Analysis of a frictionless contact problem for elastic-viscoplastic materials

We consider a dynamic frictionless contact problem for elastic-viscoplastic materials with damage. The contact is modelled with normal compliance condition. The adhesion of the contact surfaces is considered and is modelled with a surface variable, the bonding field whose evolution is described by a first order differential equation. We derive variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of nonlinear evolution equations with monotone operators, a classical existence and uniqueness result on parabolic inequalities, differential equations and fixed-point arguments

A frictional contact problem with wear and damage for electro-viscoelastic materials

summary:We consider a quasistatic contact problem for an electro-viscoelastic body. The contact is frictional and bilateral with a moving rigid foundation which results in the wear of the contacting surface. The damage of the material caused by elastic deformation is taken into account, its evolution is described by an inclusion of parabolic type. We present a weak formulation for the model and establish existence and uniqueness results. The proofs are based on classical results for elliptic variational inequalities, parabolic inequalities and fixed point arguments

A history-dependent frictional contact problem with wear for thermoviscoelastic materials

In this manuscript we study a contact problem between a deformable viscoelastic body and a rigid foundation. Thermal effects, wear and friction between surfaces are taken into account. A variational formulation of the problem is supplied and an existence and uniqueness result is proved. The idea of the proof rested on a recent result on history-dependent quasivariational inequalities. Finally, a perturbation of the data is initiated and a convergence result is demonstrated when the perturbation parameter converges to zero