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- ItemGlobal spatial regularity for time dependent elasto-plasticity and related problems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Knees, DorotheeWe 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
- ItemAnalytical and numerical aspects of time-dependent models with internal variables(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Gruber, Peter; Knees, Dorothee; Nesenenko, Sergiy; Thomas, MaritaIn 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
- ItemHomogenization in gradient plasticity(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Hanke, HaukeThis paper yields a two-scale homogenization result for a rate-independent elastoplastic system. The presented model is a generalization of the classical model of linearized elastoplacticity with hardening, which is extended by a gradient term of the plastic variables. The associated stored elastic energy density has periodically oscillating coefficients, where the period is scaled by e > 0 . The additional gradient term of the plastic variables z is contained in the elastic energy with a prefactor e? (? = 0) . We derive different limiting models for e ? 0 in dependence of &gamma ;. For ? > 1 the limiting model is the two-scale model derived in [MielkeTimofte07], where no gradient term was present. For ? = 1 the gradient term of the plastic variable survives on the microscopic cell poblem, while for ? ? [0,1) the limit model is defined in terms of a plastic variable without microscopic fluctuation. The latter model can be simplified to a purely macroscopic elastoplasticity model by homogenisation of the elastic part