考虑损伤效应的正交各向异性板的弹塑性静动力分析

基于弹塑性力学和损伤理论,建立了一个与应力球张量有关的正交各向异性材料的混合硬化屈服准则,该准则无量纲化后与各向同性材料的Mises准则同构,进而建立了混合硬化正交各向异性材料的增量型弹塑性损伤本构方程和损伤演化方程.基于经典Kirchhoff板理论,获得了正交各向异性薄板的增量型运动控制方程,且采用有限差分法和迭代法进行求解.数值算例中,讨论了损伤演化、外载荷参数等因素对正交各向异性薄板弹塑性静动力性质的影响,数值结果表明,考虑结构的损伤和损伤演化时,结构的力学性质将发生显著的变化.     

准脆性材料的弹塑性各向异性损伤耦合本构模型研究

针对准脆性材料的非线性特征：强度软化和刚度退化、单边效应、侧限强化和拉压软化、不可恢复变形、剪胀及非弹性体胀，在热动力学框架内，建立了准脆性材料的弹塑性与各向异性损伤耦合的本构关系。对准脆性材料的变形机理和损伤诱发的各向异性进行了诠释，并给出了损伤构形和有效构形中各物理量之间的关系。在有效应力空间内，建立了塑性屈服准则、拉压不同的塑性随动强化法则和各向同性强化法则。在损伤构形中，采用应变能释放率，建立了拉压损伤准则、拉压不同的损伤随动强化法则和各向同性强化法则。基于塑性屈服准则和损伤准则，构建了塑性势泛函和损伤势泛函，并由正交性法则，给出了塑性和损伤强化效应内变量的演化规律，同时，联立塑性屈服面和损伤加载面，给出了塑性流动和损伤演化内变量的演化法则。将损伤力学和塑性力学结合起来，建立了应变驱动的应力-应变增量本构关系，给出了本构数值积分的要点。以单轴加载-卸载往复试验识别和校准了本构材料常数，并对单轴单调试验、单轴加载-卸载往复试验、二轴受压、二轴拉压试验和三轴受压试验进行了预测，并与试验结果作了比较，结果表明，所建本构模型对准脆性材料的非线性材料性能有良好的预测能力。     

具确定弱区域正交各向异性薄板的弹塑性屈曲分析

基于弹塑性力学和损伤理论,建立了一个与应力球张量有关的具损伤正交各向异性材料的混合硬化屈服准则,该准则无量纲化后与各向同性材料的Mises准则同构,在此基础上,建立了正交各向异性材料的增量型和全量型弹塑性损伤本构方程,并以具确定弱区域正交各向异性矩形薄板为例,根据屈曲时的能量准则和全量理论,以等效塑性应变为内变量,对其弹塑性屈曲问题进行了分析,讨论了几何参数和弱区域对正交各向异性薄板弹塑性屈曲临界应力的影响.     

考虑晶体滑移面分解正应力的细观损伤模型

材料内部的解理、滑移面剥离等细观损伤是引起宏观失效的根源, 从细观尺度研究损伤的发生和发展有助于深入认识材料的变形和失效过程. 本文基于晶体塑性理论, 从滑移系的受力和变形出发研究材料的细观损伤, 建立了考虑滑移面分解正应力的细观损伤模型, 为晶体材料解理断裂的分析提供了新方法. 首先, 在晶体弹塑性变形构型的基础上引入损伤变形梯度张量的概念, 从变形运动学着手建立了考虑损伤能量耗散的本构方程, 并推导了塑性流动方程与损伤演化方程; 然后, 建立了相应的数值计算方法, 给出了应力与状态变量的更新算法, 推导了Jacobian矩阵的表达式; 接着, 以$[100]$取向的单晶铜材料为例, 通过有限元计算与试验结果的对比, 并采用粒子群优化算法标定了11个材料细观参数; 最后, 将所提细观损伤模型应用于RVE单轴拉伸过程的模拟, 得到了考虑损伤影响的应力应变曲线, 并分析了材料的塑性流动与损伤演化过程. 结果表明, 本文所提模型能够计算材料在受载过程中的损伤累积效应, 合理反映晶体材料的细观损伤机理.      

耦合蠕变损伤的Chaboche粘塑性模型的研究

Chaboche粘塑性统一本构模型由于没有包含损伤变量,在应力恒定时只能得到不变的塑性应变速率,因此不能描述蠕变第三阶段的加速过程.该文按照Lemaitre有效应力的概念,采用Kachanov损伤演化方程,推导了耦合损伤的Chaboche粘塑性流动方程和硬化方程,并链接到有限元软件ANSYS中,将之用于高温合金钢P91的蠕变寿命计算,结果表明耦合损伤模型的模拟值与实验数据基本吻合;为该模型描述蠕变损伤和疲劳交互作用奠定了基础.     

基于介观力学信息的颗粒材料损伤——愈合与塑性宏观表征

本文在二阶计算均匀化框架下提出了颗粒材料损伤--愈合与塑性的多尺度表征方法. 颗粒材料结构在宏观尺度模型化为梯度Cosserat连续体,在其有限元网格的每个积分点处定义具有离散颗粒介观结构的表征元. 建立了表征元离散颗粒系统的非线性增量本构关系. 表征元周边介质作用于表征元边界颗粒的增量力与增量力偶矩以表征元边界颗粒的增量线位移与增量转动角位移、当前变形状态下表征元离散介观结构弹性刚度、以及凝聚到表征元边界颗粒的增量耗散摩擦力表示. 基于平均场理论与Hill定理,导出了基于介观力学信息的梯度Cosserat连续体增量非线性本构关系. 在等温热动力学框架下定义了表征颗粒材料各向异性损伤--愈合和塑性的损伤、愈合张量因子与综合损伤、愈合效应的净损伤张量因子和塑性应变. 此外,定义了损伤和塑性耗散能密度与愈合能密度,以定量比较材料损伤、愈合、塑性对材料失效的效应. 应变局部化数值例题结果显示了所建议的颗粒材料损伤--愈合--塑性表征方法的有效性.      

材料变形及损伤演化的微观物理动力机理

利用微观物理动力学对材料变形及损伤的演化进行了研究。探讨现有的简单应力状态及复杂应力状态的模型之间的内在联系，研究了损伤对材料变形及损伤演化的影响，得到了在考虑损伤时材料的变形及损伤的近似演化方程，该文研究表明微观物理动力学对描述材料的变形及损伤具有广泛可能性。     

正交各向异性材料的弹塑性损伤本构关系

基于弹塑性力学和损伤理论，建立了一个与应力球张量有关的正交各向异性材料的混合 硬化屈服准则，该准则无量纲化后与各向同性材料的Mises准则同构，在此基础上，进而建 立了混合硬化正交各向异性材料的增量型弹塑性损伤本构方程，并以具局部损伤的正交各向 异性矩形薄板为例，采用Galerkin法和迭代法，对其弹塑性屈曲问题进行了分析，讨论了局 部损伤对正交各向异性矩形薄板弹塑性屈曲临界应力的影响.     

考虑温度效应的弹性损伤一般理论

现有的各种损伤理论基本上都是关于等温问题的 ,且在不同程度上依赖于某些经验假设。本文在严格的不可逆热力学理论基础之上 ,建立了考虑温度效应的弹性损伤一般理论。推导出热弹性各向同性与各向异性损伤材料全部本构方程的一般形式 ,其中包括应力 应变关系、熵密度方程、损伤对偶张量表达式、热 固 损伤耦合的热传导方程和损伤演化方程。它们的特殊形式包含了等温各向同性与各向异性弹性损伤的本构方程     

含损伤材料的热粘塑性本构关系和柱壳破裂研究

以含内变量的本构关系理论为基础 ,结合材料损伤演化方程 ,并考虑了温度和损伤对材料参数的影响 ,得到了增量形式的热粘塑性本构关系的普适显式表达式。然后使用Bodner幂函数型粘塑性模型 ,具体推导了其增量形式的热粘塑性本构方程。接着结合在实践中有重要意义的内部爆炸载荷作用下的柱壳破裂问题 ,建立了含损伤热粘塑性柱壳破裂问题的完备方程组 ,使用有限差分方法 ,完成了对问题的数值模拟 ,并对结果进行了分析。计算结果与实验结果符合良好。     

基于正则结构的各向异性损伤演化律

在Rice的正则结构框架下，推导出基于共轭力的各向异性损伤演化律。其中损伤变量采用二阶裂隙张量，它是固体内微裂纹的一个宏观测度。推导过程不涉及自由能的具体形式，主要结果包括损伤势函数及演化方程的解析表达式。在唯象的损伤力学模型里，损伤演化方程经常以唯象方程的形式出现。研究了唯象方程成立的条件及损伤特征张量的解析表达式。引入了广义裂隙张量及脆性指数的概念，并介绍了它们的作用和意义。     

Anisotropic damage–plasticity model for concrete

A material model for concrete is proposed here within the framework of a thermodynamically consistent elasto-plasticity–damage theory. Two anisotropic damage tensors and two damage criteria are adopted to describe the distinctive degradation of the mechanical properties of concrete under tensile and compressive loadings. The total stress tensor is decomposed into tensile and compressive components in order to accommodate the need for the above mentioned damage tensors. The plasticity yield criterion presented in this work accounts for the spectral decomposition of the stress tensor and allows multiple hardening rules to be used. This plastic yield criterion is used simultaneously with the damage criteria to simulate the physical behavior of concrete. Non-associative flow rule for the plastic strains is used to account for the dilatancy of concrete as a frictional material. The thermodynamic Helmholtz free energy concept is used to consistently derive dissipation potentials for damage and plasticity and to allow evolution laws for different hardening parameters. The evolution of the two damage tensors is accounted for through the use of fracture-energy-based continuum damage mechanics. An expression is derived for the damage–elasto-plastic tangent operator. The theoretical framework of the model is described here while the implementation of this model will be discussed in a subsequent paper.     

A new damage model for microcrack-weakened brittle solids

In the present paper, a micromechanically based damage model for microcrack-weakened solids is developed. The concept of the domain of microcrack growth (DMG) is defined and used to describe the damage state and the anisotropic properties of brittle materials. After choosing an appropriate fracture criterion of microcrack, we obtain the analytical expression of DMG under a monotonically increasing proportional plane stress. Under a complex loading path, the evolution equation of DMG and the overall effective compliance tensor of damaged materials are given. The project supported by National Natural Science Foundation of China     

弹脆性材料的损伤本构关系及应用

本文根据连续损伤力学方法,对弹脆性材料损伤的力学响应进行一般分析。理论分析中,材料与损伤都是各向异性的。还导出了计算损伤张量、有效弹性张量、真实应力张量以及损伤能耗率张量的实用表达式。     

Anisotropic damage law of evolution

A formulation for anisotropic damage is established in the framework of the principle of strain equivalence. The damage variable is still related to the surface density of microcracks and microvoids and, as its evolution is governed by the plastic strain, it is represented by a second order tensor and is orthotropic. The coupling of damage with elasticity is written through a tensor on the deviatoric part of the energy and through a scalar taken as its trace on the hydrostatic part. The kinetic law of damage evolution is an extension of the isotropic case. Here, the principal components of the damage rate tensor are proportional to the absolute value of principal components of the plastic strain rate tensor and are a nonlinear function of the effective elastic strain energy. The proposed damage evolution law does not introduce any other material parameter. Several series of experiments on metals give a good validation of this theory. The coupling of damage with plasticity and the quasi-unilateral conditions of partial closure of microcracks naturally derive from the concept of effective stress. Finally, a study of strain localization makes it possible to determine the critical value of the damage at mesocrack initiation.     

Modeling of deformation induced anisotropy in free-end torsion

The main purpose of this work is to develop a phenomenological model, which accounts for the evolution of the elastic and plastic properties of fcc polycrystals due to a crystallographic texture development and predicts the axial effects in torsion experiments. The anisotropic portion of the effective elasticity tensor is modeled by a growth law. The flow rule depends on the anisotropic part of the elasticity tensor. The normalized anisotropic part of the effective elasticity tensor is equal to the 4th-order coefficient of a tensorial Fourier expansion of the crystal orientation distribution function. Hence, the evolution of elastic and viscoplastic properties is modeled by an evolution equation for the 4th-order moment tensor of the orientation distribution function of an aggregate of cubic crystals. It is shown that the model is able to predict the plastic anisotropy that leads to the monotonic and cyclic Swift effect. The predictions are compared to those of the Taylor–Lin polycrystal model and to experimental data. In contrast to other phenomenological models proposed in the literature, the present model predicts the axial effects even if the initial state of the material is isotropic.     

A physically motivated anisotropic tensorial representation of damage with separate functions for void nucleation,growth, and coalescence

A phenomenological anisotropic damage progression formulation for porous ductile metals with second phases is described through mechanisms of void nucleation, growth and coalescence. The model is motivated from fracture mechanisms and microscale physical observations. To describe the creation of new pores, the decohesion at the particle–matrix interface and the fragmentation of second phase particles, the void-crack nucleation equation is related to several microstructural parameters (fracture toughness, length scale parameter, particle size, volume and fraction of second phase), the plastic strain level, and the stress state. Nucleation is represented by a general symmetric second rank tensor, and its components are proportional to the absolute value of the plastic strain rate components. Based on the Rice and Tracey model, void growth is a scalar function of the trace of damage tensor and the positive triaxiality. Like nucleation, coalescence is a second rank tensor governed by the plastic strain rate tensor and the stress state. The coalescence threshold is related to the void length scale for void impingement and void sheet mechanisms. The coupling of damage with the Bammann–Chiesa–Johnson (BCJ) plasticity model is written in the thermodynamic framework and derives from the concept of effective stress assuming the hypothesis of energy equivalence. A full-implicit algorithm is used for the stress integration and the determination of the consistent tangent operator. Finally, macroscale correlations to cast A356 AL alloy and wrought 6061-T6 AL alloy experimental data are completed with predictive void-crack evolution to illustrate the applicability of the anisotropic damage model.     

Elasto-plastic postbuckling of damaged orthotropic plates

Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionless form is isomorphic with the Mises criterion for isotropic materials. Furthermore, the incremental elasto-plastic damage constitutive equations and damage evolution equations are established. Based on the classical nonlinear plate theory, the incremental nonlinear equilibrium equations of orthotropic thin plates considering damage effect are obtained, and solved with the finite difference and iteration methods. In the numerical examples, the effects of damage evolution and initial deflection on the elasto-plastic postbuckling of orthotropic plates are discussed in detail.     

On a finite-strain viscoplastic law coupled with anisotropic damage: theoretical formulations and numerical applications

Based on a dissipation inequality at finite strains and the effective stress concept, a Chaboche-type infinitesimal viscoplastic theory is extended to finite-strain cases coupled with anisotropic damage. The anisotropic damage is described by a rank-two symmetric tensor. The constitutive law is formulated in the corotational material coordinate system. Thus, the evolution equations of all internal variables can be expressed in terms of their material time derivatives. The numerical algorithm for implementing the material model in a finite element programme is also formulated, and several numerical examples are shown. Comparing the numerical simulations with experimental observations indicates that the present material model can describe well the primary, secondary and tertiary creep. It can also predict the anisotropic damage modes observed in experiments correctly.