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## Frictional viscoelastic contact problem

Let be  a viscoelastic body in  The smooth boundary  is divided into three disjoint open parts : . The body is subjected to volume forces of density . On  we have zero displacements and on  are prescribed tractions. On  the body comes in contact with the foundation. Denote by  the displacement field, by  is the stress tensor, by  the strain tensor. Further  is the mass density and  and  are the elasticity and viscoelasticity tensors, which are symmetric and elliptic.

In a strong formulation the problem is the following: Find  such that  and for all

Boundary conditions are:
is the outward normal unit vector. Note that  and . The index  or  stands for normal or tangential components. We have  and . Now we produce a normal compliance law for the contact with the Coulomb friction law on . This normal compliance problem was introduced by Martins JAC and Oden JT in 1987. We assume
where from  follows  and  then there exists a constant  with . Here  represents the initial gap mostly assumed to be zero.

A last reference: J-M. Ricaud, E. Pratt (2001) Analysis of time discretization for an implicit variational inequality modelling dynamic contact problems with friction, MMAS, 24, ???-???.

Nächste Seite:Navier-Stokes equations (NSE) forAufwärts:Models of Mathematical PhysicsVorherige Seite:Relativistic Vlasov-Poisson equation (RVM)
collected and worked out by Wolfgang Sprößig, TU-Bergakademie Freiberg