An energetic material model for time-dependent ferroelectric behaviour: existence and uniqueness

Abstract

Communicated by P. Colli SUMMARYWe discuss rate-independent engineering models for the multi-dimensional behaviour of ferroelectric materials. These models capture the non-linear and hysteretic behaviour of such materials. We show that these models can be formulated in an energetic framework which is based on the elastic and the electric displacements as reversible variables and on interior, irreversible variables like the remanent polarization. We provide quite general conditions on the constitutive laws which guarantee the existence of a solution. Under more restrictive assumptions we are also able to establish uniqueness results.

A thermodynamically consistent phenomenological model for ferroelectric and ferroelastic hysteresis

“…For a mathematical analysis of some thermodynamically consistent models we refer to [1,19,30]. Whereas most of the so far existing models are designed for the simulation of polarization, depolarization or cycling along the main hysteresis loop, the simulation of actuators requires the accurate simulation of minor loops as well.…”

A variational characterization of rate‐independent evolution

“…For instance, they arise in elasto-plasticity [6,12,14,15,38], phase-transformation in shape memory alloys [2,25,29,31,35], fracture propagation [3,9,13,16,33], delamination and damage phenomena [17,26], ferro-electricity [32], as well as in many other contexts. The common feature of these systems is that they show no (or very short) intrinsic time-scale and react immediately to changes of external actions [22,40], see below.…”

Considerations About Controlled Capacitors

“…From the previous theoretical and experimental work, [10][11][12][13][14][15], related to ferroelectric dielectrics which allow the dielectric permittivity variation against temperature, a capacitor based on BaSrTiO 3 dielectric, has been achieved like a good solution. This is a thermal controlled capacitor and can be used at static switching processes from different automatic control and protection systems.…”