Thermodynamics of perfect plasticity

Tomáš Roubíček

doi:10.3934/dcdss.2013.6.193

Article Contents

2013, Volume 6, Issue 1: 193-214. Doi: 10.3934/dcdss.2013.6.193

This issue Previous Article A characterization of energetic and $BV$ solutions to one-dimensional rate-independent systems Next Article Thermalization of rate-independent processes by entropic regularization

Thermodynamics of perfect plasticity

Tomáš Roubíček^1,

1.
Mathematical Institute, Charles University, Sokolovská 83, CZ-186 75 Praha 8

Received: April 2011

Revised: August 2011

Published: February 2013

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Abstract

Viscoelastic solids in Kelvin-Voigt rheology at small strains exhibiting also stress-driven Prandtl-Reuss perfect plasticity are considered quasistatic (i.e. inertia neglected) and coupled with heat-transfer equation through dissipative heat production by viscoplastic effects and through thermal expansion and corresponding adiabatic effects. Enthalpy transformation is used and existence of a weak solution is proved by an implicit suitably regularized time discretisation.

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Mathematics Subject Classification: Primary: 35K85; Secondary: 49S05, 74C05, 80A17.

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