WIAS Preprint No. 1460, (2009)

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


  • Gruber, Peter
  • Knees, Dorothee
  • Nesenenko, Sergiy
  • Thomas, Marita
    ORCID: 0000-0001-6771-0742

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.

Appeared in

  • ZAMM Z. Angew. Math. Mech., 90 (2010) pp. 861--902.

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