A quasistatic frictional contact problem with damage involving viscoelastic materials with short memory. (November 2016) - Li, Yunxiang; Migórski, Stanisław; Han, Jiangfeng
We consider a mathematical model which describes the frictional contact between a deformable body and a foundation. The process is assumed to be quasistatic and the material behaviour is described by a viscoelastic constitutive law with damage. The friction and contact are modeled with subdifferential boundary conditions. We derive the variational formulation of the problem which is a coupled system of a hemivariational inequality for the velocity and a parabolic variational inequality for the damage field. Then we prove the existence of a unique weak solution to the model. The proof is based on arguments of time-dependent stationary inclusions and a fixed point theorem.