Analysis of a quasistatic displacement-traction problem for viscoelastic materials

We consider an initial and boundary value problem which describes the evolu tion of a viscoelastic body submitted to body forces and surface tractions. The viscoelastic constitutive law is assumed to be nonlinear and the proce ss is quasistatic. We prove the existence and the uniqueness of the solutio n using arguments of monotone operators theory and a version of Cauchy-Lypc hitz theorem. We establish the continuous dependence of the solution on the elasticity operator. Finally, we study the behavior of the solution when t he viscosity operator converges to zero. (C) 2000 Elsevier Science Ltd. All rights reserved.