2007/02/28 by Linxiang X. Wang, Wang, Linxiang X., Roderick Melnik +2
Engineering · Materials Science · Physics and Astronomy · #Elasticity and Material Modeling #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Shape Memory Alloy Transformations #Thermoelastic and Magnetoelastic Phenomena #cond-mat.mtrl-sci
paper · pdf · doi:10.48550/arxiv.cond-mat/0702689
Keywords: nonlinear waves, thermo-mechanical coupling, martensite transformations, Ginzburg-Landau theory, Chebyshev collocation method
arxiv created 2007/02/28 · openalex publication_date 2007/02/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Many new applications of ferroelastic materials require a better understanding of their dynamics that often involve phase transformations. In such cases, an important prerequisite is the understanding of wave propagation caused by pulse-like loadings. In the present study, a mathematical model is developed to analyze the wave propagation process in shape memory alloy rods. The first order martensite transformations and associated thermo-mechanical coupling effects are accounted for by employing the modified Ginzburg-Landau-Devonshire theory. The Landau-type free energy function is employed to characterize different phases, while a Ginzburg term is introduced to account for energy contributions from phase boundaries. The effect of internal friction is represented by a Rayleigh dissipation term. The resulted nonlinear system of PDEs is reduced to a differential-algebraic system, and Chebyshev's collocation method is employed together with the backward differentiation method. A series of numerical experiments are performed. Wave propagations caused by impact loadings are analyzed for different initial temperatures. It is demonstrated that coupled waves will be induced in the material. Such waves will be dissipated and dispersed during the propagation process, and phase transformations in the material will complicate their propagation patterns. Finally, the influence of internal friction and capillary effects on the process of wave propagation is analyzed numerically.