Nonlinear modeling and finite element simulation of magnetoelectric coupling and residual stress in multiferroic composites

The coupling of magnetic and electric fields due to the constitutive behavior of a material is commonly denoted as magnetoelectric (ME) effect. The latter is only observed in a few crystal classes exhibiting a very weak coupling which can hardly be exploited for technical applications. Much larger coupling coefficients are obtained in composite materials, where ferroelectric and ferromagnetic constituents are embedded in a matrix. The ME effect is then induced by the strain of the matrix converting electrical and magnetic energies based on the ferroelectric and magnetostrictive effects. In this paper, the theoretical background of linear and nonlinear constitutive multifield behavior as well as the finite element implementation is presented. A nonlinear material model describing the magnetoferroelectric behavior is presented. On this basis, polarization switching in the ferroelectric phase is simulated and the influence on stress distribution and ME coupling is analyzed. Numerical homogenization is performed, in order to supply ME-coupling constants, which are compared to experimental results for both the perfect poling state of a linear calculation and the more realistic case of nonlinear magnetoferroelectricity. The numerical tools supply useful means for the optimization of multiferroic composites with respect to strength and functionality.