Nonlinear finite element model for 3D Galfenol systems

This work addresses the development of an advanced modeling tool which describes the full nonlinear coupling in three-dimensional (3D) Galfenol transducers to provide system level input–output relationships. Maxwell's equations for electromagnetics and Navier's equations for mechanical systems are formulated in weak form. The constitutive behavior of Galfenol is described through a nonlinear discrete energy-averaged model. The overall system is approximated hierarchically; first, piecewise linearization is used to describe quasi-static responses and magnetic bias calculations. A linear dynamic solution with piezomagnetic coefficients computed at a given magnetic bias describes the system dynamics for moderate inputs. Dynamic responses at large input fields and stresses are quantified through an implicit dynamic solution based on the trapezoidal rule. The model simultaneously incorporates the effects of eddy currents, flux leakage, structural dynamics and nonlinear material behavior. A case study on a Galfenol unimorph actuator validates the model in quasistatic and dynamic conditions