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An anisotropic phase‐field model for transversely isotropic barium titanate with bounded moduli
Author(s) -
Nadgir Omkar,
Keip MarcAndré,
Miehe Christian
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610222
Subject(s) - transverse isotropy , barium titanate , isotropy , moduli , anisotropy , bounded function , materials science , phase (matter) , positive definiteness , field (mathematics) , invariant (physics) , mathematical analysis , mathematics , physics , dielectric , pure mathematics , mathematical physics , optics , quantum mechanics , positive definite matrix , eigenvalues and eigenvectors , optoelectronics
This contribution presents a phase‐field model for transversely isotropic barium titanate, which allows for the adjustment of the full set of anisotropic material parameters. It is a direct extension of the work by Schrade et al. [1] who proposed a phase‐field model for ferroelectrics in the framework of invariant theory. In the present contribution, the loss of positive definiteness is avoided by formulating energetic terms that provide upper and lower bounds for all material moduli involved. We show the characteristics of the formulation by a set of numerical examples in two and three dimensions. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)