Dynamics of shape memory alloys patches with mechanically induced transformations | Zendy

Linxiang Wang | Zendy; Roderick Melnik | Zendy

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Dynamics of shape memory alloys patches with mechanically induced transformations

Author(s) -

Linxiang Wang,

Roderick Melnik

Publication year - 2006

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2006.15.1237

Subject(s) - shape memory alloy , nonlinear system , coupling (piping) , partial differential equation , basis (linear algebra) , algebraic number , thermal , algebraic properties , algebraic equation , mechanics , mathematical analysis , mathematics , physics , computer science , materials science , geometry , thermodynamics , quantum mechanics , metallurgy , artificial intelligence , pure mathematics

A mathematical model is constructed for the modelling of two dimensional thermo-mechanical behavior of shape memory alloy patches. The model is constructed on the basis of a modified Landau-Ginzburg theory and includes the coupling effect between thermal and mechanical fields. The free energy functional for the model is exemplified for the square to rectangular transformations. The model, based on nonlinear coupled partial differential equations, is reduced to a system of differential-algebraic equations and the backward differentiation methodology is used for its numerical analysis. Computational experiments with representative distributed mechanical loadings are carried out for patches of different sizes to analyze thermo-mechanical waves, coupling effects, and 2D phase transformations.

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