On One Class of Dual Problems of Mechanics of Deformable Solids

Abstract

Inelastic body's plane deformation is described by two vector fields: vector stress potential (gradient of Airy stress function) and vector displacement field. Conditions for possibility of proceeding to the dual problem, when variables change the roles, are described: stress potential is interpreted as displacement field and vice versa. Both a perfectly plastic body model and its dual model of perfectly solidifying matter are considered.