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Nonlinear Constitutive Relations for Magnetostrictive Materials with Applications to 1-D Problems

In this paper, we present a nonlinear constitutive relation for magnetostrictive materials that includes nonlinear coupling effects arising between temperature/preload and magnetic field strengths. The relations are derived from thermodynamic principles using Gibbs free energy expanded in a Taylor series with only the pertinent constants included as determined from experimental evidence present in existing literature. By assuming that the magnetostrictive material is operated in a biased magnetic field and perturbing this field with a small value, relations between the nonlinear material constants and linear coefficients present in existing literature are derived. The accuracy of the nonlinear constitutive relation is evaluated by comparing experimental results obtained on a Terfenol-D rod operating under both magnetic field and stress biases with theoretical values. Results indicate that the model adequately predicts the nonlinear strain/field relations in specific regimes. The nonlinear constitutive relations are also integrated into a 1-dimensional nonlinear finite element model for studying structural components. The coupled magneto elasticity problem is derived using a weighted residual method along with a Newton-Raphson iteration technique. Results of the analytical model indicate that linear approaches are inappropriate for modeling the response of this material in a structure.