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Bifurcations in the regularized Ericksen bar model

Grinfeld, M. and Lord, G.J. (2008) Bifurcations in the regularized Ericksen bar model. Journal of Elasticity, 90 (2). pp. 161-173. ISSN 0374-3535

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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.