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 paper, 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 quasi-static regime. As demanding examples, we study the effectiveness of cylindrical elastodynamic cloaks of the Cosserat type and approximations thereof.

References in corpus (4)

• Achieving control of in-plane elastic waves
• Hyperelastic cloaking theory: Transformation elasticity with pre-stressed solids
• Controlling solid elastic waves with spherical cloaks
• Elastodynamic cloaking and field enhancement for soft spheres

Cited by in corpus (6)

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• Relaxed micromorphic model of transient wave propagation in anisotropic band-gap metastructures
• Control of Rayleigh-like waves in thick plate Willis metamaterials
• Elastic wave cloaking via symmetrized transformation media
• Dynamic cloaking of a diamond-shaped hole in elastic plate
• Cloaking and anamorphism for light and mass diffusion