DYNAMIC STRESS-CONCENTRATION AROUND A HOLE IN A VISCOELASTIC PLATE

The transient hoop stresses which are generated at the circumference of a circular hole in a large viscoelastic plate when a radial pressure pulse acts on the hole boundary, are determined. An analytical/numerical approach is employed which is based on the use of Laplace transform and Hankel functions, and the Dubner-Abate-Crump technique for inverting the Laplace-transformed solution. In our formulation of the problem, a general linear-viscoelastic material for the plate is considered, but numerical results are extracted only for a three-parameter model (standard linear solid). The present work accompanies recent efforts by Georgiadis on analogous transient viscoelastodynamic problems involving finite-length cracks in a stress-wave environment. The mathematically simpler problem considered here demonstrates the influence of viscoelastic effects on the dynamic-stress-concentration in marked similarity with the dynamic-stress-intensity behavior of crack-tip viscoelastic stress fields. Besides that, the present problem generalizes the classical Kromm-Selberg-Miklowitz problem in the sense that it considers viscoelastic response. The latter solutions were not utilized here through the usual elastic/viscoelastic correspondence principle but, instead, an independent solution was derived by simple means.