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Abstract
Wave propagation in periodic elastic composites whose phases may have not only highly contrasting but possibly also (in particular) highly anisotropic stiffnesses and moderately contrasting densities is considered. A possibly interconnected (i.e. not necessarily isolated) "inclusion" phase is assumed generally much softer than that in the connected matrix, although some components of its stiffness tensor may be of the same order as in the matrix. For a critical scaling, generalizing that of a "double porosity"type for the highly anisotropic elastic case, we use the tools of "nonclassical" (high contrast) homogenization to derive, in a generic setting, twoscale limiting elastodynamic equations. The partially highcontrast results in a constrained microscopic kinematics described by appropriate projectors in the limit equations. The effective equations are then uncoupled and explicitly analyzed for their bandgap structure. Their macroscopic component describes plane waves with a dispersion relation which is generally highly nonlinear both in the frequency and in the wave vector. While it is possible in this way to construct bandgap materials without the high anisotropy, the number of propagating modes for a given frequency (including none, i.e. in the bandgap case) is independent of the direction of propagation. However the introduction of a high anisotropy does allow variation in the number of propagating modes with direction if the inclusion phase is interconnected, including achieving propagation in some directions and no propagation in the others. This effect is explicitly illustrated for a particular example of a highly anisotropic fibrous composite
Original language  English 

Pages (fromto)  434447 
Number of pages  14 
Journal  Mechanics of Materials 
Volume  41 
Issue number  4 (Sp. Iss. SI) 
DOIs  
Publication status  Published  Apr 2009 
Event  44th Annual Technical Meeting of the SocietyofEngineeringScience  College Station, TX Duration: 1 Apr 2007 → … 
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Dive into the research topics of 'Propagation and localization of elastic waves in highly anisotropic periodic composites via twoscale homogenization'. Together they form a unique fingerprint.Projects
 1 Finished

Boundary Integral Equation Methods for HF Scattering Problems
Graham, I. & Smyshlyaev, V. P.
Engineering and Physical Sciences Research Council
24/03/09 → 23/09/12
Project: Research council