Structural properties of stress relaxation and convergence from viscoelasticity to polyconvex elastodynamics

Corrado Lattanzio*, Athanasios Tzavaras

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

We consider a model of stress relaxation approximating the equations of elastodynamics. Necessary and sufficient conditions are derived for the model to be equipped with a global free energy and to have positive entropy production. The resulting class allows for both convex and non-convex equilibrium potentials. For convex equilibrium potentials, we prove a strong dissipation estimate and two relative energy estimates for: the relative entropy of the relaxation process and the modulated relative energy. Both give convergence results to smooth solutions. For polyconvex equilibrium potentials, an augmenting of the system of polyconvex elastodynamics and the null-Lagrangian structure suggest an appropriate notion of relative energy. We prove convergence of viscosity approximations to polyconvex elastodynamics in the regime where the limit solution remains smooth. A modulated relative energy is also obtained for the polyconvex case which shows stability of relaxation approximations.

Original languageEnglish (US)
Pages (from-to)449-492
Number of pages44
JournalArchive for Rational Mechanics and Analysis
Volume180
Issue number3
DOIs
StatePublished - Jun 1 2006

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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