Nonlinear magnetoelastic deformations of elastomers

TLDR: In this paper, the problem of axial shear of a circular cylindrical tube subject to a radial magnetic field was formulated and then solved for a specific constitutive law with a magnetic field that is initially radial.

Abstract: Magneto-sensitive (MS) elastomers are “smart materials” whose mechanical properties may be changed rapidly by the application of a magnetic field Such materials typically consist of micron-sized ferrous particles dispersed within an elastomeric matrix The equations governing deformations of these materials were discussed in a recent paper by the present authors and applied in a particular specialization of the constitutive model to the problem of axial shear of a circular cylindrical tube subject to a radial magnetic field In the present paper we develop the governing equations for a more general form of constitutive model and provide alternative forms of the equations, including a Lagrangian formulation To illustrate the theory the problem of azimuthal shear of a circular cylindrical tube is formulated and then solved for a specific constitutive law with a magnetic field that is initially radial The results, which show the stiffening of the azimuthal shear stress/strain response with increasing magnetic field strength, are illustrated graphically