Scattering of Waves by a Shear Band

The incremental behaviour of a prestressed, elastic, anisotropic and incompressible material is analyzed in the dynamic regime, under the plain strain condition. Dynamic perturbations of stress/deformation incident wave fields, caused by a shear band of finite length, formed inside the material at a certain stage of continued deformation, are investigated. At the base of the proposed dynamic perturbation approach is the time-harmonic infinite-body Green’s function for incremental displacements obtained by Bigoni and Capuani [5] for small isochoric and plane deformation superimposed upon a nonlinear elastic and homogeneous strain. The integral representation relating the incremental stress at any point of the medium to the incremental displacement jump across the shear band faces, is obtained. Finally, a numerical procedure based on a collocation method is used to solve the boundary integral equation for incident wave scattering by a shear band.