- Pavel Krejči, Academy of Sciences of the Czech Republic, Czech Republic
"Dynamic contact of elastoplastic bodies treated as a system of equations
with hysteresis operators"
A classical mathematical approach to contact problems consists in applying
different variants of the penalty method, with the intention to let the
penalty parameter tend to infinity. Here instead, in the case of an
elastoplastic body in contact with an elastoplastic obstacle, we propose to
reformulate the problem equivalently as a PDE with hysteresis operators both
in the constitutive law and in the contact boundary condition. Analytical
properties of the hysteresis operators (Lipschitz continuity in suitable
function spaces, monotonicity, energy inequalities) enable us to construct a
regular solution by conventional methods and prove its uniqueness and
continuous data dependence. The hysteresis dissipation terms then appear as
sources of heat in the bulk and on the boundary in the energy balance. Under
assumptions, the resulting non-isothermal system of momentum and
energy balance equations then turns out to be well-posed, too.
This is a
joint work with Adrien Petrov, INSA Lyon.