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The deformation of flat ellipsoidal cavities under large confining pressures

DEPARTMENT OF MATHEMATICS UNIVERSITY OF BRADFORD, BRADFORD, YORKSHIRE England
DEPARTMENT OF GEOLOGY UNIVERSITY COLLEGE LONDON, GOWER STREET, LONDON WC1E 6BT England

Abstract

The problem concerns an elastic body containing ellipsoidal cavities with principal axes a, b, and c (a b >> c) which are closed by pressure and sheared. It is found that the deformed cavity remains ellipsoidal in shape, so that closure occurs simultaneously over the whole boundary, but the deformed axes are rotated with respect to the undeformed axes. The pressure required to close a cavity, in a material with Poisson's ratio v and shear modulus µ is µ(c/b)/(1 - v) (where is the elliptic integral of the second kind with modulus k² = 1 - b²/a² and argument /2, and 1 /2). A relationship is obtained between the cavity closure stress (P^C₃₃) and the uniaxial tensile strength (K^*₁) for a brittle body, and it is shown that P^C₃₃ 10K*₁ which is in accord with experimental observations. The uniform tractions acting on the surface of the closed cavity are found to be P^A₁₃, P^A₂₃ and P^A₃₃ + P^C₃₃ where the P^A_ij are the applied stresses (refer to the cavity axes) at large distances from the cavity.

Footnotes

^* Present address: Koninklijke/Shell Laboratorium, Rijswijk, The Netherlands.

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