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Z. Naturforsch. 67a, 230 – 238
(2012)
doi:10.5560/ZNA.2012-0016
One Dimensional Model of Martensitic Transformation Solved by Homotopy Analysis Method
1 Department of Mechanics and Engineering Science, Fudan University, Shanghai 200433, China
2 Department of Mechanical Engineering and Materials Science, Rice University, 6100 Main Street, Houston, Texas 77005, United States
Received June 2, 2011 / revised December 12, 2011 / published online May 2, 2012
Reprint requests to: Y. H.; E-mail:
yzhuo@fudan.edu.cn
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.
Key words: Homotopy Analysis Method; Martensitic Phase Transformation; Double-Well Potential; Bifurcation.