Finite element modelling and simulation of magnetostrictive materials

Magnetostriction is a nonlinear phenomenon observed in all ferromagnetic materials that couples elastic, electric and magnetic fields. Its industrial applications include sensors, actuators, adaptive or functional structures, robotics, transducers and MEMS. While many of these applications can at present be addressed by simple analytical methods, it is expected that in the near future new very small or very big devices will require more sophisticated analysis of the numerical type. In this work we formulate new governing equations, which are fully coupled, 3-D, nonlinear (except for material properties), partially dynamic under small deformation and based on linear constitutive equations resembling piezoelectricity. Important effects, such as eddy currents responsible for heat generation, can be directly evaluated. If technological developments make it necessary, other effects such as full thermal coupling, elastic dynamics and/or shock waves, and material non-linearity can be added by adapting advanced features from Computational Mechanics. The formulation is implemented in the research finite element code FEAR In order to validate both the method and the implementation, we present results for several elastic and electromagnetic simple problems.