A two-speed model for rate-independent elasto-plasticity

In the first part of this talk I will develop a model for (phenomenological) large-strain evolutionary elasto-plasticity that aims to find a balance between physical accuracy and mathematical tractability. Starting from a viscous dissipation model I will show how a time rescaling leads to the new concept of "two-speed" solutions, which combine a rate-independent "slow" evolution with rate-dependent "fast" transients during jumps. An existence theorem for two-speed solutions to fully nonlinear elasto-plasticity models is the long-term goal and as a first step I will present an existence result for the small-strain situation in this new framework. This theorem combines physically realistic behaviour on jumps with minimisation in the "elastic" variables. The proof hinges on a time-stepping scheme that alternates between elastic minimisation and elasto-plastic relaxation. The key technical ingredient the "propagation of (higher) regularity" from one step to the next.