2009, Knees, Dorothee

We study the global spatial regularity of solutions of generalized elasto-plastic models with linear hardening on smooth domains. Under natural smoothness assumptions on the data and the boundary we obtain that the displacements belong to L^8((0,T);H^(3/2-d)(O)) whereas the internal variables belong to L^8((0,T);H^(1/2-d)(O)). The key step in the proof is a reflection argument which gives the regularity result in directions normal to the boundary on the basis of tangential regularity results

2009, Gruber, Peter, Knees, Dorothee, Nesenenko, Sergiy, Thomas, Marita

In this paper some analytical and numerical aspects of time-dependent models with internal variables are discussed. The focus lies on elasto/visco-plastic models of monotone type arising in the theory of inelastic behavior of materials. This class of problems includes the classical models of elasto-plasticity with hardening and viscous models of the Norton-Hoff type. We discuss the existence theory for different models of monotone type, give an overview on spatial regularity results for solutions to such models and illustrate a numerical solution algorithm at an example. Finally, the relation to the energetic formulation for rate-independent processes is explained and temporal regularity results based on different convexity assumptions are presented