Inversion algorithms for the homogenized energy model for hysteresis in ferroelectric and shape memory alloy compounds

Ferroelectric and ferromagnetic materials have the advantage of broadband and dual actuator and sensor capabilities. Ferroelastic compounds such as shape memory alloys have large energy densities and are biocompatible. However, to take full advantage of these properties, it is necessary to employ models and control designs that account for the rate-dependent hysteresis, creep, and constitutive nonlinearities inherent to the materials. Inverse compensation is one technique that achieves this purpose. We present an inversion algorithm based on a binary search of a discretized input grid and apply this to the homogenized energy model for modeling hysteresis. The inversion algorithm is shown to provide a reasonable balance between accuracy and computational speed. Numerical examples are presented for three specific cases of the homogenized energy model.