A constitutive model for orthotropic elasto-plasticity at large strains

Summary The paper presents a thermodynamically consistent constitutive model for elasto-plastic analysis of orthotropic materials at large strain. The elastic and plastic anisotropies are assumed to be persistent in the material but the anisotropy axes can undergo a rigid rotation due to large plastic deformations. The orthotropic yield function is formulated in terms of the generally nonsymmetric Mandel stress tensor such that its skew-symmetric part is additionally taken into account. Special attention is focused on the convexity of the yield surface resulting in the nine-dimensional stress space. Of particular interest are new convexity conditions which do not appear in the classical theory of anisotropic plasticity. They impose additional constraints on the material constants governing the plastic spin. The role of the plastic spin is further studied in simple shear accompanied by large elastic and large plastic deformations. If the plastic spin is neglected, the shear stress response is characterized by oscillations with an amplitude strictly dependent on the degree of the plastic anisotropy.accepted for publication 2 March 2004     

A numerical model for reinforced concrete structures

This paper describes a two-dimensional approach to model fracture of reinforced concrete structures under (increasing) static loading conditions. The first part is dedicated to the concrete material. The concrete is described in compression by a non-local isotropic damage constitutive law. In tension, a fictitious crack/crack band model is proposed. The influence of biaxial stress states is incorporated in the constitutive relations. In the second part a bond model is described. It accounts for different failure mechanisms, a pullout failure and a splitting failure. This approach is applied to prestressed concrete beams with different failure mechanisms. The numerical results are compared to experimental data and show good agreement.     

Homogenised constitutive model coupling damage and debonding for reinforced concrete structures under cyclic solicitations

A new stress resultant constitutive model for reinforced concrete plates under cyclic solicitations is presented. This model is built by the periodic homogenisation approach using the averaging method and couples damage of concrete and periodic debonding between concrete and steel rebar. In one-dimensional situations, we derive a closed-form solution of the local problem useful to verify and set up the plate problem. The one dimensional macroscopic constitutive model involves a limited number of parameters, the sensibility of which is studied. Comparison to experimental results underlines the pertinence of the model by considering internal debonding in order to properly represent the mechanical dissipation occurring during cyclic loadings on reinforced concrete panels.     

A fracture model of reinforced concrete

Analyzed in this work is the failure mechanism of unidirectionally reinforced concrete under general stress state. The fracture process is described analytically by establishing the relation between loading and damage that involves the constitutive parameters of the reinforced concrete. Taken into account are the stiffnesses of mortar and reinforcement, bond strength of interface and mortar fracture toughness. An estimate on the ultimate strength is made with results given to the shear strength of a concrete slab.     

A two-dimensional,higher-order,elasticity-based micromechanics model

A new, two-dimensional (2D) homogenization theory is proposed. The theory utilizes a higher-order, elasticity-based cell model (ECM) analysis. The material microstructure is modeled as a 2D periodic array of unit cells where each unit cell is discretized into four subregions (or subcells). The analysis utilizes a (truncated) eigenfunction expansion of up to fifth order for the displacement field in each subcell. The governing equations for the theory are developed by satisfying the pointwise governing equations of geometrically linear continuum mechanics exactly up through an order consistent with the order of the subcell displacement field. The formulation is carried out independently of any specified constitutive models for the behavior of the individual phases (in the sense that the general governing equations hold for any constitutive model). The fifth order theory is subsequently specialized to a third order theory. Additionally, the higher order analyzes reduce to a theory equivalent to the original 2D method of cells (MOC) theory when all higher order terms are eliminated. The proposed 2D theory is the companion theory to an equivalent 3D theory [T.O. Williams, A three-dimensional, higher-order, elasticity-based micromechanics model, Int. J. Solids Struc., in press].Comparison of the predicted bulk and local responses with published results indicates that the theory accurately predicts both types of responses. The high degree of agreement between the current theory results and published results is due to the correct incorporation of the coupling effects between the local fields.The proposed theory represents the necessary theoretical foundations for the development of exact homogenization solutions of generalized, two-dimensional microstructures.     

A three-dimensional,higher-order,elasticity-based micromechanics model

The three-dimensional (3D) version of a new homogenization theory [A Two-Dimensional, Higher-Order, Elasticity-Based Micromechanics Model, in print] is presented. The 3D theory utilizes a higher-order, elasticity-based cell model (ECM) analysis for a periodic array of 3D unit cells. The unit cell is discretized into eight subregions or subcells. The displacement field within each subcell is approximated by a (truncated) eigenfunction expansion of up to fifth order. The governing equations are developed by satisfying the pointwise governing equations of geometrically linear continuum mechanics exactly up through the given order of the subcell displacement fields. The specified governing equations are valid for any type of constitutive model used to describe the behavior of the material in a subcell. The specialization of the theory to lower orders and to two-dimeinsions (2D) and to the exact one-dimensional (1D) theory is discussed.Since the proposed 3D homogenization theory correctly reduces to both 2D and 1D the validation process applied to the 2D theory [A Two-Dimensional, Higher-Order, Elasticity-Based Micromechanics Model, in print] directly applies to the current formulation. Additional comparisons of the predicted responses obtained from the 3D ECM theory with existing published results are conducted. The good agreement obtained shows that the current theory represents a viable 3D homogenization tool. The improved agreement between the current theory results and published results as compared to the comparison of the MOC results and the published results is due to the correct incorporation of the coupling effects between the local fields. Additional results showing the convergence behavior of the average fields as a function of the order of the analysis is presented. These results show that the 1st order theory may not accurately predict the local averages but that consistent and converged behavior is obtained using the higher order ECM theories.The proposed theory represents the necessary theoretical foundations for the development of exact homogenization solutions of generalized, three-dimensional microstructures.     

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。     

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。     

A new higher-order elastoplastic beam model for reinforced concrete

Meccanica - The present paper introduces a new elastoplastic beam model for reinforced concrete based on a higher-order beam model previously developed (Int J Numer Methods Eng....     

钢筋混凝土开裂角软化薄膜模型

开裂角介于固定角和转动角之间,是裂缝实际的开展方向角.通过建立平衡方程、协调方程、钢筋和混凝土本构方程、泊松比效应系数方程,提出了钢筋混凝土开裂角软化薄膜模型,该模型考虑了拉应变与压应变的相互作用.本文还给出从应力到应变的计算方法,与传统从应变到应力的计算方法相比,该方法无须进行反复试算,计算简便.通过与8块钢筋混凝土薄板试验结果的比较,验证了所提出开裂角软化薄膜模型及其算法的正确性.     

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。

     

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.     

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.     

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 smeared / layered reinforced concrete model for finite element analysis

A new reinforced concrete model, in which the reinforcement steel is assumed as smeared / layered in concrete, is established and installed into a currently used finite element code for nonlinear analysis. It performs the nonlinear behaviors of both concrete and the reinforcement steel. The results of examples are in good agreement with the experimental data.     

混凝土的一种标量损伤弹塑性本构模型

荷载作用下材料性能的劣化是混凝土结构的微观损伤机理,其宏观表现为结构刚度的折减和承载力的降低。论文推导了基于不可逆热力学过程的弹塑性标量损伤本构,给出时间离散的屈服准则。采用基于向后Euler法的应力更新算法——两步图形返回的最近点投影法,推导了满足迭代结果收敛假设的塑性参数及算法刚度张量,给出了空间梁单元本构积分算法的Jacobi矩阵。将模型用于混凝土简支梁的承载力试验模拟,与计算数据对比表明了模型和算法的合理性和有效性。     

冲击荷载作用下混凝土材料的细观本构模型

将混凝土材料看成是水泥砂浆基体和粗骨料颗粒组成的2相复合材料,假设水泥砂浆基体和粗骨料颗粒均为弹性、均匀、各向同性的,粗骨料颗粒为球形。基于Mori-Tanaka理论和Eshelby 等效夹杂理论推出了混凝土材料弹性模量的计算公式。在Horii和Nemat-Nasser提出的脆性材料在双轴向压应力作用下破坏的滑移裂纹模型基础上,运用细观力学方法推导了微裂纹对材料弹性模量的弱化作用以及微裂纹的损伤演化方程。建立了混凝土材料在冲击荷载作用下的一维动态本构模型,模拟曲线与实验曲线符合良好,因而可以用该模型模拟混凝土材料在冲击荷载下的动态特性。     

钢筋混凝土结构改进型分离式数值模型

提出一种考虑粘结滑移效应的钢筋混凝土改进型分离式数值模型。在混合物理论基础上,该模型兼顾混凝土基体和钢筋的力学行为,且基于钢筋混凝土界面粘结滑移模型,获得了钢筋等效模型。改进型分离式数值模型由于对钢筋及其界面无显式离散要求,使得钢筋的运用完全独立于其几何形状,同时对混凝土网格没有约束,并且不增加计算成本,因此该模型可适用于钢筋混凝土宏观结构层面分析。通过钢筋混凝土构件-结构的爆炸实验,对改进型分离式数值模型进行层次化验证。对比结果表明,考虑粘结滑移效应的有限元模型能够更好地预测钢筋混凝土结构的宏观力学行为。     

钢筋混凝土桥墩弯剪数值分析模型

基于修正的压力场理论MCFT(The Modified Compression Field Theory)和纤维单元模型建立了钢筋混凝土桥墩的弯剪数值分析模型,以MCFT理论确定桥墩的剪切力-剪切位移关系,并与考虑桥墩弯曲变形的纤维单元模型组合,共同考虑桥墩的弯-剪-轴力耦合作用.通过与六个弯剪破坏控制的圆形截面钢筋混凝土桥墩拟静力试验结果的对比,对分析模型进行了验证.主要认识结论为基于MCFT理论可准确地计算弯剪破坏桥墩的屈服荷载、极限荷载和弹性阶段剪切刚度,剪切开裂是引起钢筋混凝土构件剪切力-剪切位移关系刚度突变的主要因素,而弯曲开裂与纵筋屈服对刚度的影响较小;分析模型对弯剪破坏桥墩的滞回曲线、弯曲与剪切变形成分均进行了较为准确的模拟分析.