TY - JOUR
T1 - Multiple bifurcations and local energy minimizers in thermoelastic martensitic transformations
AU - Xuan, Chen
AU - Ding, Shurong
AU - Huo, Yongzhong
N1 - Publisher Copyright:
© 2015, The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg.
PY - 2015/9/23
Y1 - 2015/9/23
N2 - Thermoelastic martensitic transformations in shape memory alloys can be modeled on the basis of nonlinear elastic theory. Microstructures of fine phase mixtures are local energy minimizers of the total energy. Using a one-dimensional effective model, we have shown that such microstructures are inhomogeneous solutions of the nonlinear Euler–Lagrange equation and can appear upon loading or unloading to certain critical conditions, the bifurcation conditions. A hybrid numerical method is utilized to calculate the inhomogeneous solutions with a large number of interfaces. The characteristics of the solutions are clarified by three parameters: the number of interfaces, the interface thickness, and the oscillating amplitude. Approximated analytical expressions are obtained for the interface and inhomogeneity energies through the numerical solutions.
AB - Thermoelastic martensitic transformations in shape memory alloys can be modeled on the basis of nonlinear elastic theory. Microstructures of fine phase mixtures are local energy minimizers of the total energy. Using a one-dimensional effective model, we have shown that such microstructures are inhomogeneous solutions of the nonlinear Euler–Lagrange equation and can appear upon loading or unloading to certain critical conditions, the bifurcation conditions. A hybrid numerical method is utilized to calculate the inhomogeneous solutions with a large number of interfaces. The characteristics of the solutions are clarified by three parameters: the number of interfaces, the interface thickness, and the oscillating amplitude. Approximated analytical expressions are obtained for the interface and inhomogeneity energies through the numerical solutions.
KW - Bifurcation
KW - Energy minimizer
KW - Microstructures
KW - Nonlinear elasticity
KW - Thermoelastic martensitic transformation
UR - http://www.scopus.com/inward/record.url?scp=84946532372&partnerID=8YFLogxK
U2 - 10.1007/s10409-015-0491-9
DO - 10.1007/s10409-015-0491-9
M3 - Article
AN - SCOPUS:84946532372
SN - 0567-7718
VL - 31
SP - 660
EP - 671
JO - Acta Mechanica Sinica/Lixue Xuebao
JF - Acta Mechanica Sinica/Lixue Xuebao
IS - 5
ER -