Analytical and numerical aspects of time-dependent models with internal variables

作者：Gruber Peter; Knees Dorothee^*; Nesenenko Sergiy; Thomas Marita

来源：Zeitschrift fur Angewandte Mathematik und Mechanik, 2010, 90(10-11): 861-902.

DOI：10.1002/zamm.200900387

• 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.

• 出版日期2010-10