A thermodynamically consistent phenomenological model for ferroelectric and ferroelastic hysteresis

TL;DR

This paper introduces a thermodynamically consistent phenomenological model for ferroelectric and ferroelastic hysteresis, accurately capturing electromechanical coupling in piezoelectric materials and ensuring well-posedness of the coupled PDE system.

Contribution

It presents a novel hysteretic model satisfying thermodynamic principles, with a proof of existence and uniqueness of solutions for the coupled electromechanical PDEs.

Findings

Model agrees well with experimental data

Proves well-posedness of the PDE system

Introduces a new Lipschitz continuity theorem

Abstract

We propose a hysteretic model for electromechanical coupling in piezoelectric materials, with the strain and the electric field as inputs and the stress and the polarization as outputs. This constitutive law satisfies the thermodynamic principles and exhibits good agreement with experimental measurements. Moreover, when it is coupled with the mechanical and electromagnetic balance equations, the resulting PDE system is well-posed under the hypothesis that hysteretic effects take place only in one preferred direction. We prove the existence and uniqueness of its global weak solutions for each initial data with prescribed regularity. One of the tools is a new Lipschitz continuity theorem for the inverse Preisach operator with time dependent coefficients.