Local H¹-regularity and H^1/3−δ-regularity up to the boundary in time dependent viscoplasticity

Article type: Research Article

Authors: Alber, Hans-Dieter | Nesenenko, Sergiy

Affiliations: Department of Mathematics, Darmstadt University of Technology, Schlossgartenstr. 7, 64289 Darmstadt, Germany. E-mails: {alber, nesenenko}@mathematik.tu-darmstadt.de

Abstract: Local and boundary regularity for quasistatic initial-boundary value problems from viscoplasticity is studied. The problems considered belong to a general class with monotone constitutive equations modelling materials showing kinematic hardening. A standard example is the Melan–Prager model. It is shown that the strain/stress/internal variable fields have the regularity H4/3−δ/H1/3−δ/H1/3−δ up to the boundary. The proof uses perturbation estimates for monotone operator equations.

Keywords: regularity, plasticity, viscoplasticity, maximal monotone operator, difference quotient technique, interpolation, model of Melan–Prager

DOI: 10.3233/ASY-2009-0933

Journal: Asymptotic Analysis, vol. 63, no. 3, pp. 151-187, 2009