Phenomenological constitutive modeling of ferromagnetic shape memory alloys considering the effects of loading history on reorientation start conditions

Ferromagnetic shape memory alloys (FSMAs) are a branch of smart materials which can undergo inelastic deformation when exposed to magnetic fields. In this work, experiments are carried out on an FSMA consisting of elastic interruptions during reorientation to study the effects of loading history on reorientation start conditions. Correspondingly, a phenomenological approach is introduced to propose appropriate kinetic laws capable of modeling cases in which loading history plays an important role. Conventional phase diagrams in 2D field-stress space are generalized to 3D reorientation surfaces to directly enter the effects of loading history on reorientation start conditions. Algebraic approaches are utilized to find conditions guaranteeing the continuation of variant reorientation. Further experiments are also carried out to verify the proposed model under various incomplete loading-unloading cycles and minor loops. Comparison between numerical and experimental results indicates the validity of the proposed model. Appropriate continuation conditions for the biaxial loading case are proposed, and biaxial results are used to verify the proposed model.