This talk is motivated by recently developed interest in so-called 'smart' materials whose mechanical behavior changes dramatically on the application of magnetic fields. Examples of applications include devices that are used to control the damping characteristics of vibration bsorbers. In particular, we are concerned here with elastomers that contain a distribution of ferrous particles embedded within their bulk so that they respond to the application of magnetic fields by changing significantly their stress-strain behavior. Recent theoretical work concerning the coupling of mechanical and magnetic effects in these aterials is outlined, and the theory is applied to some simple prototype boundary-value problems of practical interest. A notable feature of the results is that, for particular combinations of deformation and magnetic field, restrictions are placed on the admissible class of constitutive laws and that these restrictions depend on which magnetic field vector is used as the independent variable.
Ray Ogden has been George Sinclair Professor in the Department of Mathematics at Glasgow University since 1984. He gained his undergraduate and graduate degrees at the University of Cambridge, his PhD adviser having been Professor Rodney Hill. Before moving to Glasgow he held faculty appointments at the universities of East Anglia, Bath and Brunel. He was Head of Department in Glasgow for more than eight years. His research interests include: fundamental aspects of nonlinear elasticity theory and its applications, particularly applications to the mechanics of rubberlike materials; analysis of the stability of elastic bodies subject to finite deformations; studies of the influence of finite strain on the propagation of waves and vibrations in elastic solids; the biomechanics of soft tissue; damage mechanics and stress softening behavior of solids; the mechanics and stability of fiber-reinforced solids; magnetoelastic and electroelastic behavior of elastomeric solids. He has published more than 150 articles and books, including the classic text â€˜Non-Linear Elastic Deformationsâ€™, which is now available as a Dover paperback. He was Editor of the IMA Journal of Applied Mathematics for ten years and is currently a member of the editorial board of the International Journal of Engineering Science, the Quarterly Journal of Mechanics and Applied Mathematics, Mathematics and Mechanics of Solids, Proceedings of the Royal Society of London A, International Journal of Nonlinear Mechanics, Biomechanics and Modeling in Mechanobiology, Zeitschrift fÃ¼r Angewandte Mathematik und Physik (ZAMP), Archives of Mechanics, and Journal of Elasticity. He is also very active in the organization of advanced courses, such as those run at the International Centre for Mechanical Sciences in Italy, and international conferences.