  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.
