**Nächste Seite:**Navier-Stokes
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Vlasov-Poisson equation (RVM)

##
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) for**Aufwärts:**Models
of Mathematical Physics**Vorherige Seite:**Relativistic
Vlasov-Poisson equation (RVM)
collected and worked out by Wolfgang Sprößig, TU-Bergakademie
Freiberg