### Tuesday, 12 October 2004 - 9:15 AM

### This presentation is part of : Rajagopal Symposium

### Nonlinear magnetoelastic deformations: theory and applications

**Ray W. Ogden**, University of Glasgow, Department of Mathematics, 15 University Gardens, Glasgow, G12 8QW, United Kingdom and Luis Dorfmann, Institute of Structural Engineering, Peter Jordan Str. 82, Vienna, A-1190, Austria.
This work is motivated by recent renewed interest in the subject of electromagnetic continua generated by the development of so-called ‘smart’ materials used, for example, in devices for controlling the damping characteristics of vibration absorbers. Specifically, such materials are elastomers with a distribution of ferrous particles embedded within their bulk. We first summarize a new and simple formulation of the governing (equilibrium) equations and constitutive laws for a solid material capable of large magnetoelastic deformations. The general constitutive law for an isotropic material in the presence of a magnetic field is described and expressed in a compact form. The equations are applied and solutions obtained, in the case of an incompressible material, for certain representative boundary-value problems involving circular cylindrical geometry, specifically (a) the helical shear of a circular cylindrical tube, its specializations to axial and azimuthal shear, and (b) the problem of extension and torsion of a circular cylindrical tube. These are classical problems in the context of finite elasticity, but here we include the influence of either an initially axial or an azimuthal magnetic field, the latter generated by a steady current with a central concentric core. Additionally, if time is available, we examine the effect of an initially uniform magnetic field on the bending of a rectangular block into a sector of a circular cylinder. For each problem, the dependence of the mechanical response on the magnitude of the applied magnetic field is discussed.

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