Formulation of the plastic source method for plane inelastic problems Part 1: Green's functions for plane inelastic deformation

Abstract

Green's function representation of the residual stress caused by any plane inelastic strain is given for the infinite region with a simple defect such as a crack or an elliptic hole. The plane inelastic strain developed within an infinitesimal region is represented by a double couple whose Green's functions (or complex potentials) are derived using the analytic function theory. The inelastic strain over a finite region is, then, represented by a continuous distribution of such double couples and its complex potentials by area integrals. Closed form expression for the stress field arising from the uniform inelastic strain distribution is given for the general polygonal region withn sides.