WIAS Preprint No. 1643, (2011)
Emergence of rate-independent dissipation from viscous systems with wiggly energies
- Mielke, Alexander
2010 Mathematics Subject Classification
- 74N30 74D10 70K70
- Gamma convergence for evolution, De Giorgi formulation, rate-independent plasticity, viscous gradient flow, wiggly energy
We consider the passage from viscous system to rate-independent system in the limit of vanishing viscosity and for wiggly energies. Our new convergence approach is based on the (R,R*) formulation by De Giorgi, where we pass to the Γ limit in the dissipation functional. The difficulty is that the type of dissipation changes from a quadratic functional to one that is homogeneous of degree 1. The analysis uses the decomposition of the restoring force into a macroscopic part and a fluctuating part, where the latter is handled via homogenization.
- Contin. Mech. Thermodyn., 24 (2012) pp. 591--606.