Finite element simulation of magnetoelectric coupling in multiferroic composites

Abstract eng:
summarized and compared to each other. Ferroelectric materials exposed to electromagnetic fields are described by the constitutive equations: a” = Cijkz(€kz — 8,15?) — ell-jEl, D1 = elij (5U- — 811]”) + KmEn + Pf", Bk = ,ukam [1]. Within a microphysical framework, the irreversible strain eff] and polarization Pf" are due to domain wall motion. Considering plane problems, a grain consists of four domain species separated by 90° - and 180° - domain walls. The formulation of a nonlinear constitutive law thus requires at least four internal variables and associated evolution equations locally describing the switching of unit cells on the micro level. Due to intended applications within a multiferroic framework, the ferroelectric material is allocated a magnetic permeability expressed by the third equation relating the magnetic field Hm and the induction Bk. The elastic, piezoelectric, dielectric and magnetic permeability tensors cU-kl, ell-j, Km and ,um also depend on the internal variables, giving rise to an additional source of nonlinearity, even in the magnetic properties. The other quantities are stress 0”, electric field E and electric displacement D1.

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