IFIP TC 7 / 2013 - Minisymposia

  • Pavel KrejĨi, 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 appropriate
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.