This investigation focuses on the development of unified techniques for mathematically modeling the hysteresis and constitutive nonlinearities inherent to ferroelectric, ferromagnetic and ferroelastic materials at moderate to high drive levels. Motivating materials include piezoceramics, relaxor ferroelectrics, magnetostrictives and shape memory alloys, but the modeling approach is sufficiently general to include a large variety of ferroic compounds. The nonlinear and hysteretic behavior of these materials can be attributed to their underlying domain structure and this common ferroic framework is utilized to construct unified constitutive models for the materials. These models are constructed in two steps. In the first, thermodynamic principles are employed to quantify the anhysteretic behavior which would result in the absence of inclusions in the material. In the second step, energy relations are employed to quantify the irreversible and reversible motion of domains walls about pinning sites in the material. The resulting models are formulated as low-order ordinary differential equations. The performance and behavior of the models are illustrated for piezoceramic, magnetostrictive and shape memory compounds.
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