A laminate‐based modelling approach for rate‐dependent switching in ferroelectric materials

Abstract

This contribution focuses on the sequential laminate-based modelling approach for the numerical simulation of the complex electromechanical material behaviour of ferroelectric single crystals. The construction of engineered domain configurations by using the method of sequential lamination in order to study the domain evolution and polarisation switching in ferroelectric single crystals has recently been carried out in the works of [1][2][3][4]. By fulfilling the kinematic and polarisation compatibility conditions between the domain structures in a crystal, the proposed laminate-based formulation is governed by an energyenthalpy function and by a dissipation potential. The mixed energy-enthalpy, written in terms of the total strains, electric field and a set of internal variables, here the multi-rank laminate volume fractions, governs the dissipative electromechanical response of the ferroelectric crystal, whereas the rate-dependent dissipation potential formulated in terms of the flux of the internal variables describes the time-dependent evolution of the multi-rank laminate volume fractions, subjected to inequality constraints. The model reproduces experimentally observed hysteresis and butterfly curves, characteristic for single crystal ferroelectric materials, when subjected to homogeneous electromechanical loading conditions.

A laminate‐based framework for switching and microstructure evolution in polycrystalline ferroelectrics

“…[1][2][3]. This contribution extends the ratedependent laminate-based model [1], established for single crystal ferroelectrics, in order to predict the polarisation switching of polycrystalline ferroelectric materials, in particular barium titanate (BaTiO 3 ). The polycrystal laminate-based model is then embedded into a finite element framework to solve inhomogeneous boundary value problems with practical applications.…”

“…[5], with ε M (µ) and P M (µ) denoting the remnant strain and polarisation, respectively, of a single crystal grain, see [1]. The thermodynamical potential, used to compute the constitutive quantities and the driving forces of domain evolution, reads…”

“…The boundary value problem is discretised by 200 tri-linear brick elements with each finite element representing a single crystal grain. Keeping the lower electrode grounded at all times, the upper counterpart is subjected to an alternating electric potential with φ max = ±170 V. Considering the single crystal BaTiO 3 parameters, as used in [1], the dielectric displacements and the total strains are computed iteratively. The distribution of dielectric displacement D 3 along with remnant polarisation vectors are shown in Figs.…”

“…Laminate-based models based on mixture theory ansatz are considered for describing the non-linear hysteretic response of single crystal ferroelectrics under combined electromechanical loads, see e.g. [1][2][3]. This contribution extends the ratedependent laminate-based model [1], established for single crystal ferroelectrics, in order to predict the polarisation switching of polycrystalline ferroelectric materials, in particular barium titanate (BaTiO 3 ).…”