Modelling and Control in Contact Mechanics
Mircea Sofonea (Universite de Perpignan, France) and Dan Tiba (IMAR,
Phenomena of contact between deformable bodies or between deformable and rigid bodies abound in industry and everyday life. Contact of braking pads with wheels, tires
with roads, pistons with skirts are just a few simple examples. Common industrial
processes such as metal forming, metal extrusion, involve contact evolutions. Owing to
their inherent complexity, contact phenomena are modeled by nonlinear evolutionary
problems involving a high degree of difficulty.
In this workshop we discuss new models for contact problems expressed in terms of variational and hemivariational inequalities. We pay a particular attention to the analysis
of these models, including existence and uniqueness results. We also investigate optimal control and shape optimization problems associated to such models. In addition,
we deal with the analysis of approximation schemes including convergence results of
the discrete solutions, optimal error estimates and construction of reliable algorithms
with guaranteed convergence.