Dynamical Contact Problems for Viscoelastic Bodies

Abstract

The aim of this contribution is to present a surway about author’s recent results in the field concel nine; the existence and regularity of solutions. It is well known that it is very hard to solve dynamical contact problem (cf. Amerlo and Prouse, 1975, Bamberger and Schatzmann, 1983, Ma.rtto, 1985, Schatztnaun, 1983 etc., for a global information C’abannes and Citrini, 1987 etc.) due to its hyperbolic character for which the convenient constraint formulation is in velocities while, tine the obvious physical reality, the constraint should be formulated in displacement;. This yields the necessity to put displacement into the variational inequality which gives the opposite sign at. the velocity term after the integration by parts. The visroef asticity approach can overcome such probletu, since it enables to prove the strong convergence of velocities. In this context we study two types of models:

• 1. the material has a certain singular memory of the Hencky type

• 2. the stress tensor depends on the gradient of velocities

We note that the viscoclasticity “parabolizes” the problem in soute t.euse. (this phenomenon is more temarkable at the second approach).