Low Dimensional Approximations to Ferroelastic Dynamics and Hysteretic Behavior Due to Phase Transformations
Wang, L.X. and Melnik, R.V.N.
Journal of Applied Mechanics - Transactions of the ASME, 77 (3), 031015, 2010
In this paper, a low dimensional model is constructed to approximate the nonlinear ferroelastic dynamics involving mechanically and thermally-induced martensite transformations. The dynamics of the first order martensite transformation is first modeled by a set of nonlinear coupled partial differential equations (PDEs), which is obtained by using the modified Ginzburg-Landau theory. The Chebyshev collocation method is employed for the numerical analysis of the PDE model. An extended proper orthogonal decomposition is then carried out to construct a set of empirical orthogonal eigenmodes of the dynamics, with which system characteristics can be optimally approximated (in a specified sense) within a range of different temperatures and under various mechanical and thermal loadings. The performance of the low dimensional model is analyzed numerically. Results on the dynamics involving mechanically and thermally-induced phase transformations and the hysteresis effects induced by such transformations are presented.