弹塑性耦合张量的宏细观对耦形式

依据弹塑性耦合问题的不同类型，应用广义正交原理，在应变空间上推导出已知宏、细观形变规律情况下两种不同形式的弹塑性耦合张量理论表达式及其显形式。该两类弹塑性耦合张量作为宏、细观的对耦形式可应用于体胞模型的损伤力学理论分析与数值计算。     

弹塑性耦合张量的宏细观对偶形式

依据弹塑性耦合问题的不同类型，应用广义正交原理，在应变空间上推导出已知宏、细观形变规律情况下两种不同形式的弹塑性耦合张量理论表达式及其显形式。该两类弹塑性耦合张量作为宏、细观的对耦形式可应用于体胞模型的损伤力学理论分析与数值计算。     

增量型各向异性损伤理论与数值分析

考虑到目前各向异性损伤理论存在一些不足,该文在增量型各向异性损伤理论的框架下,引入二阶对称张量,构造四阶对称有效损伤张量,建立了有效应力方程．类似于塑性流动分析方法,定义了增量弹性应力．应变关系．利用von Mises塑性屈服准则,并考虑各向异性损伤效应,推导出四阶对称的弹．塑性变形损伤刚度张量,其对称性反映了材料的固有特性．根据物体的变形和现时损伤状态,构造了材料损伤演化方程,方程中各项具有明确的物理意义．通过对A12024-T3金属薄板单向拉伸的有限元分析,确定了损伤演化参数,验证了损伤演化方程的正确性．此外还对含孔口薄板做有限元模拟,讨论了反力—位移曲线的变化规律以及它所揭示变形性质,给出了损伤场的分布规律。     

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     

偏心环空层流螺旋流速度的近似解析解

本文分析计算了石油钻井工程偏心环空中内管转动的螺旋流动。将偏心环空的三维流动简化为环空薄层内的二维流动，从黎曼空间曲面张量表达的动量方程出发，求得了偏心环空层流螺旋流动速度的近似解析解，用此方程的同心环空表达式与精确解比较，精度较高。     

极分解的一类近似计算与比较

基于级数展开给出了极分解中右伸长张量 的级数表示,通过对级数的项的选取得到右伸长张量的不同近似表达式。针对不同级数展开表示,得到表达式最小误差的级数展开形式。进而结合一些简单实例,验证误差了近似公式的有效性。最后与黄模佳等关于计算右伸长张量 和转动张量 的近似表达式进行了比较,本文的级数展开方式得到的右伸长张量 和转动张量 的近似表达式不但简洁,而且计算精度更高、适用范围更广。     

裂隙岩体损伤局部化破坏分岔模型及其应用

采用概率统计方法分析节理裂隙岩体的几何特征，定义了反映裂隙岩体几何特征的组构张量．基于不可逆热力学理论，通过裂纹扩展的细观分析，得出了损伤的发展机理和演化方程，把损伤演化和裂隙的几何特征的变化联系起来，建立了弹塑性损伤本构关系．为分析含有节理裂隙岩体在发生局部化破坏时的特征，通过对发生局部化时的裂隙岩体的分析。构造了适用于节理裂隙岩体局部化分析的不连续分岔模型．利用非线性规划数值解法，可以得出局部化破坏的方向特征．在有限元方法中，根据该模型给出了节理裂隙岩体相关的算例，分析表明该模型用于分析裂隙岩体的局部化破坏是有效的．     

损伤体有效弹性性质的细观分析和不变性描述—— 一个考虑微缺陷相互作用的一般理论模式

通过引进微缺陷相互作用张量，建立了一个二维情况下考虑微缺陷（微裂纹或微孔洞）间相互作用的损伤固体有效弹性性质的一般理论模式模型中考虑了微缺陷的几何形状、取向分布和空间分布所造成的有效柔度张量的各向异性和材料中微缺陷之间的相互作用所引起的损伤柔度张量的高阶效应针对微椭圆孔、微圆孔和微裂纹问题，求得了相互作用张量的解析形式     

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。     

高应变率下延性多孔介质中孔洞的动态演化

本文提出了一个新的材料延性动态损伤模型，模型中不但包括了率效应，同时还考虑了惯性效应，孔洞表面能变化和材料硬化对孔洞演化的影响。此外，在模型中同时考虑了体应力和偏应力对孔洞演化的作用，从孔洞演化方程地接到了孔洞增长和压缩应力临界表达式，Ｃａｒｒｏｌｌ和Ｈｏｌｔ结果作为该表达式的一个特例而得出，模型的数值分析得出以下结论：①延性孔洞的动太增长对率效应十分敏感，应变率越高，孔洞增长越快；②惯性效应在主     

Damage theory of materials with microstructure

A new form of damage theory of materials is proposed, that is valid for the case of nonconservative stresses. The partial entropy, strain and microstructure parameters are taken as the state variables. Without assuming the free energy to be a state function, the basic governing equations are derived. According to the balance of released and dissipated energy, the general form of damage evolution equation is obtained. Further, assuming the existence of independent damage mechanisms, the normality of damage evolution equation is proven. The generalized damage variables are discussed. Finally, some examples are given to show the applications of the theory. Projects Sponsered by the Joint Seismological Science Foundation.     

First-order gradient damage theory

Taking the strain tensor, the scalar damage variable, and the damage gradient as the state variables of the Helmholtz free energy, the general expressions of the firstorder gradient damage constitutive equations are derived directly from the basic law of irreversible thermodynamics with the constitutive functional expansion method at the natural state. When the damage variable is equal to zero, the expressions can be simplified to the linear elastic constitutive equations. When the damage gradient vanishes, the expressions can be simplified to the classical damage constitutive equations based on the strain equivalence hypothesis. A one-dimensional problem is presented to indicate that the damage field changes from the non-periodic solutions to the spatial periodic-like solutions with stress increment. The peak value region develops a localization band. The onset mechanism of strain localization is proposed. Damage localization emerges after damage occurs for a short time. The width of the localization band is proportional to the internal characteristic length.     

A Formulation of Anisotropic Elastic Damage Using Compact Tensor Formalism

An anisotropic elastic-damage model for initially-isotropic materials is presented. The model is based on a pseudo-logarithmic second-order damage tensor rate. To derive the complete expression of the tangent stiffness entering the rate constitutive law, various tensor operations and derivatives of tensor functions must be developed. Such derivations have been performed in compact form. Some useful tensor derivatives and a table of tensor algebra operations are given in Appendix. This note should interest engineering researchers involved in the development of constitutive models through tensor formalism. This revised version was published online in July 2006 with corrections to the Cover Date.     

Load-induced oriented damage and anisotropy of rock-like materials

Theoretical model for deformability of brittle rock-like materials in the presence of an oriented damage of their internal structure is formulated and verified experimentally. This model is based on the assumption that non-linearity of the stress–strain curves of these materials is a result of irreversible process of oriented damage growth. It was also assumed that a material response, represented by the strain tensor, is a function of two tensorial variables: the stress tensor and the damage effect tensor that is responsible for the current state of the internal structure of the material. The explicit form of the respective non-linear stress–strain relations that account for the appropriate damage evolution equation was obtained by employing the theory of tensor function representations and by using the results of own experiments on damage growth. Such an oriented damage that grows in the material, described by the second order symmetric damage effect tensor, results in gradual development of the material anisotropy. The validity of the constitutive equations proposed was verified by using the available experimental results for concrete subjected to the plane state of stress. The relevant experimental data for sandstone and concrete subjected to tri-axial state of stress were also used.     

The implicit standard material theory for modelling the nonassociative behaviour of metals

Summary  Modelling the elastoplastic or elastoviscoplastic behaviour of metallic materials exhibiting strain hardening and damage leads to complex nonassociative constitutive equations, sources of many theoretical and numerical troubles. The usual modelling of a nonassociative constitutive equation leads to the loss of the interesting and very useful properties of generalised standard materials deriving from the key concepts of convexity and normality. The argument that will be developed is that the bipotential concept is an appropriate answer. In the first part, after introducing the state variables generally used to describe the behaviour of metallic materials, the constitutive equations subjected to the principles of thermodynamics are derived from two potentials. The state potential gives the state laws, and the bipotential of dissipation delivers the evolution laws for state variables, through the implicit normality assumption. The second part is devoted to several particular applications to metal elastoplasticity and elastoviscoplasticity models. Received 29 March 2000; accepted for publication 26 September 2000     

Constitutive Theory of Plasticity Coupled with Orthotropic Damage for Geomaterials

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A finite strain kinematic hardening constitutive model based on Hencky strain: General framework, solution algorithm and application to shape memory alloys

The logarithmic or Hencky strain measure is a favored measure of strain due to its remarkable properties in large deformation problems. Compared with other strain measures, e.g., the commonly used Green-Lagrange measure, logarithmic strain is a more physical measure of strain. In this paper, we present a Hencky-based phenomenological finite strain kinematic hardening, non-associated constitutive model, developed within the framework of irreversible thermodynamics with internal variables. The derivation is based on the multiplicative decomposition of the deformation gradient into elastic and inelastic parts, and on the use of the isotropic property of the Helmholtz strain energy function. We also use the fact that the corotational rate of the Eulerian Hencky strain associated with the so-called logarithmic spin is equal to the strain rate tensor (symmetric part of the velocity gradient tensor). Satisfying the second law of thermodynamics in the Clausius-Duhem inequality form, we derive a thermodynamically-consistent constitutive model in a Lagrangian form. In comparison with the available finite strain models in which the unsymmetric Mandel stress appears in the equations, the proposed constitutive model includes only symmetric variables. Introducing a logarithmic mapping, we also present an appropriate form of the proposed constitutive equations in the time-discrete frame. We then apply the developed constitutive model to shape memory alloys and propose a well-defined, non-singular definition for model variables. In addition, we present a nucleation-completion condition in constructing the solution algorithm. We finally solve several boundary value problems to demonstrate the proposed model features as well as the numerical counterpart capabilities.     

45#钢的损伤演化方程和层裂准则研究

通过唯象分析和细观物理统计相结合的方法建立了一种韧性材料的损伤演化方程。在试验结果和内变量理论的基础上得到了45#钢的含损伤热—粘塑性本构关系。用有限差分方法计算了45#钢平板撞击所产生的应力波传播规律、损伤演化规律及层裂进程。通过自由面速度历史的数值模拟,并基于计算结果与试验结果间的最佳一致性,得到了损伤演化方程中的材料参数和极限损伤数值,并以此为依据建立了材料的应力率层裂准则。