Scattering problems in elastodynamics

TL;DR

This paper develops a new PML-based scattered-field formulation for elastodynamics, enabling efficient numerical solutions for wave scattering problems in continuum mechanics, including cloaking applications.

Contribution

It introduces a novel PML approach for the Navier equation in elastodynamics, accommodating all polarizations and directions, and applicable to quasi-static regimes.

Findings

PMLs based on complex coordinate transformations are effective in elastodynamics.

The method works in two dimensions for all polarizations and directions.

Demonstrated applications include elastodynamic cloaks of Cosserat type.

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.