弹性介质中的一种各向异性损伤模型

A Model for Anisotropic Elastic Materials with Damage

各向同性损伤理论是建立在材料是均匀的、各向同性的以及损伤也是各向同性的假设基础之上.对于初始各向异性材料,损伤演化也呈明显的各向异性.一般地可用一八阶的损伤张量来描述这种材料的损伤,利用应变等效原理可将损伤张量减少到四阶.这个四阶损伤张量中独立元素的个数和材料及损伤的对称性有关,对各向同性损伤,损伤材料独立的材料参数只有两个,它们可用无损伤时材料的Lam e系数和损伤参数来表示.

The theory of isotropy damage is based on the hypothesis that the material and damage are symmetrical and isotropic. Even material is isotropic initially, the damage will induce the material anisotropic. Generally, the material damage requires description by an eighth order damage tensor but that the principle of strain equivalence permits a reduction to a tensor of order four. The actual number of independent damage parameters in such a tensor is related to the material and damage symmetry. For isotropic case, there must be two independent damage material parameters ,which can be expressed by Lame coefficient and damage parameters.