Coupled analysis of composite laminate with embedded magnetostrictive patches

A new finite element formulation for composite laminates containing embedded magnetostrictive patches is studied using anhysteretic, coupled, linear properties of magnetostrictive materials, which will act both as sensors and actuators. Constitutive relationships of magnetostrictive materials are represented through two equations, one for actuation and the other for sensing, both of which are coupled through a magneto-mechanical coefficient. The coupled model is studied without assuming any explicit direct relationship with the magnetic field. This is unlike the uncoupled model, where the magnetic field is assumed to be proportional to the actuation current and coil turns per unit length. Hence, both mechanical and magnetic (smart) degrees of freedoms are required to take care of the total mechanical and magnetic energy in the system. In this model, the elastic modulus, the permeability and magneto-elastic constant are assumed not to vary with the magnetic field. Actuation and sensing coils are considered to activate patches and sense the changes in stress in patches. When the actuator patch is excited dynamically by passing an alternating current through the actuation coil, it introduces stress in the structure due to the magneto-mechanical coupling effect, which in turn produces magnetic flux in the sensing patches. This magnetic flux generates open circuit voltage in the sensing coils. A number of numerical experiments are performed to show the essential difference between coupled and uncoupled analyses. For this, static, frequency response and time history analyses are performed in 1D structures. It is found that the ply sequence has a phenomenal effect on the overall response due to coupling.