Coupling of rate-independent and rate-dependent systems with application to delamination processes in solids
This talk addresses the modeling of delamination processes in elastic solids
using an internal delamination variable with a rate-independent, unidirectional evolution law.
This covers models for brittle, Griffith-type delamination, which describe sharp
cracks in terms of a non-smooth constraint confining displacement jumps across
interfaces to the null set of the delamination variable, as well as adhesive contact models,
which regularize this constraint by a finite surface energy contribution.
A notion of solution suited for non-smooth PDE -systems of coupled rate-dependent and rate-independent dynamics introduced.
Existence results for the delamination models are deduced.
In this context, for a viscoelastic solid with dynamic effects,
the limit passage from models for adhesive contact to brittle, Griffith-type delamination is discussed in the sense of evolutionary Gamma-convergence.
Fine properties of the solutions are established by studying a simplified model.