Abstract
A Green's function representation of the plane inelastic deformation in isotropic solids is given using a complex variable method of Muskhelishvili. Based on the fact that the inelastic deformation in a plane infinitesimal region (which we call a plastic source) can be represented by a double couple, its Green's functions are derived in terms of the complex potential functions; these Green's functions, then, are used as the kernel functions in an area integral representation of the complex potential functions for the inelastic deformation of a finite extent. Emphasis is placed on deriving the area integral representation of the two basic complex potential functions (i.e., ϕ and ψ in Muskhelishvili's notation); once they are obtained, any physical quantities such as the displacement, the stress, and the traction can be calculated by simply following the formulae of Muskhelishvili.
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