Abstract
An energy-based model of the ferroelectric polarization process is presented in the current contribution. In an energy-based setting, dielectric displacement and strain (or displacement) are the primary independent unknowns. As an internal variable, the remanent polarization vector is chosen. The model is then governed by two constitutive functions: the free energy function and the dissipation function. Choices for both functions are given. As the dissipation function for rate-independent response is non-differentiable, it is proposed to regularize the problem. Then, a variational equation can be posed, which is subsequently discretized using conforming finite elements for each quantity. We point out which kind of continuity is needed for each field (displacement, dielectric displacement and remanent polarization) is necessary to obtain a conforming method, and provide corresponding finite elements. The elements are chosen such that Gauss’ law of zero charges is satisfied exactly. The discretized variational equations are solved for all unknowns at once in a single Newton iteration. We present numerical examples gained in the open source software package Netgen/NGSolve.
Highlights
Piezoceramics are widely used as so-called smart materials for high-precision actuation and sensing
Polarization aligned with the electric field builds up, and a remanent polarization is maintained as this poling field is removed
We have presented energy-based model of the ferroelectric polarization process
Summary
Piezoceramics are widely used as so-called smart materials for high-precision actuation and sensing. The remanent polarization state can change under sufficiently high electrical or mechanical loadings In applications such as some macrofibre composites (MFCs), the poling electric field is not unidirectional, which will lead to non-standard polarization patterns Semenov et al (2010) provide a multi-directional energy based model using a vector potential for the dielectric displacement They propose to discretize the vector potential in the finite element method, and provide consistent tangent moduli for the implementation. The authors of the present work have analyzed such an energy-based formulation in the framework of variational inequalities Pechstein et al (2020) This concept has been used in the mathematical analysis of other nonlinear problems in mechanics, such as elastoplasticity Han and Reddy (1999) or contact mechanics Sofonea and Matei (2011).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have