Huygens’ principle, radiation conditions, and integral formulas for the scattering of elastic waves

Helmholtz‐ and Kirchhoff‐type integral formulas are presented for elastic waves in isotropic and anisotropic solids. The displacement vector field at points interior and exterior to a region bounded by a closed surface is expressed in terms of a volume integral of the body sources and a surface integral of the sources on the closed surface, namely, the traction and the displacement. The kernels of these integrals are the well‐known Green’s displacement dyadic and a third rank Green’s stress tensor. The latter is related to the former by generalized Hooke’s law. From these formulas radiation conditions for both steady‐state and transient elastic waves are established in terms of the traction, displacement, and particle velocity. In the Kirchhoff‐type formula, the retardation in time for the surface and volume sources is made with respect to the travel times for dilatational and shear waves, respectively. This clearly illustrates Huygens’ principle for the two wave fronts of the elastic wave field.Subject C...