Time-harmonic Green's function and boundary integral formulation for incremental nonlinear elasticity: dynamics of wave patterns and shear bands

Superimposed dynamic, time-harmonic incremental deformations are considered in an elastic, orthotropic and incompressible, infinite body, subject to plane, homogeneous-but otherwise arbitrary-deformation. The dynamic, infinite body Green's function is found and, in addition, new boundary integral equations are obtained for incremental in-plane hydrostatic stress and displacements. These findings open the way to integral methods in incremental, dynamic elasticity. Moreover, the Green's function is employed as a dynamic perturbation to analyze interaction between wave propagation and shear band formation. Depending on anisotropy and pre-stress level, peculiar wave patterns emerge with focussing and shadowing effects of signals, which may remain undetected by the usual criteria based on analysis of weak discontinuity surfaces.