Bifurcations in a boundary-value problem of a nonlinear model for stress-induced phase transitions

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Original languageEnglish
Pages (from-to)3231-3247
Journal / PublicationInternational Journal of Bifurcation and Chaos
Issue number11
Publication statusPublished - Nov 2011


In this paper, some methodology in nonlinear dynamics is used to study a boundary-value problem of a nonlinear model arisen in phase transitions in a slender cylinder composed of a compressible hyperelastic material. We transform the original system of boundary-value problem to an initial-value (dynamical) problem of finding periodic solutions of coupled nonlinear autonomous oscillators in a four-dimensional space. Hopf-like bifurcation analysis of the periodic solutions of the system is studied. Both analytical and numerical solutions are obtained by using a nonlinear transformation formulation. The accuracy of analytical solutions is investigated by comparing with the numerical solutions. The engineering stress-strain curve is plotted and compared with that from the normal form equation, which is a simplification of the original system. © 2011 World Scientific Publishing Company.

Research Area(s)

  • bifurcation, Nonlinear boundary-value problem, perturbation-incremental method, phase transformation