3D Dynamic Finite Element Model for Magnetostrictive Galfenol-based Devices

Galfenol is an alloy of iron and gallium which possesses a unique combination of structural strength and significant magnetostriction. This alloy can be machined, welded and extruded into complex geometries opening up avenues for a new class of load-bearing transducers with 3D functionality. This work addresses the development of an advanced modeling tool to aid in the design of Galfenol transducers. The model describes the full nonlinear coupling between the electrical, magnetic and mechanical domains in 3D Galfenol structures, yielding complete system input-output relationships. Maxwell's equations for electromagnetics and Navier's equations for mechanical systems are formulated in weak form. An energy-averaged constitutive model is employed to relate magnetization and strain to magnetic field and stress in the Galfenol domain. 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 the bias point describes the system dynamics for moderate inputs. Dynamic responses at large input fields and stresses are described through an implicit dynamic solution based on the trapezoidal rule. The model equations are solved on a commercial finite element solver. A case study consisting of a Galfenol unimorph is presented which illustrates the model's ability to describe transient dynamic responses.