Global continuation in second-gradient nonlinear elasticity

Anita Mareno, Timothy J. Healey

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We consider three-dimensional elastic bodies characterized by a general class of stored-energy functions dependent upon the first and second gradients of the deformation. We assume that the dependence on the higher-order term ensures strong ellipticity. With only modest assumptions on the lower-order term, we use the Leray-Schauder degree to prove the existence of global solution continua to the Dirichlet problem. With additional, physically reasonable restrictions on the stored-energy function, we then demonstrate that our global solution branch is unbounded.

Original languageEnglish (US)
Pages (from-to)103-115
Number of pages13
JournalSIAM Journal on Mathematical Analysis
Volume38
Issue number1
DOIs
StatePublished - Mar 1 2006

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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