Critical Buckling Load of Magnetostrictive Sensors Under Compression

Magnetostrictive materials are smartmaterials that have a wide range of applications for actuation and detection. They have been widely used in the industry for the development of variousdevices, such as actuators, sensors, transducers, speakers, vibration dampers,and fast relays. This special class of materials shows an inherent couplingbetween magnetic field and deformation. Structures made of magnetostrictivematerials are capable of simultaneously changing their dimensions, and elasticand/or electromagnetic properties in the presence of a magnetic field. The objective of this work is to model andnumerically simulate the instability phenomenon of magnetostrictive sensorssubject to compressive loadings. The mechanical modeling of the consideredsensor is done using a one-dimensional elastic magnetostrictive beam undercompression subjected to a magnetic field. The formulation of the problem iscarried out using the Euler-Bernoulli beam theory and taking into account thecoupling of the mechanical and magnetic effects via the behavior relations ofmagnetostrictive materials. The equilibrium equation of the sensor was obtainedby applying the Lagrangian formalism. The buckling loads and the critical loadof the compressed beam were calculated analytically and numerically using anapproach based on the Finite Element Method (FEM). Different boundaryconditions were considered.