Finite Volume Analysis of Nonlinear Thermo-mechanical Dynamics of Shape Memory Alloys

In this paper, the finite volume method is developed to analyze coupled dynamic problems of nonlinear thermoelasticity. The major focus is given to the description of martensitic phase transformations essential in the modelling of shape memory alloys. Computational experiments are carried out to study the thermo-mechanical wave interactions in a shape memory alloy rod, and a patch. Both mechanically and thermally induced phase transformations, as well as hysteresis effects, in a one-dimensional structure are successfully simulated with the developed methodology. In the two-dimensional case, the main focus is given to square-to-rectangular transformations and examples of martensitic combinations under different mechanical loadings are provided.Comment: Keywords: shape memory alloys, phase transformations, nonlinear thermo-elasticity, finite volume metho

Numerical Model For Vibration Damping Resulting From the First Order Phase Transformations

A numerical model is constructed for modelling macroscale damping effects induced by the first order martensite phase transformations in a shape memory alloy rod. The model is constructed on the basis of the modified Landau-Ginzburg theory that couples nonlinear mechanical and thermal fields. The free energy function for the model is constructed as a double well function at low temperature, such that the external energy can be absorbed during the phase transformation and converted into thermal form. The Chebyshev spectral methods are employed together with backward differentiation for the numerical analysis of the problem. Computational experiments performed for different vibration energies demonstrate the importance of taking into account damping effects induced by phase transformations.Comment: Keywords: martensite transformation, thermo-mechanical coupling, vibration damping, Ginzburg-Landau theor

Thermo-Mechanical Wave Propagation In Shape Memory Alloy Rod With Phase Transformations

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.Comment: Keywords: nonlinear waves, thermo-mechanical coupling, martensite transformations, Ginzburg-Landau theory, Chebyshev collocation metho