Micromechanically motivated constitutive model embedded in two-dimensional polygonal finite element framework for magnetostrictive actuators

A two-dimensional constitutive model based on micromechanical domain rotation events is presented in this work to demonstrate the nonlinear actuator behavior of magnetostrictive materials, in particular, Galfenol. The model constructed upon thermodynamic principles accounts back fields which resist or aid the domain rotation events inside a grain due to external magnetomechanical loading. The developed model is then incorporated into the polygonal finite element technique that combines Voronoi-based discretization with the hybrid finite element method. In this approach, the stress and magnetic flux density are treated as approximate functions inside the element, but the mechanical displacement and magnetic potential, which act as degrees of freedom, are defined only along the element boundary. This approach allows each randomly generated Voronoi polygon in the plane discretization to act as a single finite element mimicking an individual magnetomechanical grain in a polycrystalline Galfenol, eliminating the need for further subdiscretization of the Voronoi polygon. This coupled framework simulates the nonlinear actuator characteristics of the magnetostrictive material under complex magnetomechanical loading conditions in line with the experimental observations reported in the literature.