Scattering problems in elastodynamics

Abstract : In electromagnetism, acoustics, and quantum mechanics, scattering problems can routinely be solved numerically by virtue of perfectly matched layers (PMLs) at simulation domain boundaries. Unfortunately, the same has not been possible for general elastodynamic wave problems in continuum mechanics. In this Rapid Communication, we introduce a corresponding scattered-field formulation for the Navier equation. We derive PMLs based on complex-valued coordinate transformations leading to Cosserat elasticity-tensor distributions not obeying the minor symmetries. These layers are shown to work in two dimensions, for all polarizations, and all directions. By adaptative choice of the decay length, the deep subwavelength PMLs can be used all the way to the quasistatic regime. As demanding examples, we study the effectiveness of cylindrical elastodynamic cloaks of the Cosserat type and approximations thereof.
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Contributor : Sébastien Guenneau <>
Submitted on : Saturday, November 12, 2016 - 8:55:10 AM
Last modification on : Monday, March 4, 2019 - 2:04:25 PM

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Andre Diatta, Muamer Kadic, Martin Wegener, Sebastien Guenneau. Scattering problems in elastodynamics. Physical Review B : Condensed matter and materials physics, American Physical Society, 2016, 94 (10), pp.100105. ⟨10.1103/PhysRevB.94.100105⟩. ⟨hal-01395829⟩

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