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Improved L p ‐estimates for the strain velocities in hardening problems
Author(s) -
Frehse Jens,
Löbach Dominique
Publication year - 2011
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.201110002
Subject(s) - hardening (computing) , differentiable function , von mises yield criterion , isotropy , mathematics , strain hardening exponent , mathematical analysis , geometry , physics , mathematical physics , materials science , composite material , thermodynamics , finite element method , optics , layer (electronics)
Problems of elastic plastic deformation with kinematic or isotropic hardening and von Mises flowrule are considered. It is shown that the velocities of the stresses, strains and hardening parameters satisfy an improved L p ‐property that is σ , ξ , ∇ u ∈ L ∞ (0, T ; L 2+2 δ (Ω)) with some δ > 0. For dimension n = 2 this implies continuity of u in spatial direction, furthermore it can be used as tool to prove boundary differentialbility σ , ξ ∈ L ∞ (0, T ; L 1+ ε ) and σ , ξ ∈ L ∞ (0, T ; 1/2+ δ ′,2 ), where 1/2 + δ ′ is the order of fractional Nichol'skii differentiability (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)