Homogenized Strain Model for Ni—Mn—Ga Driven with Collinear Magnetic Field and Stress

Prior experimental measurements by the authors demonstrated large reversible strains of ·0.41% along the [001] crystal direction of a cylindrical Ni ₅₀ Mn _28.7 Ga _21.3 rod driven with a magnetic field along the same direction and no external restoring force. The origin of the reversibility is attributed to internal bias stresses generated by impurities absorbed during manufacture of the alloy. This article presents a macroscopic constitutive model for Ni—Mn—Ga strain in collinear field and stress configuration. The switching between two variant orientations in the presence of Zeeman energy and the pinning energy of the impurities is formulated through a Gibbs energy function for the crystal lattice. Inhomogeneous local interaction fields and impurity distributions are addressed through stochastic homogenization techniques. Attributes of the model are illustrated through comparison of model results with strain—field measurements collected at various compressive loads. Constrained optimization is used to determine the necessary parameters and an error analysis is performed to assess the accuracy of the model for various loading conditions. The collinear field and stress configuration can lead to solenoid transducers with enhanced energy density and bandwidth relative to standard electromagnet devices.