Transient Stress Concentration by a Spherical Cavity in an Elastic Medium

The problem of transient scattering of a plane step dilatational wave by a spherical cavity in an elastic medium is solved by a Laplace-transform-series-solution technique. The solution is obtained in the form of rational functions of the transform variable suitable for facilitating exact inverse transformation. The convergence and effectiveness of the series solution for accurate computation of the time history of the transient stress concentration at the cavity boundary are examined. It is found that, except in the immediate neighborhood of the defracted stress wave front, the series solution converges quite fast and it suffices to use only two (first and third) terms to calculate the maximum hoop stress due to the incidence of a step dilatational wave.