On the Uniqueness of Energy Minimizers in Finite Elasticity

Jeyabal Sivaloganathan, Scott J Spector

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3 Citations (Scopus)
27 Downloads (Pure)

Abstract

The uniqueness of absolute minimizers of the energy of a compressible, hyperelastic body subject to a variety of dead-load boundary conditions in two and three dimensions is herein considered. Hypotheses under which a given solution of the corresponding equilibrium equations is the unique absolute minimizer of the energy are obtained. The hypotheses involve uniform polyconvexity and pointwise bounds on derivatives of the stored-energy density when evaluated on the given equilibrium solution. In particular, an elementary proof of the uniqueness result of Fritz John (Commun. Pure Appl. Math. 25:617–634, 1972) is obtained for uniformly polyconvex stored-energy densities.

Original languageEnglish
Pages (from-to)73-103
Number of pages31
JournalJournal of Elasticity
Volume133
Issue number1
Early online date5 Feb 2018
DOIs
Publication statusPublished - 1 Oct 2018

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Keywords

  • Energy minimizers
  • Equilibrium solutions
  • Finite elasticity
  • Nonlinear elasticity
  • Nonuniqueness
  • Strict polyconvexity
  • Strongly polyconvex
  • Uniform polyconvexity
  • Uniqueness

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

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