Two-dimensional wave scattering from a cylindrical obstacle in an incompressible pre-stressed nonlinear elastic media

We develop a series expansion approach to the scattering coefficients of transverse elastic waves from a cylindrical obstacle as they propagate through an incompressible pre-stressed nonlinear elastic material. Popular neo-Hookean and Mooney–Rivlin strain energy functions are considered for the elastic material, and rigid or hollow cylinders are considered as obstaclers. From the static configuration, a small-on-large approach is constructed via a series expansion of the wave equation inhomogeneous coefficients which allows to compute both the scattered wave and the induced pressure field, and their dependence on the applied pre-stress. In the far field limit, the pre-stress effect on the scattering coeffiecients is calculated via the scattered wave decomposition in partial waves. The formalism can be expanded to include three-dimensional media with different obstacle symmetries.