ABSTRACT:
Interest in cloaking theory (i.e. rendering objects near-invisible to incident waves) and its practical realization has grown significantly since the early theoretical work in 2006 of Leonhardt and the Pendry group in optics and electromagnetism respectively. Methods have largely been based on the idea of coordinate transformations, which motivate the design of cloaking metamaterials. These materials are able to guide waves around a specific region of space. Research has subsequently focused on the possibility of cloaking in the contexts of acoustics, surface waves in fluids, heat transfer, fluid flow and linear elastodynamics. It was shown by Milton and co-workers that elastodynamic cloaking is made difficult due to the lack of invariance of Navier’s equations under general coordinate transformations which retain the symmetries of the elastic modulus tensor. Invariance of the governing equations can be achieved if assumptions are relaxed on the minor symmetries of the elastic modulus tensor but commonly occurring elastic materials do not possess this property. In this talk we shall show that it is theoretically possible to construct elastodynamic cloaks by pre-stressing hyperelastic solids. We shall discuss an initial simple case (antiplane waves) as was studied in [1] and describe various generalizations including finite cloaks and more general elastodynamic wave cloaking problems. Much of this work has been done in collaboration with Prof. Andy Norris (Rutgers, USA).
[1] Parnell, W.J. “Nonlinear pre-stress for cloaking from antiplane elastic waves”,
Proc Roy Soc A, online version now available: doi: 10.1098/rspa.2011.0477.
ADDITIONAL INFORMATION:
William Parnell’s interests are in wave propagation in complex media, multiple scattering theory, linear and nonlinear elasticity, pre-stress, homogenization, micromechanics, mathematical modelling of complex materials, ultrasound in bone, industrial mathematics and application and development of mathematical methods. http://www.maths.manchester.ac.uk/~wparnell