RPC200塑性与各向异性损伤耦合本构建模研究

针对活性粉末混凝土 (RPC200:Reactive Powder Concrete 200MPa)的非线性行为,将连续损伤力学和塑性力学结合起来,建立了RPC200的弹塑性各向异性损伤耦合本构。在有效应力空间内,采用非关联流动法则和非均匀等向强化法则建立了RPC200的塑性本构。基于损伤能释放率建立了损伤准则,并由正交法则给出损伤演化法则,同时采用两个不同的损伤硬化法则来描述拉、压性能不同的损伤硬化。证明了该文所建模型与热动力学基本原理的相容性。最后,给出了RPC弹塑性各向异性损伤耦合本构模型数值计算流程,并以简单例证证明了所建模型的预测能力。     

A nonlocal continuum damage mechanics approach to simulation of creep fracture in ice sheets

We present a Lagrangian finite element formulation aimed at modeling creep fracture in ice-sheets using nonlocal continuum damage mechanics. The proposed formulation is based on a thermo-viscoelastic constitutive model and a creep damage model for polycrystalline ice with different behavior in tension and compression. In this paper, mainly, we detail the nonlocal numerical implementation of the constitutive damage model into commercial finite element codes (e.g. Abaqus), wherein a procedure to handle the abrupt failure (rupture) of ice under tension is proposed. Then, we present numerical examples of creep fracture under four-point bending, uniaxial tension, and biaxial tension in order to illustrate the viability of the current approach. Finally, we present simulations of creep crack propagation in idealized rectangular ice slabs so as to estimate calving rates at low deformation rates. The examples presented demonstrate the mesh size and mesh directionality independence of the proposed nonlocal implementation.     

A Plastic Damage Model with Stress Triaxiality-Dependent Hardening for Concrete

Emphases of this study were placed on the modelling of plastic damage behaviour of prestressed structural concrete, with special attention being paid to the stress-triaxiality dependent plastic hardening law and the corresponding damage evolution law. A definition of stress triaxiality was proposed and introduced in the model presented here. Drucker-Prager -type plasticity was adopted in the formulation of the plastic damage constitutive equations. Numerical validations were performed for the proposed plasticity-based damage model with a driver subroutine developed in this study. The predicted stress-strain behaviour seems reasonably accurate for the uniaxial tension and uniaxial compression compared with the experimental data reported in references. Numerical calculations of compressions under various hydrostatic stress confinements were carried out in order to validate the stress triaxiality dependent properties of the model.     

A continuous damage fracture model to predict formability of sheet metal

A continuous damage fracture model, which consists of a fracture criterion and a continuum damage constitutive law was proposed in this paper to calculate formability of sheet metal. In this model, an extension of the McClintock void growth model was selected as the fracture criterion to be incorporated with a coupled damage‐plasticity Gurson‐type constitutive law. Also, by introducing a Lode angle dependent parameter to define the loading asymmetry condition, the shear effect was phenomenologically taken into account. The proposed fracture model was implemented in user defined material subroutines in ABAQUS. The model was calibrated and correlated by the uniaxial tension, shear and notched specimens tests. Application of the fracture criterion for the Limit dome height tests was discussed and the simulation results were compared with the experimental data.     

Numerical model for CFRP confined concrete elements subject to monotonic and cyclic loadings

Uniaxial cyclic and monotonic compression tests were carried out on partially and fully wrapped concrete cylinders with Carbon Fibre Reinforced Polymer (CFRP) wet lay-up sheets. The influence of the concrete compressive strength, CFRP stiffness, geometric confinement arrangement and loading type on the compressive behaviour of reinforced concrete column elements of circular cross-section up to their failure was assessed. A uniaxial stress–strain constitutive model is proposed, and the results obtained from the experimental tests were used to calibrate some of the parameters of this model, and to appraise the model performance. This model allows the simulation of reinforced concrete members by using Timoshenko one-dimensional elements, in the context of the finite element method (fibre model). Good agreement was obtained between numerical simulations and experimental results for both monotonic and cyclic loading tests.     

Characterising fibre compression fracture toughness of composites using bearing tests

In this paper we propose the use of a bearing test with a coupled experimental–numerical approach to characterise the critical strain energy release rate, or “fracture toughness”, for fibre compression failure in bearing. This property is used in continuum damage mechanics (CDM) approaches for progressive failure analysis of composite laminates. In the proposed approach, experimental results for a standard bearing test are used to calibrate the fracture toughness with a progressive failure analysis using a CDM damage model. The approach is demonstrated for a plain weave carbon/epoxy material using the CDM damage model available in a commercial finite element package (Abaqus). The results indicate that the bearing test method provides a simple and convenient means of quantifying fibre compression fracture toughness. Analysis results applying the characterised value show good comparison with experimental results, and confirm the value of the bearing test as part of a novel material characterisation technique.     

砼受压损伤力学本构模型的研究

本文利用ＭＴＳ公司８１５．０２型电液伺服试验系统对砼进行了等应变速率加载控制的应力一应变全曲线试验，应用不可逆热力学和内变量理论的成果建立了砼损伤力学模型，并用概率统计的观点分析了损伤的演化规律。由于考虑了不可逆变形的影响，本文所建本构模型与实验吻合较好。     

CDM based modelling of damage and fracture mechanisms in concrete under tension and compression

Anisotropic damage evolution and crack propagation in the elastic–brittle materials is analysed by the concepts of continuum damage mechanics (CDM) and finite element method (FEM). The modified Murakami–Kamiya (MMK) model of elastic-damage material is used to describe damage anisotropy in concrete. The Helmholtz free energy representation is discussed. The unilateral crack opening/closure effect is incorporated in such a way that the continuity requirement during unloading holds. The incremental form of the stress–strain equations is developed. The general failure criterion is proposed by checking the positive definiteness of the Hessian matrix of the free energy function. The local approach to fracture (LAF) by FEM is applied to the pre-critical damage evolution that precedes the crack initiation, and the post-critical damage/fracture interaction. Crack is modelled as the assembly of failed finite elements in the mesh, the stiffness of which is reduced to zero when the critical points at stress–strain curves are reached. A concrete specimen with the pre-load, inclined crack is analysed in order to simulate different fracture mechanisms in tension or compression. The constitutive model is capable of predicting the kinked-type crack under tension and the wing-type crack under compression.     

混凝土弹塑性损伤帽盖模型参数确定研究

摘要:基于连续损伤力学和塑性力学理论形成的弹塑性损伤帽盖模型是一个高级混凝土本构关系模型,但模型涉及的参数过多却给运用造成了不便。本文对模型参数进行详细解释基础上,采用已有的混凝土材料试验数据给出了其子午线强度参数、帽盖参数、脆性损伤和延性损伤参数取值,大大方便了工程运用。最后以单轴拉伸和单轴压缩为例数值演示了模型基本力学特性。     

Damage model for concrete reinforced with sliding metallic fibers

This contribution presents an effective and practical three dimensional (3D) numerical model to predict the behaviour of concrete matrix reinforced with sliding metallic fibers. Considering fiber-reinforced concrete (FRC) as two-phase composite, constitutive behaviour laws of plain concrete and sliding metallic fibers were described first and then they were combined according to anisotropic damage theory to predict the mechanical behaviour of FRC. The behaviour law used for the plain concrete is based on damage and plasticity theories able to manage localized crack opening in 3D. The constitutive law of the action of sliding metallic fibers in the matrix is based on the effective stress carried by the fibers. This effective stress depends on a damage parameter related to on one hand, on the content and mechanical properties of fibers and on the other hand, on the fiber–matrix bond which itself depends on the localized crack opening. The proposed model for FRC is easy to implement in most of the finite element codes based on displacement formulation; it uses only measurable parameters like Young’s modulus, tensile and compressive strengths, fracture energies and strains at peak stress in tension and compression. A comparison between the experimental data and model results has been also provided in this paper.     

一个钢筋混凝土损伤塑性本构模型及工程应用

以ABAQUS大型程序为平台,采用应变协调假设和强度等效假设,给出了一个描述钢筋混凝土材料与结构损伤塑性分析的本构模型。这里的钢筋强化特性是通过定义强化了的拉伸塑性应力-应变曲线来实现的。模型中的钢筋不再以独立的金属材料形式出现,而是被等效钢筋混凝土代表体元模型包含进去了,用拉伸应力-应变曲线峰值后区的硬化-软化强度曲线直接定义强化功能。这个模型着重对ABAQUS软件中给出的损伤塑性模型的拉伸强化-软化阶段的特性进行了完善。采用试件受单向拉伸和简支梁受集中力载荷两个简单算例说明了模型的有效性。最后该研究将这个模型用于一个受地表堆积载荷、土压力和地下水压力联合作用下的钢筋混凝土墙体结构的ABAQUS有限元损伤塑性数值分析中。     

ABAQUS中混凝土本构模型用于模拟结构静力行为的比较研究

对大型通用有限元程序ABAQUS中的混凝土弥散开裂模型和塑性损伤模型进行了详细的介绍,包括单轴应力-应变关系、裂缝模型、屈服准则、流动法则和滞回规则等。然后对混凝土本构模型中影响结构构件静力行为的关键因素进行了详细的对比分析,并结合采用不同混凝土模型对钢筋混凝土构件和钢-混凝土组合结构构件的受力行为的模拟结果,指出了分析实际结构构件时不同混凝土材料本构模型的适用情况,可供研究设计参考。     

Gradient damage modeling of brittle fracture in an explicit dynamics context

In this contribution, we propose a dynamic gradient damage model as a phase‐field approach for studying brutal fracture phenomena in quasi‐brittle materials under impact‐type loading conditions. Several existing approaches to account for the tension–compression asymmetry of fracture behavior of materials are reviewed. A better understanding of these models is provided through a uniaxial traction experiment. We then give an efficient numerical implementation of the model in an explicit dynamics context. Simulations results obtained with parallel computing are discussed both from a computational and physical point of view. Different damage constitutive laws and tension–compression asymmetry formulations are compared with respect to their aptitude to approximate brittle fracture. Copyright © 2016 John Wiley & Sons, Ltd.     

Computational modelling of static indentation-induced damage in glass

The present paper is focused on the numerical simulation of a glass plate subjected to static indentation by a spherical indenter. For this purpose, a combined approach of continuum damage mechanics (CDM) and fracture mechanics is performed. Results provided by an axisymmetric finite element model were compared with analytical solutions. A CDM based constitutive model with an anisotropic damage tensor was selected and implemented into a finite element code to study the damage of glass. The numerical results were analysed through the framework of the stress and damage distribution. Various regions with critical damage values were therefore predicted in good agreement with the experimental observations in the literature. In these regions, the directions of crack propagation, including both cracks initiating on the surface as well as in the bulk, were predicted using the strain energy density factor. Predicted directions were found in good agreement with those experimentally obtained in the literature results.     

考虑材料组成特性的混凝土轴拉破坏过程细观数值模拟

为反映骨料、砂浆及其之间的界面过渡区的组合特点和材料性能,基于材料细观非均匀性和有限元方法的混凝土破坏过程细观数值模拟需进行复杂、细致的网格剖分,导致了繁重的前处理工作和可观的计算量。该文对混凝土材料细观单元材质组成的单一化假定进行改进,将内嵌界面过渡区材料的规则化单元视为一种广义复合材料单元,建立了复合型界面损伤模型。采用等效方法确定单元的复合弹性关系,通过有限元法计算单元的局部应力;用细观层次上弹性力学性能的弱化描述单元组成材料的损伤,混凝土材料的破坏过程通过单元各组分的损伤模拟。应用该复合型界面损伤模型研究了混凝土试件的单轴拉伸破坏过程,细观数值模拟结果符合混凝土试件的宏观破坏特征,表明该模型可作为分析混凝土材料破坏过程的一种有效途径。     

Hyper-elastic constitutive equations of conjugate stresses and strain tensors for the Seth-Hill strain measures

The use of hypo-elastic constitutive equations for large strains in nonlinear finite element applications usually requires special considerations. For example, the strain does not tend to zero upon unloading in some elastic loading-unloading closed cycles. Furthermore, these equations are based on objective material time rate tensors, which require incrementally objective algorithms for numerical applications and integration. Hyper-elastic constitutive equations on the other hand do not require such considerations. However, their behaviour for large elastic strains is important and may differ in tension and compression. In the present work, Hyper-elastic constitutive equations for the Seth-Hill strains and their conjugate stresses are explored as a natural generalisation of Hook’s law for finite elastic deformations. Based on the uniaxial and simple shear tests, the response of the material for different constitutive equations is examined. Together with an objective rate model, the effect of different constitutive laws on Cauchy stress components is compared. It is shown that the constitutive equation based on logarithmic strain and its conjugate stress gives results closer to that of the rate model. In addition, the use of Biot stress-strain pairs for a bar element results in an elastic spring which obeys the Hook’s law even for large deformations and has the same behaviour in both tension and compression. The effect of the constitutive equation on the volume change of the material has also been considered here.     

Large strain constitutive modelling and computation for isotropic,creep elastoplastic damage solids

A three-dimensional fully coupled creep elastoplastic damage model at finite strain for isotropic non-linear material is developed. The model is based on the thermodynamics of an irreversible process and the internal state variable theory. A hyperelastic form of stress–strain constitutive relation in conjunction with the multiplicative decomposition of the deformation gradient into elastic and inelastic parts is employed. The pressure-dependent plasticity with strain hardening and the damage model with two damage internal variables are particularly considered. The rounding of stress–strain curves appearing in cycling loading is reproduced by introduction of the creep mechanism into the model. A numerical integration procedure for the coupled constitutive equations with three hierarchical phases is proposed. A consistent tangent matrix with consideration of the fully coupled effects at finite strain is derived. Numerical examples are tested to demonstrate the capability and performance of the present model at large strain.     

Modelling of concrete behaviour in uniaxial compression and tension with DEM

The paper focuses on the DEM modelling of the behaviour of plain concrete during uniaxial compression and uniaxial tension using the discrete element method. The model takes into account the concrete heterogeneity at the meso-scale level. The effects of concrete density, size of aggregate grains and specimen size on the stress–strain curve, volume changes and fracture process are studied. In addition, the evolution of contact forces, grain rotations, displacement fluctuations and strain localization during deformation is investigated. The elastic, kinetic, plastic and numerical dissipated energy is calculated and analysed at a different stress–strain stage. Concrete is described as a 1-phase or 3-phase material. The macroscopic 2D and 3D results are compared with the corresponding experiments. A satisfactory agreement between experiments and calculations is achieved.

     

单向受拉状态下的钢纤维混凝土本构模型

在混凝土中添加随机分布的钢纤维能有效提高混凝土力学性能。为了更好地考虑纤维对单向受拉状态下钢纤维混凝土（SFRC）的增强作用，提出一个钢纤维混凝土的弥散开裂本构模型。在弹性阶段，纤维混凝土被视为简单复合材料，基于两相复合材料理论，对SFRC的弹性刚度矩阵进行修正；在受拉开裂后，混凝土的塑性变形量被视为纤维与混凝土界面脱粘过程中滑移量，利用粘结滑移模型计算纤维在混凝土开裂面上的桥接作用。该文通过有限元软件ABAQUS中子程序二次开发接口Umat，进行Fortran编程，在ABAQUS中实现该本构模型。通过数值模拟结果与受拉实验数据进行对比，验证了该本构模型的准确性。通过数值模拟分析，进一步探究钢纤维混凝土相关参数对抗拉性能的影响，为钢纤维混凝土在实际的工程中的应用提供建议。     

基于连续介质损伤力学的复合材料层合板低速冲击损伤模型

基于连续介质损伤力学（CDM）方法,建立了分析复合材料层合板低速冲击问题的三维数值模型。该模型考虑了层内损伤（纤维和基体损伤）、层间分层损伤和剪切非线性行为,采用最大应变失效准则预测纤维损伤的萌生,双线性损伤本构模型表征纤维损伤演化,基于物理失效机制的三维Puck准则判断基体损伤的起始,根据断裂面内等效应变建立混合模式下基体损伤扩展准则。横向基体拉伸强度和面内剪切强度采用基于断裂力学假设的就地强度（in-situ strength）。纤维和基体损伤本构关系中引入单元特征长度,有效降低模型对网格密度的依赖性。层间分层损伤情况由内聚力单元（cohesive element）预测,以二次应力准则为分层损伤的起始准则,B-K准则表征分层损伤演化。分别通过数值分析方法和试验研究方法对复合材料典型铺层层合板四级能量低速冲击下的冲击损伤和冲击响应规律进行分析,数值计算和试验测量的接触力-时间曲线、分层损伤的形状和面积较好吻合,表明该模型能够准确地预测层合板低速冲击损伤和冲击响应。