The paper presents a unified modeling framework for ferroelectric, ferromagnetic and ferroelastic materials with a particular focus on their hysteretic and nonlinear behavior. At the micro-scale, the physical mechanisms, which produce hysteresis and constitutive nonlinearities in these materials, differ quite considerably. At the meso-scale, however, these materials exhibit very similar features, which can be characterized by multi-well free energy functions typical for phase transformations. Based on statistical thermodynamics and the theory of thermally activated processes, a unified thermodynamic model for the temperature and rate-dependent hysteretic behavior at the macro-scale is derived and illustrated through comparison with experimental data for piezoceramic, magnetostrictive and shape memory alloy (SMA) materials.

The talk concludes with an application of a phase field formulation of the above model. Representative for a number of typical applications such as micro-actuators or stent components, a coupled multi-field finite element analysis of a SMA cantilever beam using COMSOL is presented.