Scattering of elastic waves by a shear band

Localized deformations in the form of shear bands are known to be preferential near-failure deformation modes of ductile materials. The development of shear localization bands has been also shown to be possible in anisotropic composite materials consisting of random distributions of aligned rigid fibres of elliptical cross section in a soft elastomeric matrix. In the present work, 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. A shear band of finite length can be seen as a very thin layer of material across which the normal component of incremental displacement and of nominal traction remain continuous, but the incremental nominal tangential traction vanishes , while the corresponding displacement becomes unprescribed. Therefore, it is possible to model such a shear band as a weak surface whose faces can freely slide, but are constrained to remain in contact. At the base of the proposed dynamic perturbation analysis is the time-harmonic infinite-body Green's function for incremental displacements obtained by Bigoni & Capuani 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 collocation method is formulated to solve the boundary value incremental problem of incident wave scattering by a shear band