COMPLEX VARIABLE APPROACH TO INELASTIC BOUNDARY VALUE PROBLEMS.

This paper presents a complex variable formulation of inelastic boundary value problems in plane strain and plane stress of isotropic solids. The formulation is based on a physical interpretation of an extended form of Somigliana's identity which includes the effect of inelastic deformation. While the inelastic deformation is represented in terms of a continuous planar distribution of double couples, the effect of the boundary traction and the displacement is represented by continuous distributions of point forces and of dislocation dipoles, respectively, along the boundary of the finite domain imagined to be embedded in the infinite matrix of the same material. The only approximation introduced consists of the discretization and of the use of trial functions for the boundary and the inelastic domain.