INTERACTION OF PLANE STRESS WAVES WITH A SPHERICAL CAVITY IN ELASTIC AND VISCOELASTIC MEDIA.
Abstract
Methods are given for the determination of stresses in the vicinity of a spherical cavity in an unbounded elastic or viscoelastic medium as a result of a step wave engulfing the cavity. Incident longitudinal and shear waves are considered. Two approaches are used for the solution. In the first, the solution is expressed in terms of generating functions which are determined from the boundary conditions at the cavity wall. For the elastic case, this method is analogous to the d'Alembert solution in one-dimensional wave propagation in which the general solution of the wave equation is used. The elastic case requires the solution of coupled systems of ordinary differential equations of initial value type. In the viscoelastic case, these are replaced by systems of integro-differential equations of Volterra type. Numerical methods are used for the solution of the equations. The second method proceeds by finding the Laplace transforms of the desired stresses and performing the inversions numerically. Viscoelastic materials represented by the Maxwell model and the standard linear model have been used for the computations presented. On the basis of these computations, conclusions are drawn concerning the effect of viscoelasticity of rock on the dynamic stress concentrations around a cavity in the rock making use of properties of rock determined for low stress levels. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1966
- Accession Number
- AD0631501
Entities
People
- A. R. Robinson
- D. E. Allen
Organizations
- University of Illinois Urbana–Champaign