Non-convex sweeping processes in contact mechanics

We propose a model for irreversible dynamics of the rail foundation under the effects of rail traffic, taking into account the granular structure of the ballast subject to changing void ratio and to mechanical degradation. The rail is modeled as an Euler–Bernoulli beam with distributed forcing terms representing the moving traffic load as well as the interaction with the foundation. This interaction is described by an implicit variational inequality with non-convex constraint depending in turn on the solution of the underlying PDE. The problem is reduced to a fixed point problem in a suitable Banach space, and its unique solvability is proved using the contraction principle.