Materials with internal variables and relaxation to conservation laws

Athanasios Tzavaras*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

53 Scopus citations

Abstract

The theory of materials with internal state variables of COLEMAN & GURTIN [CG] provides a natural framework to investigate the structure of relaxation approximations of conservation laws from the viewpoint of continuum thermomechanics. After reviewing the requirements imposed on constitutive theories by the principle of consistency with the Clausius-Duhem inequality, we pursue two specific theories pertaining to stress relaxation and relaxation of internal energy. They each lead to a relaxation framework for the theory of thermoelastic non-conductors of heat, equipped with globally defined "entropy" functions for the associated relaxation process. Next, we consider a semilinear model problem of stress relaxation. We discuss uniform stability and compactness for solutions of the relaxation system in the zero-relaxation limit, and establish convergence to the system of isothermal elastodynamics by using compensated compactness. Finally, we prove a strong dissipation estimate for the relaxation approximations proposed in JIN & XIN [JX] when the limit system is equipped with a strictly convex entropy.

Original languageEnglish (US)
Pages (from-to)129-155
Number of pages27
JournalArchive for Rational Mechanics and Analysis
Volume146
Issue number2
DOIs
StatePublished - May 28 1999

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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