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Hysteresis is an important issue in modeling piezoelectric materials, forexample, in applications to energy harvesting, where hysteresis losses mayinfluence the efficiency of the process. The main problem in numericalsimulations is the inversion of the underlying hysteresis operator. Moreover,hysteresis dissipation is accompanied with heat production, which in turnincreases the temperature of the device and may change its physicalcharacteristics. More accurate models therefore have to take the temperaturedependence into account for a correct energy balance. We prove here that theclassical Preisach operator with a fairly general parameter-dependence admits aLipschitz continuous inverse in the space of right-continuous regulatedfunctions, propose a time-discrete and memory-discrete inversion algorithm, andshow that higher regularity of the inputs leads to a higher regularity of theoutput of the inverse.

Inverse parameter-dependent Preisach operator in thermo-piezoelectricity modeling