. Based on the nonorthogonal flow rule implemented by fractional order derivative, the direction of plastic strain increment is directly determined by the nonorthogonal gradient of the yield function without the need for plastic potential function. The comparison with the test data shows that the proposed model can capture the strength and deformation characteristics of concrete reasonably. Finally, the model is implemented into ABAQUS via an open-source user defined material subroutine UMAT (https://github.com/zhouxin615/CFCH%5fmodel.git) based on the implicit return mapping algorithm. In particular, the integral-type nonlocal approach was adopted to regularise FE solution. Moreover, through the structural analysis of reinforced concrete columns, the operation process of the friction and cohesion mechanism of concrete materials is well reproduced. [ABSTRACT FROM AUTHOR]

Concrete is a geotechnical material characterized by cohesive-frictional properties. However, there is currently a paucity of specialized experimental research to elucidate these features and their potential mechanisms. This study addresses this gap by designing and conducting 72 experimental sets on C30, C40, and C50 concrete to investigate their cohesive-frictional attributes. Utilizing two comprehensive conventional triaxial compression tests halted upon reaching constant stress with increasing strain, this research examines the mechanisms and corresponding mechanical behaviors of cohesion and friction. During the initial loading test, the macroscopic mechanical behavior, incorporating both cohesive and frictional properties, is observed. The same specimen is then subjected to a second triaxial test under identical conditions, predominantly revealing frictional mechanical behavior. By comparing the results from the initial and subsequent loadings of the same specimen, the cohesive and frictional properties of concrete are decoupled, allowing for the determination of independent deformation and strength laws for cohesion and friction. Based on the experimental findings, this study thoroughly discusses the deformation mechanisms and strength evolution laws of both properties, elucidating the manifestation mechanisms of cohesion and friction in concrete. Furthermore, a comparative analysis with the nonlinear unified strength criterion and the strength laws on the triaxial compression meridian plane is performed. The novel experimental method proposed in this study, which is designed to investigate the cohesion-friction properties of concrete, has successfully decoupled the cohesive strength and frictional strength of concrete for the first time from an experimental perspective. This research provides a foundational experimental basis and mechanistic insight into the fundamental mechanical properties of concrete materials, which will facilitate the establishment of cohesive-frictional strength theories and constitutive models. • An innovative experimental method is proposed for investigating the cohesive-frictional properties of concrete. • The decoupling of cohesive strength and frictional strength in concrete has been achieved. • The deformation mechanism of cohesion and friction in concrete has been revealed. • The rules underlying the manifestation of cohesive and frictional properties in concrete have been elucidated. [ABSTRACT FROM AUTHOR]

A plastic damage model with the non-orthogonal flow rule is developed, which is consisted of the damage part driven by plastic strain and the plastic part based on effective stress. In the damage characterization, the degeneration law of elastic stiffness is described by the damage variable in the form of exponential function. In the plastic characterization, the evolution for plastic strain increment (PSI) is characterized from the magnitude and direction perspective. The direction of PSI is obtained directly by the fractional gradient of yield surface and the need for the construction of plastic potential function is bypassed. The magnitude of PSI is calculated based on the effective hardening function and the yield function, where the effective hardening function corresponding to the undamaged material is derived by both the normal hardening/softening function corresponding to the damaged material and the damage variable. The Next Increment Corrects Error (NICE) algorithm integrating the computational accuracy and efficiency is used for the numerical implementation of model. The ability of model to capture the complex mechanical behavior of concrete is assessed by the monotonous and cyclic test data from the literature. • Plastic flow direction is determined based on the non-orthogonal flow rule. • Effective hardening function is obtained by normal hardening and damage behavior. • Permanent deformation and stiffness degradation behavior of concrete is captured. • Numerical implement of model integrates computational accuracy and efficiency. [ABSTRACT FROM AUTHOR]