Simple geometrically nonlinear viscoelastic models for martensitic phase
transformations and their simulation using spectral methods

We present a methodology for modeling some features of martensitic phase transformations using geometrically nonlinear elasticity. We then describe how to simulate these models using Fourier and Chebyshev spectral methods. The computational methods used may be useful for simulating other similarly structured semi-linear partial differential equations where high spatial resolution is required.