The theory of electromagnetic continua has received considerable stimulus in the last few years because of the rapid development of elastomeric and polymeric materials that can respond dramatically to the application of an electric and/or magnetic field. Such materials, often referred to as ‘smart materials’, are being used in a variety of applications, ranging from high-speed actuators and sensors, and active car suspensions and vibration isolators, to artificial muscles, and other biomedical applications. The key point is that the mechanical properties of the materials can be changed rapidly and substantially by externally applied electric or magnetic fields. Thus, the coupling between mechanics and electromagnetism is both strong and highly nonlinear. The coupling in the material response is typically achieved and optimized by distributing within an elastomeric matrix nano- or micron-sized ferrous particles. Crosslinking may occur, for example, in the presence of an applied field, whereby particles form chain-like structures aligned along the applied field direction. The material is then characterized by two families of preferred directions, which can be utilized to produce highly controllable smart materials. Mathematical and computational methods pervade research, development, testing, and evaluation problems encountered by researchers in the field of smart materials, and associated modelling issues have a fundamental role in the analysis of problems that arise in such complex materials.
The purpose of the course is to present a state-of-the-art overview of the continuum theory of both electro- and magneto-sensitive materials capable of large deformations, particularly elastomers and polymers. This will include discussion of the underlying physics and of the mechanical properties of magneto-and electro-sensitive elastomers, nematic elastomers and gels. and computational formulations related to the modelling of these materials from the point of view of material properties and, in particular, control of their mechanical properties will be treated in detail.
The presentations will include carefully crafted overviews of the fundamental formulation of the three-dimensional theory from several points of view. They will also include solutions to boundary-value problems which are amenable to experimental verification, and the numerical implementation of solution strategies that take coupling between field and deformation effects into account. A further aspect of the course will be discussion of stability of equilibria in the presence of electromagnetic coupling together with extensions of the classical energy criterion of elastic stability based on thermodynamical considerations. Additional topics will include extensions of the concept of material, or ‘configurational’ forces, the theory of incremental fields and small-amplitude waves, and the consistent derivation of large-deformation models of electro-magneto-elastic membranes and plates.

Coordinators: Raymond W. Ogden (University of Glasgow, UK) David J. Steigmann (University of California, Berkeley, CA, USA)