A Domain Wall Model for Hysteresis in Ferroelastic Materials

We develop a model that quantifies constitutive nonlinearities and hysteresis inherent to ferroelastic compounds, with emphasis placed on shape memory alloys. We formulate the model in two steps. First, we use the Landau theory of phase transitions to characterize the effective Gibbs free energy for both single-crystal and polycrystalline ferroelastics. The resulting nonlinear equations model equilibrium material behavior in the absence of impurities. Second, we incorporate pinning losses to account for the energy required to move domain walls across material inclusions. The full model is analogous to those developed by Jiles and Atherton for ferromagnetic compounds and Smith and Hom for ferroelectric materials. We illustrate aspects of the model through numerical simulations and comparisons with experimental stress-strain data.