Expression of Elastic Deformation of Inhomogeneous Medium by Dislocations Distributed in Homogeneous Elastic Medium

Abstract

Discussions are made on the possibility of expressing elastic deformation of an inhomogeneous material by dislocations distributed in a homogeneous elastic medium. A model of the inhomogeneous material is employed, which is composed of plane rectangular regions with different elastic constants. The model is analytically replaced by models with both discrete dislocations and continuum dislocations distributed in a rectangular network. Strain distribution in the dislocation models is compared with that in a rectangular inhomogeneous material, where constraint ratio is used as a parameter for expressing the mode of deformation. It is concluded that the elastic deformation of the inhomogeneous material is expressed approximately by the dislocations distributed in elastic homogeneous materials, so far as proper correspondence between the model of inhomogeneous material and dislocation model is chosen.