各向异性非线性固体力学的规范空间理论

Standard Space Theory of Anisotropic Nonlinear Solids

本文在弹性规范空间概念基础上，利用非平衡态热力学理论，证明了各向异性固体力学非线性问题规范空间场以及不可逆过程本征解的存在。损伤对结构刚度的弱化效应和损伤诱发各向异性效应分别反映在本征弹性和相应的模态向量中。在简正坐标中考察各向异性体变形时，材料的行为以六个普通的粘弹性Ｍａｘｗｅｌｌ方程描述，总的响应由模态叠加得到。以此为基础给出的非线性本构方程具有坐标转换不变性，最后给出了二个具体的算例。

Based on the conception of the standard space of elastic body, the existence that the field of thestandard space and the. eigenvalue of irreversible process of anisotropic nonlinear solids by using thetheory of nonequilibrium thermodynamics is proved. The softening effect of damage on material stiffness and the anisotropy induced by damage are given expression to the eigenmodulus of elasticity andthe relative modal vector respectively. When studing the deformation of anisotropic body under thenormal coordinates, six common viscoelastic Maxwell models can be used in describing the behavior ofthe body, from which the total response can be obtained by the modality superimposition and is invariant under coordinate transformation. In final part of the paper, two specific examples as application ofthe theory are given, they show that the theory presented here is superior to the existing theory foranisotropic nonlinear solids.