Non-convex variational inequalities in contact mechanics

Abstract: We propose a new mathematical model for the dynamics of a rail represented by a straight elastic or elastoplastic beam in contact with the foundation and subject to a moving load. The foundation consists of a granular material which undergoes irreversible structural changes such as grain degradation and decreasing void ratio. The theory of non-convex sweeping processes makes it possible to evaluate the energy exchange between the rail and the foundation, and to exploit the energy balance equation to prove existence and uniqueness of solutions to the full system consisting of a fourth order PDE coupled with a variational inequality with a non-convex state-dependent constraint.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)