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An accurate and computationally efficient non-linear magnetostrictive constitutive model is required to properly develop novel magnetostrictive technologies. While the authors have recently shown exact analytical solutions are available for one-dimensional constitutive models built with statistical mechanics, there are currently no known closed form three-dimensional solution. Instead, this presentation will evaluate the use of several different approximation techniques in a three-dimensional model including: Laplace’s method, series expansions, and multivariate spline interpolation. We will show the conditions under which each approximation is numerically accurate and present a model that maintains numerical accuracy over a wide range of applied fields and stresses.
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Alecsander N. Imhof, John P. Domann, "3D constitutive model of transversely isotropic magnetostrictive materials," Proc. SPIE PC12044, Behavior and Mechanics of Multifunctional Materials XVI, (18 April 2022); https://doi.org/10.1117/12.2612866