One dimensional model of martensitic transformation solved by: Homotopy analysis method

Chen Xuan, Cheng Peng, Yongzhong Huo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


The homotopy analysis method (HAM) is applied to solve a nonlinear ordinary differential equation describing certain phase transition problem in solids. Both bifurcation conditions and analytical solutions are obtained simultaneously for the Euler-Lagrange equation of the martensitic transformation. HAM is capable of providing an analytical expression for the bifurcation condition to judge the occurrence of the phase transition, while other numerical techniques have difficulties in bifurcation analysis. The convergence of the analytical solutions on the one hand can be adjusted by the auxiliary parameter and on the other hand is always obtainable for all relevant physical parameters satisfying the bifurcation condition.

Original languageEnglish
Pages (from-to)230-238
Number of pages9
JournalZeitschrift fur Naturforschung - Section A Journal of Physical Sciences
Issue number5
Publication statusPublished - 2012
Externally publishedYes


  • Bifurcation
  • Double-well potential
  • Homotopy analysis method
  • Martensitic phase transformation

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