TY - JOUR
T1 - One dimensional model of martensitic transformation solved by
T2 - Homotopy analysis method
AU - Xuan, Chen
AU - Peng, Cheng
AU - Huo, Yongzhong
N1 - Funding Information:
The authors thank the support of the National Natural Science Foundation of China (No. 10772049 & 11072062) and the National High Technology Research and Development Program 863 of China (No. 2009AA04Z408). We also express our sincere gratitude to Prof. Shijun Liao for providing precious suggestions.
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - Bifurcation
KW - Double-well potential
KW - Homotopy analysis method
KW - Martensitic phase transformation
UR - http://www.scopus.com/inward/record.url?scp=84867723971&partnerID=8YFLogxK
U2 - 10.5560/ZNA.2012-0016
DO - 10.5560/ZNA.2012-0016
M3 - Article
AN - SCOPUS:84867723971
SN - 0932-0784
VL - 67
SP - 230
EP - 238
JO - Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences
JF - Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences
IS - 5
ER -