Uniqueness Criterion of Deformation of Voigt Type Viscoelastic Body

Abstract

The paper deals with the criterion of uniqueness between the stress state and the deformation of the Voigt type viscoelastic body, of which stress-strain relations are the Lagrangian form. If the deformed state is given, the forces acting in the body and on its surface are uniquely specified. Conversely, the uniqueness criterion of the infinitesimal displacements for the given infinitesimal variations of body force, surface force and surface displacement, is that a function of the elastic potential and the dissipation function is positive definite.