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.
Issue Section:
Research Papers
Keywords:
Chebyshev approximation,
eigenvalues and eigenfunctions,
elastic hysteresis,
ferroelastic transitions,
Galerkin method,
Ginzburg-Landau theory,
martensitic transformations,
nonlinear differential equations,
partial differential equations,
thermoelasticity,
ferroelastic dynamics,
phase transformations,
coupled dynamic thermoelasticity,
optimal approximation,
extended proper orthogonal decomposition,
Galerkin projection,
multiphase solids,
smart materials and structures,
shape memory alloys,
metastable phases,
low dimensional models,
multiscale problems,
model reduction
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, and Melnik
, R. V. N.
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, R. V. N.
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.Copyright © 2010
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