Variational methods for fluids of Prandtl-Eyring type and plastic materials with logarithmic hardening

Abstract

We study the slow steady-state flow of a fluid of Prandtl–Eyring type and prove (partial) regularity of the strain velocity by investigating an appropriate variational problem. We further discuss local minimizers of variational integrals which occur in the theory of plasticity with logarithmic hardening. For this model we show that the deformation gradient in the three–dimensional case is smooth up to a closed set of vanishing Lebesgue measure. The paper also presents an introduction into various function spaces which are needed to formulate the problems. Copyright © 1999 John Wiley & Sons, Ltd.