Model for the magnetomechanical behavior of NiMnGa driven with collinear field and stress

摘要

This paper presents a model for NiMnGa transducers driven with collinear magnetic fields and stresses. Prior work by the authors demonstrates the existence of reversible strains under the application of collinear magnetic fields and stresses oriented along the [001] crystallographic axis of a cylindrical rod of single-crystal Ni_(50)Mn_(28.7)Ga_(21.3). Internal bias stresses from pinning sites in the material are believed to provide the restoring force which allows for the reversibility of the strain. A constitutive model to describe the motion of twin boundaries in the presence of energetically strong pinning sites is presented. The effective pinning strength is represented by an internal bias stress oriented transversely. Stochastic homogenization is then used to account for variability in the bias stresses throughout the material and inhomogeneity in the interaction field intensity. The internal rod dynamics are modeled through force balancing with boundary conditions dictated by the constructive details of the transducer and mechanical load. The model is formulated in variational form, resulting in a second-order temporal system with magnetic field induced strain as the driving mechanism. Model result for unloaded conditions is compared with experimental measurements.