Inverse parameter-dependent Preisach operator in thermo-piezoelectricity modeling

Pavel Krejčí; Giselle A. Monteiro

doi:10.3934/dcdsb.2018299

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2019, Volume 24, Issue 7: 3051-3066. Doi: 10.3934/dcdsb.2018299

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Inverse parameter-dependent Preisach operator in thermo-piezoelectricity modeling

Pavel Krejčí and
Giselle A. Monteiro^,

Institute of Mathematics, Czech Academy of Sciences, Žitná 25,115 67 Praha 1, Czech Republic

* Corresponding author: Giselle A. Monteiro
* Corresponding author: Giselle A. Monteiro

Received: February 28, 2018

Revised: May 31, 2018

Early access: October 2018

Published: May 2019

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Abstract

Hysteresis is an important issue in modeling piezoelectric materials, for example, in applications to energy harvesting, where hysteresis losses may influence the efficiency of the process.The main problem in numerical simulations is the inversion of the underlying hysteresis operator.Moreover, hysteresis dissipation is accompanied with heat production, which in turn increases thetemperature of the device and may change its physical characteristics. More accurate models thereforehave to take the temperature dependence into account for a correct energy balance.We prove here that the classical Preisach operator with a fairly general parameter-dependenceadmits a Lipschitz continuous inverse in the space of right-continuous regulated functions, propose a time-discrete and memory-discrete inversion algorithm, and show that higher regularity of the inputs leads to a higher regularity of the output of the inverse.

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Mathematics Subject Classification: Primary: 34C55, 47J40; Secondary: 58C07, 49J40.

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