混凝土的弹塑性损伤双面本构模型

针对混凝土材料拉压应变空间下损伤机制的不同,结合连续损伤力学和塑性理论建立了一个全新的本构模型。该模型中损伤和塑性变形的演变由应变空间的同一个非弹性曲面来控制,但对拉压应变空间中非弹性曲面的演变分别采用了随动强化法则和各向同性演化规律。计算结果表明,该模型能较好地描述混凝土材料在单轴及多轴单调加载和低周反复荷载下的典型非线性特征。     

一个新的钢筋混凝土损伤塑性模型

为了准确、高效地对拆除爆破工程进行数值模拟,考虑钢筋混凝土受拉刚化效应以及配筋率对受拉刚化效应的影响和受压箍筋约束效应,采用组合模量的方法给出了一个简化的钢筋混凝土本构关系,在LS-DYNA有限元软件中的混凝土损伤塑性模型的基础上,通过参数修改建立新的钢筋混凝土损伤塑性模型模拟来钢筋混凝土。在实验验证的基础上,采用钢筋混凝土损伤塑性等效模型对一双切口钢筋混凝土烟囱延时爆破拆除效果进行数值模拟,数值模拟结果表明该模型可以准确反映烟囱倒塌破坏及运动过程。

     

A model framework for anisotropic damage coupled to crystal (visco)plasticity

We develop a model framework for anisotropic damage coupled to crystal (visco)plasticity, which is based on the concept of a fictitious (undamaged) configuration. The theoretical setting is that of finite strains, which is natural when studying crystal inelasticity even in the case of actual small strains. It turns out that the evolution law for damage, which reflects degradation in the slip planes and which is the key new relation, bears strong resemblance with the inelastic flow rule. Some numerical results showing qualitatively the anisotropic development of damage concludes the paper.     

A plasticity model for pressure-dependent anisotropic cellular solids

The initial and subsequent yield surfaces for an anisotropic and pressure-dependent 2D stochastic cellular material, which represents solid foams, are investigated under biaxial loading using finite element analysis. Scalar measures of stress and strain, namely characteristic stress and characteristic strain, are used to describe the constitutive response of cellular material along various stress paths. The coupling between loading path and strain hardening is then investigated in characteristic stress–strain domain. The nature of the flow rule that best describes the plastic flow of cellular solid is also investigated. An incremental plasticity framework is proposed to describe the pressure-dependent plastic flow of 2D stochastic cellular solids. The proposed plasticity framework adopts the anisotropic and pressure-dependent yield function recently introduced by Alkhader and Vural [Alkhader M., Vural M., 2009a. An energy-based anisotropic yield criterion for cellular solids and validation by biaxial FE simulations. J. Mech. Phys. Solids 57(5), 871–890]. It has been shown that the proposed yield function can be simply calibrated using elastic constants and flow stresses under uniaixal loading. Comparison of stress fields predicted by continuum plasticity model to the ones obtained from FE analysis shows good agreement for the range of loading paths and strains investigated.     

A simple anisotropic clay plasticity model

An anisotropic clay plasticity constitutive model is extended to include a non-associative flow rule for the successful simulation of the response under undrained loading for some normally consolidated sensitive clays, including possible softening response, without altering otherwise the simple basic structure of the formulation. The model has been developed within the framework of critical state soil mechanics (CSSM) for the triaxial space. The model's structure deviates, in general, from the particular premises of CSSM in regards to a unique critical state line in the space of void ratio and effective pressure, in order to simulate observed experimental data.     

Fractal effect and anisotropic constitutive model for concrete

An elasto-anisotropic damage constitutive model for concrete is developed in this work. Disregarding the coupling between the isotropic and the anisotropic damage, the isotropic damage variables are defined as functions of the microcrack fractal dimension, and the anisotropic parts are expressed by the lengths of cracks in concrete which various in different directions. The Helmholtz free energy is decomposed into the elastic deforming, damage and irreversible deforming components, with the last component used to replace the plastic deformation. Therefore the damage constitutive formulas for concrete are derived based on continuum damage mechanics. Evolution laws for both isotropic and anisotropic damage variables are derived, in which the anisotropic parts are obtained by modifying an empirical model. The critical fracture stress and the fracture toughness are investigated for materials with a single fractal crack based on the fractal geometry and the Griffith fracture criterion. Numerical computation is conducted for concrete under the uniaxial and the biaxial compression. The results indicate that the material stiffness degradation can be well addressed when the anisotropic damage is incorporated; the irreversible deformation is greatly related to the behavior of the descending branch beyond the peak load. The validation of the presented model is proofed by comparing results with the experimental data. This model provides an approach to link the macro properties of a material with its micro-structure change.     

A damage model for concrete beams in compression

A usual class of phenomenological “1 − d” damage models is revisited: starting from experimental observations showing that the Young’s and tangent moduli evolve linearly during a compression test on concrete, an appropriate expression for the damage threshold is obtained, which differs from the usual ones. The linear variation of the moduli with respect to the strain variation allows to simplify the incremental equilibrium equations and to improve the accuracy of the simulation.     

On the coupling of anisotropic damage and plasticity models for ductile materials

In this contribution various aspects of an anisotropic damage model coupled to plasticity are considered. The model is formulated within the thermodynamic framework and implements a strong coupling between plasticity and damage. The constitutive equations for the damaged material are written according to the principle of strain energy equivalence between the virgin material and the damaged material. The damaged material is modeled using the constitutive laws of the effective undamaged material in which the nominal stresses are replaced by the effective stresses. The model considers different interaction mechanisms between damage and plasticity defects in such a way that two-isotropic and two-kinematic hardening evolution equations are derived, one of each for the plasticity and the other for the damage. An additive decomposition of the total strain into elastic and inelastic parts is adopted in this work. The elastic part is further decomposed into two portions, one is due to the elastic distortion of the material grains and the other is due to the crack closure and void contraction. The inelastic part is also decomposed into two portions, one is due to nucleation and propagation of dislocations and the other is due to the lack of crack closure and void contraction. Uniaxial tension tests with unloadings have been used to investigate the damage growth in high strength steel. A good agreement between the experimental results and the model is obtained.     

ABAQUS混凝土损伤塑性模型中损伤因子的率相关性及实现方法

ABAQUS程序中最常用的混凝土损伤塑性（concrete damage plasticity, CDP）模型无法实现损伤因子与应变率相关。为了准确描述混凝土材料在高应变率下的损伤特性,基于CDP模型定义了新的应变率场变量,编制了VUSDFLD用户子程序,开发了能够考虑损伤因子率相关性的改进的CDP（modified CDP,MCDP）模型。MCDP模型采用能量法求解混凝土拉压损伤因子,主求解程序能够随着应变率场变量的变化而自动更新不同应变率对应的损伤参数,计算得到的混凝土单轴静态加载结果与CDP模型吻合较好。MCDP模型对高应变率下动态压缩性能的模拟结果表明：混凝土材料在不同应变率下的拉压损伤对其动态力学性能有显著影响,编制的VUSDFLD子程序和MCDP模型能够有效地解决损伤应变率相关的模拟难题,可以准确地模拟爆炸荷载作用下钢筋混凝土梁的动态响应,为预测爆炸冲击等强动载作用下混凝土结构的响应和破坏提供了更可靠的技术途径。

     

On the dissipative zone in anisotropic damage models for concrete

This paper presents a three-dimensional model to simulate the behavior of plain concrete structures that are predominantly tensile loaded. This model, based on continuum damage mechanics, uses a symmetric second-order tensor as the damage variable, which permits the simulation of orthotropic degradation. The validity of the first and the second law of thermodynamics, as well as the validity of the principle of maximum dissipation rate, are required. That is attained by defining the loading functions in quantities that are thermodynamically conjugated to the damage variables. Furthermore, the evolution rule is derived by maximizing the energy dissipation rate. This formulation is regularized by means of the fracture energy approach by introducing a characteristic length. The basic and new idea in this paper is that the characteristic length should always coincide with the width of the dissipative zone appearing in the simulation. The integration points with increasing damage in one loading increment are the dissipative zone in this loading increment. The main objective of this paper is the convenient formulation of approaches for the characteristic length in order to attain the coincidence of the characteristic length with the width of the dissipative zone appearing in the simulation. It is shown that simulations are objective and yield good results if the requirement is fulfilled that the characteristic length in the constitutive law coincides with the width of the dissipative zone in the simulation.     

A two-dimensional micromechanical model of anisotropic elastic-microplastic damage evolution

Summary A two-dimensional micromechanically based model of anisotropic elastic-microplastic damage evolution is presented. The deterioration of the material is represented by equally oriented Dugdale microcracks. Assuming a physically plausible crack growth law a consequent homogenization gives the macroscopic nonlinear stress-strain behavior during a loading process as well as the evolution of the corresponding anisotropic damage and typical characteristics during a final unloading process.

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Ein zweidimensionales mikromechanisches Modell anisotroper elastisch-mikroplastischer Schädigungsentwicklung

Übersicht Es wird ein zweidimensionales mikromechanisch begründetes Modell anisotroper elastischmikroplastischer Schädigungsentwicklung dargestellt. Die Materialschädigung wird durch gleich-orientierte Dugdale-Mikrorisse modelliert. Unter der Annahme eines physikalisch plausiblen Rißwachstumsgesetzes liefert eine entsprechende Homogenisierung sowohl das makroskopische nichtlineare Spannungs-Dehnungs-Verhalten während eines Belastungsprozesses als auch die Evolution der entsprechenden anisotropen Schädigung sowie typische Charakteristika beim Entlastungsprozeß.

     

Confinement-sensitive plasticity constitutive model for concrete in triaxial compression

In this paper, a confinement-sensitive plasticity constitutive model for concrete in triaxial compression is presented, aiming to describe the strength and deformational behaviour of both normal and high-strength concrete under multiaxial compression. It incorporates a three-parameter loading surface, uncoupled hardening and softening functions following the accumulation of plastic volumetric strain and a nonlinear Lode-angle dependent plastic potential function. The various model parameters are calibrated mainly on the basis of a large experimental database and are expressed in terms of only the uniaxial compressive concrete strength, leading to a single-parameter model, suitable for practical applications. The model’s performance is evaluated against experimental results and it is found that both the increased strength and deformation capacity of confined concrete are properly captured.     

A new thermodynamically consistent continuum model for hardening plasticity coupled with damage

A phenomenological model for hardening–softening elasto-plasticity coupled with damage is presented. Specific kinematic internal variables are used to describe the mechanical state of the system. These, in the hypothesis of infinitesimal changes of configuration, are partitioned in the sum of a reversible and an irreversible part. The constitutive equations, developed in the framework of the Generalised Standard Material Model, are derived for reversible processes from an internal energy functional, postulated as the sum of the deformation energy and of the hardening energy both coupled with damage, while for irreversible phenomena from a dissipation functional.Performing duality transformations, the conjugated potentials of the complementary elastic energy and of the complementary dissipation are obtained. From the latter a generalised elastic domain in the extended space of stresses and thermodynamic forces is derived. The model, which is completely formulated in the space of actual stresses, is compared with other formulations based on the concept of effective stresses in the case of isotropic damage. It is observed that such models are consistent only for particular choices of the damage coupling. Finally, the predictions of the proposed model for some simple processes are analysed.     

混凝土率型内时损伤本构模型

混凝土是一种典型的率敏感材料,为了更好地描述混凝土结构在动力、冲击荷载作用下的强度和变形特征,本文结合内时理论和损伤理论建立了一种考虑混凝土率效应的内时损伤本构模型。该模型的特点:将混凝土材料的受力软化效应分解为密实状态的塑性效应和由微裂缝扩展引起的刚度退化效应。前者由内时理论来描述,这使该模型摆脱了一般弹塑性模型中屈服面的概念,从而更符合混凝土的变形特性,并且简化了非线性计算过程;后者由损伤理论来描述,根据混凝土的动力试验结果建立了增量型的损伤演变方程,从而使该模型能够较好地反映混凝土的动力特性。最后,应用本文建议的模型对一钢筋混凝土简支梁进行了非线性分析,结果表明:当结构承受快速荷载作用时,应变率对结构的受力性能影响较大,在进行结构分析时必须予以考虑。     

STRENGTH CRITERION FOR PLAIN CONCRETE UNDER MULTIAXIAL STRESS BASED ON DAMAGE POISSON＇S RATIO

A new unified strength criterion in the principal stress space has been proposed for use with normal strength concrete （NC） and high strength concrete （HSC） in compressioncompression-tension, compression-tension-tension, triaxial tension, and biaxial stress states. The study covers concrete with strengths ranging from 20 to 130 MPa. The conception of damage Poisson＇s ratio is defined and the expression for damage Poisson＇s ratio is determined basically. The failure mechanism of concrete is illustrated, which points out that damage Poisson＇s ratio is the key to determining the failure of concrete. Furthermore, for the concrete under biaxial stress conditions, the unified strength criterion is simplified and a simplified strength criterion in the form of curves is also proposed. The strength criterion is physically meaningful and easy to calculate, which can be applied to analytic solution and numerical solution of concrete structures.     

A crack-mechanics based model for damage and plasticity of brittle materials under dynamic loading

A rate-dependent model for damage and plastic deformation of brittle materials under dynamic loading is presented. The model improves upon a recently developed micromechanical damage model (Zuo et al., 2006) by incorporating plastic deformation of the material. The distribution of the microcracks in the material is assumed to remain isotropic, and the damage evolution is through the growth of the average crack size. Plasticity is considered through an additive decomposition of the total strain rate, and a rate-independent, von Mises model is used. The model was applied to simulate the response of a model material (SiC) under uniaxial strain loading. To further examine the behavior of the model, cyclic loading and large-strain compressive loading were considered. Numerical results of the model predictions are presented, and comparisons with those from a previous model are provided.     

On non-associative anisotropic finite plasticity fully coupled with isotropic ductile damage for metal forming

In this work, non-associative finite strain anisotropic elastoplasticity fully coupled with ductile damage is considered using a thermodynamically consistent framework. First, the kinematics of large strain based on multiplicative decomposition of the total transformation gradient using the rotating frame formulation, is recalled and different objective derivatives defined. By using different anisotropic equivalent stresses (quadratic and non-quadratic) in yield function and in plastic potential, the evolution equations for all the dissipative phenomena are deduced from the generalized normality rule applied to the plastic potential while the consistency condition is still applied to the yield function. The effect of the objective derivatives and the equivalent stresses (quadratic or non-quadratic) on the plastic flow anisotropy and the hardening evolution with damage is considered. Numerical aspects mainly related to the time integration of the fully coupled constitutive equations are discussed. Applications are made to the AISI 304 sheet metal by considering different loading paths as tensile, shear, plane tensile and bulge tests. For each loading path the effect of the rotating frame, the equivalent stress (quadratic or non-quadratic) and the normality rule (with respect to yield function or to the plastic potential) are discussed on the light of some available experimental results.     

Coupled viscoplasticity damage constitutive model for concrete materials

A coupled viscoplasticity damage constitutive model for concrete materials is developed within the framework of irreversible thermodynamics.Simultaneously the Helmholtz free energy function and a non-associated flow potential function are given, which include the internal variables of kinematic hardening,isotropic hardening and dam- age.Results from the numerical simulation show that the model presented can describe the deformation properties of the concrete without the formal hypotheses of yield criterion and failure criteria,such as the volume dilatancy under the compression,strain-rate sen- sitivity,stiffness degradation and stress-softening behavior beyond the peak stress which are brought by damages and fractures.Moreover,we could benefit from the application of the finite element method based on this model under complex loading because of not having to choose different constitutive models based on the deformation level.