ABSTRACT
This chapter describes developed interest in so-called 'smart' materials whose mechanical behaviour can be changed by the application of magnetic fields. It summarizes the mechanical and magnetic balance equations, together with the boundary conditions. The chapter explores the basic problem of simple shear, with the magnetic induction vector as the independent magnetic variable. It considers the non-homogeneous deformation of azimuthal shear of a thick-walled circular cylindrical tube in the presence of either an axial or an azimuthal magnetic field, with the magnetic field vector as the independent magnetic variable. The chapter presents formulations of the constitutive laws based separately on the magnetic field and the magnetic induction as the independent magnetic variable. Generally, elastomers are considered to be isotropic materials. Consider a magneto-sensitive body that, in the absence of mechanical loads and magnetic fields, occupies a region in a three-dimensional Euclidean space.
