Bifurcations in the regularized Ericksen bar model

M. Grinfeld, G.J. Lord

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1 Citation (Scopus)
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Abstract

We consider the regularized Ericksen model of an elastic bar on an elastic foundation on an interval with Dirichlet boundary conditions as a two-parameter bifurcation problem. We explore, using local bifurcation analysis and continuation methods, the structure of bifurcations from double zero eigenvalues. Our results provide evidence in support of Muller's conjecture [18] concerning the symmetry of local minimizers of the associated energy functional and describe in detail the structure of the primary branch connections that occur in this problem. We give a reformulation of Muller's conjecture and suggest two further conjectures based on the local analysis and numerical observations. We conclude by analysing a "loop" structure that characterizes (k, 3k) bifurcations.
Original languageEnglish
Pages (from-to)161-173
Number of pages13
JournalJournal of Elasticity
Volume90
Issue number2
DOIs
Publication statusPublished - 28 Feb 2008

Keywords

  • microstructure
  • lyapunov–schmidt analysis
  • ericksen bar model
  • numerical statistics
  • elasticity

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