Elastic Deformation of Inhomogeneous Materials Including Polycrystals under Multi-Axial Stress : II. On analytical expression of inhomogeneous deformation

Abstract

Elastic deformation of inhomogeneous materials such as polycrystals or materials with inclusion under multi-axial stress is analysed. A general relation between constraint ratio proposed by the author and strain or stress concentration factor tensor proposed Hill is obtained, and its reduced forms for special cases are studied. The relation between constraint ratio and Eshelby's tensor S is studied for spheroidal inclusion imbedded in infinite matrix. Numerical values of constraint ratio, Hill's tensor and Eshelby's tensor are calculated for several models of inhomogeneous materials and compared with each other.