A treatment of internally constrained elastic–plastic materials

Abstract

A treatment of internally constrained elastic–plastic materials is presented in the context of the Lagrangian strain-space formulation of the theory of finitely deforming elastic–plastic materials. A general type of internal constraint, represented by a smooth scalar-valued function of Lagrangian strain and a list of plastic variables, is considered. At fixed values of the plastic variables, the constraint equation determines a smooth hypersurface (the constraint manifold) imbedded in six-dimensional strain space. This manifold moves about and changes its shape as the deformation progresses. Adopting an approach introduced by Casey and Krishnaswamy for thermoelastic materials, the imbedded elasticity of elastic–plastic materials and the internal constraint are used to induce an equivalence relation on the set of unconstrained elastic–plastic materials. A unique constrained elastic–plastic material is then associated with each equivalence class of unconstrained materials, and a characterization of the constrained material is obtained from the properties of the corresponding unconstrained ones.