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 evolution laws deduced from normality structure

Generally speaking, damaging is always anisotropic even for the initially isotropic materials. This paper deals with anisotropic damage evolution laws, whose complex tensorial and high-degree nonlinear properties make them the most elusive parts of such anisotropic models and hinder their practical application. Most damage evolution laws in existing phenomenological damage models can be covered by the linear irreversible thermodynamics which is also termed as the phenomenological equations. The essential problem is to identify the conditions of the phenomenological equation and the specific form of the damage characteristic tensor J for a solid weakened by preexisting microcracks. The essential problem cannot be solved in phenomenological damage models, where the phenomenological equation is taken as a prerequisite rather than a conclusion. Even if the phenomenological equation really holds true, irreversible thermodynamics or current available experimental data is not enough to determine the damage characteristic tensors J uniquely. In this paper, the basic internal variables include numerous vector form variables which correspond to microcracks. The crack tensor is taken as the averaging measurement of the basic internal variables. The generalized crack tenor and brittle indexes are introduced to characterize the damage potential function and damage characteristic tensor. Rice's kinetic rate laws of local internal variables, with each rate being stress dependent only via its conjugate thermodynamic force, are corner stones of the normality structure. In this paper, it is revealed that the phenomenological equations emerges from normality structure if all the kinetic rate laws are homogeneous functions of the same degree in their conjugate forces. Since in most cases the relationship between propagation rate of cracks and their energy release rate can be covered by power laws, the homogeneous condition is fulfilled naturally. Therefore, it is concluded that the phenomenological equations are appropriate form for damage evolution laws. The damage characteristic tensor possesses the same symmetry and positive definiteness as the elasticity tensor. Based on the deduced analytic damage characteristic tensor, it is clear that the fourth-order identity tensor is not suitable to be taken as a damage characteristic tensor. The damage characteristic tensor depend on not only the current microstructural parameters but also the current conjugate forces.