On the Internal Stresses in a Half Plane and a Layer Containing Localized Inelastic Strains or Inclusions

Abstract

An Airy stress function has been used to formulate the internal stresses in an isotropic body in terms of the distribution of inelastic strains under the conditions of plane stress and plane strain. Formulation has been first obtained for the stresses in closed forms for an infinite plane containing a rectangular zone with uniform inelastic strains. Using method of Fourier transforms, analytic solutions have been obtained for the stresses due to the inclusion in a half plane with free, fixed and rigid, frictionless boundaries as well as in a layer lying on a rigid, frictionless foundation. Elastic strain energy has been formulated in closed form for the rectangular domain with uniform inelastic strain in an infinite plane and a half plane.