Constitutive relationship for magnetostrictive composites

Although the MS materials show nonlinear relationship, the behavior of most of these materials can be described by using a linear theory as the active materials could easily be biased. With biasing, the material behaves in a quasi-linear manner and follows the following constitutive relationship

Actuation equation

(30.1)

Sensing equation

(30.2)

Where S^H is the compliance at constant magnetic field intensity H; the permeability at constant stress , d the magneto-mechanical constant, B the flux density and the strain.