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.
By providing a fast and accurate constitutive model suitable for use in finite element analysis, a key barrier inhibiting the development of magnetostrictive technologies will be lowered. A magnetostrictive constitutive model must calculate the nonlinear magnetization and magnetostriction of a material in response to magnetic and mechanical loads. This presentation will analyze the accuracy and computational complexity of three different integration methods performing these calculations: Riemann sums, Clenshaw-Curtis (CCQ) quadrature, and Laplace’s Method. We will show how using Laplace’s method provides an accurate and computationally efficient calculation of nonlinear magnetization, magnetostriction, and material properties for use in a FEA program.
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