Analysis of Anisotropic Elasticity by Means of Internal Stress in a Reference Isotropic Elastic Body

Abstract

AbstractA method of anisotropic elasticity problems is proposed which employs superposition of the analytic solution for an isotropic elastic body and the suitable internal stress determined by the boundary condition. Employing the incompatibility tensor and Kröner's stress functions, we can establish a simple formulation for the anisotropic elasticity. The difference of the stress fields in an isotropic material and an anisotropic material can be considered as an internal stress field caused by the incompatibility which can be evaluated from the solution of the isotropic material by use of its curl curl operations for the incompatibility tensor. Though it is difficult to get the analytic solution for general cases, some special cases with Airy's stress function are analyzed as simple examples. Since the internal stress can be expressed by the dislocations distributed continuously in the isotropic body, we can gain further physical insight into the anisotropy.