Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids

Martin Fuchs, Gregory Seregin (auth.)9783540413974, 3-540-41397-9

Variational methods are applied to prove the existence of weak solutions for boundary value problems from the deformation theory of plasticity as well as for the slow, steady state flow of generalized Newtonian fluids including the Bingham and Prandtl-Eyring model. For perfect plasticity the role of the stress tensor is emphasized by studying the dual variational problem in appropriate function spaces. The main results describe the analytic properties of weak solutions, e.g. differentiability of velocity fields and continuity of stresses. The monograph addresses researchers and graduate students interested in applications of variational and PDE methods in the mechanics of solids and fluids.

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Table of contents :
Introduction….Pages 1-4
Weak solutions to boundary value problems in the deformation theory of perfect elastoplasticity….Pages 5-39
Differentiability properties of weak solutions to boundary value problems in the deformation theory of plasticity….Pages 40-130
Quasi-static fluids of generalized Newtonian type….Pages 131-206
Fluids of Prandtl-Eyring type and plastic materials with logarithmic hardening law….Pages 207-259