Elastodynamic cloaking: Transformation elasticity with prestressed hyperelastic solids Seminar

"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 after giving a brief introduction to cloaking theory and the difficulties that arise in elastodynamics, we shall show that it is theoretically possible to construct elastodynamic cloaks by pre-stressing hyperelastic (nonlinear) solids (e.g. rubber). We shall discuss an initial simple case (antiplane waves) as was studied in [1] before moving on to describe various generalizations including finite cloaks [2], more general elastodynamic cloaking pre-stress [3] and some more recent work describing more general strain energy functions and practical applications in the antiplane wave case."

 [1] Parnell, W.J. "Nonlinear pre-stress for cloaking from antiplane elastic waves", Proc Roy Soc A 468, 563-580.

[2] Parnell, W.J., Norris, A.N. and Shearer, T. "Employing pre-stress to generate finite cloaks for antiplane elastic waves." Appl. Phys. Letters 100, 171907.

[3] Norris, A.N. and Parnell, W.J. "Hyperelastic cloaking theory:

Transformation elasticity with prestressed solids". Proc. Roy. Soc. A. In press

Speaker Biography

William Parnell is a reader in applied mathematics at the University of Manchester. His research falls into the broad area of continuum mechanics. More specifically, problems in the areas of solid mechanics, acoustics, linear and nonlinear elasticity, elastodynamics, homogenization and micromechanics. He also has interests in mathematical modelling of physical processes and industrial problems, and the application and development of general mathematical methods for applied problems.

William leads the ‘Waves In Complex Continua' (WICC) group in the School of Mathematics at the University of Manchester; is associate editor for the journal Wave Motion and is the programme director for Manchester University's MSc in Applied Mathematics.