Analytical and numerical aspects of time-dependent models with internal variables
- Gruber, Peter
- Knees, Dorothee
- Nesenenko, Sergiy
- Thomas, Marita
2010 Mathematics Subject Classification
- 74C05 74C10 49N60 65M60
- Elasto-plasticity, visco-plasticity, models of monotone type, existence of solutions, monotone operator method, spatial regularity, Slant Newton Method, energetic formulation of rate-independent processes, temporal regularity
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.
- ZAMM Z. Angew. Math. Mech., 90 (2010) pp. 861--902.