Department of Mechanics: Seminar: Abstract Roubicek

Various Solution Concepts in Rate-Independent Evolution Systems

Evolution of mechanical systems is often governed by nonconvex stored energies together with dissipation potentials. If the outer loading is much slower than the time-scale of internal disipative processes, these systems can approximately be considered as rate independent and the dissipated energy potential as positively homogenoues of degree-1. Typical examples are damage, plasticity, phase transformations, or fracture in the bulk, or delamination or friction in adhesive contacts. The usual global-minimum concept for incremental problems preserves energy in the limit but may be computationally difficult and often less physical than some force-driven locally-minimal solutions. Various concepts of solutions and various time-discretisations will be discussed, together with the role of the maximum-dissipation principle. Abstract considerations will be illustrated on a delamination problem (=an adhesive contact problem), together with some of its variants as a brittle contact or a mixity-mode sensitive delamination (illustrated by numerical experiments performed by C.G.Panagiotopoulos and R.Vodicka), or a combination with a rate-dependent healing.