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 homogeneous 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 rate-dependent healing.