An existence and uniqueness theorem for incremental viscoelasticity
Introduction. The equations governing small deformations superposed on a large deformation for a body composed of viscoelastic material were established by Pipkin and Rivlin [1], Recently Iesan [2] has presented equations for small thermoelastic deformations superposed on a general nonlinear thermomechanical deformation and an existence and uniqueness theorem for these equations was proven by Navarro and Quintanilla [3]. In this paper equations are developed which describe motions of a viscoelastic body which are incremental in the sense that they are close to a nonequilibrium nonlinear deformation of the body and an existence and uniqueness theorem for these equations with Dirichlet boundary conditions is proved. The paper is concluded with the remark that the Dirichlet problem of incremental viscoelasticity is well posed.