Spherical Cavity Expansion in a Drucker-Prager Solid

[+] Author and Article Information
D. Durban

Technion-Israel Institute of Technology, Haifa 32000, Israel

N. A. Fleck

Engineering Department, Cambridge University, Cambridge CB 1PZ, U.K.

J. Appl. Mech 64(4), 743-750 (Dec 01, 1997) (8 pages) doi:10.1115/1.2788978 History: Received July 21, 1995; Revised August 08, 1996; Online October 25, 2007


A finite strain analysis is presented for the pressurized spherical cavity embedded in a Drucker-Prager medium. Material behavior is modeled by a nonassociated deformation theory which accounts for arbitrary strain-hardening. The governing equations of spherically symmetric response are reduced to a single differential equation with the effective stress as the independent variable. Some related topics are discussed including the elastic-perfectly plastic solid, the thin-walled shell, and the Mohr-Coulomb material. Spontaneous growth (cavitation limit) of an internally pressurized cavity is treated as a self-similar process and a few numerical examples are presented. These illustrate, for different hardening characteristics, the pressure sensitivity of material response and that deviations from normality always reduce the caviation pressure.

Copyright © 1997 by The American Society of Mechanical Engineers
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