This paper provides a unified modeling framework for ferroelectric, ferromagnetic and ferroelastic materials operating in hysteretic and nonlinear regimes. Whereas the physical mechanisms which produce hysteresis and constitutive nonlinearities in these materials differ at the microscopic level, shared energy relations can be derived at the lattice, or mesoscopic, scale. This yields a class of models which are appropriate for homogeneous, single crystal compounds. Stochastic homogenization techniques are then employed to construct macroscopic models suitable for nonhomogeneous, polycrystalline compounds with variable effective fields or stresses. This unified methodology for quantifying hysteresis and constitutive nonlinearities for a broad class of ferroic compounds facilitates both material characterization and subsequent model-based control design. Attributes of the models are illustrated through comparison with piezoceramic, magnetostrictive and thin film SMA data.
