A multiscale constitutive model is developed and applied to magnetostrictive materials to predict multi-axial ferromagnetic switching. The modeling framework is an extension of a one-dimensional homogenized energy model that employs a stochastic distribution of localized magnetic moments. Here, the model is extended to multi-axial ferromagnetic switching in a polycrystalline ferromagnetic material. A mean-field approximation is adopted to quantify ferromagnetic switching from multi-axial magnetic field loading at the single crystal length scale. Polycrystalline ferromagnetic behavior is modeled by homogenizing stochastic distributions of underlying microscopic fields associated with material inhomogeneities at the grain length scale. Approximations of the stochastic distributions are made to improve computational efficiency for finite element implementation. The constitutive model is numerically validated and implemented in the commercial finite element software, COMSOL.

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