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On cloaking forelasticity andphysical equationswith a transformationinvariant form Graeme W. MiltonMarc BrianeJ.R. Willis2006 год

On cloaking for elasticity and physical equations with a transformation invariant form
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Аннотация: In this paper, we investigate how the form of the conventional elastodynamic equations changes under curvilinear transformations. The equations get mapped to a more general form in which the density is anisotropic and additional terms appear which couple the stress not only with the strain but also with the velocity, and the momentum gets coupled not only with the velocity but also with the strain. These are a special case of equations which describe the elastodynamic response of composite materials, and which it has been argued should apply to any material which has microstructure below the scale of continuum modelling. If composites could be designed with the required moduli then it could be possible to design elastic cloaking devices where an object is cloaked from elastic waves of a given frequency. To an outside observer it would appear as though the waves were propagating in a homogeneous medium, with the object and surrounding cloaking shell invisible. Other new elastodynamic equations also retain their form under curvilinear transformations. The question is raised as to whether all equations of microstructured continua have a form which is invariant under curvilinear space or space-time coordinate transformations. We show that the non-local bianisotropic electrodynamic equations have this invariance under space-time transformations and that the standard non-local, time-harmonic, electromagnetic equations are invariant under space transformations.
Год издания: 2006
Авторы: Graeme W. Milton, Marc Briane, J.R. Willis
Издательство: IOP Publishing
Источник: New Journal of Physics
Ключевые слова: Acoustic Wave Phenomena Research, Thermoelastic and Magnetoelastic Phenomena, Composite Structure Analysis and Optimization
Другие ссылки: New Journal of Physics (HTML)
HAL (Le Centre pour la Communication Scientifique Directe) (HTML)
HAL (Le Centre pour la Communication Scientifique Directe) (HTML)