European Journal of Mechanics A/Solids 26 (2007) 712–727 Cylindrical cavity expansion in compressible Mises and Tresca solids Rami Masri ∗,1 , David Durban Faculty of Aerospace Engineering, Technion, Haifa 32000, Israel Received 4 April 2006; accepted 1 December 2006 Available online 17 January 2007 Abstract The elastoplastic field induced by quasi-static expansion in steady-state plane-strain conditions of a pressurized cylindrical cavity (cylindrical cavitation) is investigated. Material behavior is modeled by Mises and Tresca large strain flow theories formulated as hypoelastic. Both models account for elastic-compressibility and allow for arbitrary strain-hardening (or softening). For the Mises solid analysis centers on the axially-hydrostatic assumption (axial stress coincides with hydrostatic stress) in conjunction with a controlled error method. Introducing an error control parameter we arrive at a single-parameter-dependent quadrature expression for cavitation pressure. Available results are recovered with particular values of that parameter, and an optimal value is defined such that the cavitation pressure is predicted with high accuracy. For the Tresca solid we obtain an elegant solution with the standard model when no corner develops in the yield surface. Under certain conditions however a corner zone exists near the cavity and the solution is accordingly modified revealing a slight difference in cavitation pressure. Comparison with numerical solutions suggests that the present study establishes cylindrical cavitation analysis on equal footing with existing studies for spherical cavitation.  2007 Elsevier Masson SAS. All rights reserved. Keywords: Cavity expansion; Cavitation; Plasticity 1. Introduction The pioneering study by Bishop et al. (1945) on cavitation phenomena in elastoplastic solids, suggests that in- dentation pressure is bounded between cylindrical and spherical cavitation pressures. In recent years there has been increasing interest in elastoplastic cavitation as a basic physical model underlying penetration behavior. However, most of existing literature on elastoplastic cavitation deals with spherical patterns and quite a few issues concerned with cylindrical cavitation have remained opened. Available studies on spontaneous (self-similar) growth of pressur- ized cylindrical cavities are usually limited to incompressible Mises solids (Durban, 1979), or elastic/perfectly-plastic Tresca materials (Hill, 1950). Attempts to include compressibility effects in Mises media and strain-hardening behav- ior for the Tresca model were made by Durban (1988) and Durban and Kubi (1992), respectively. * Corresponding author. Fax: +972 4 829 2030. E-mail address: masri@aerodyne.technion.ac.il (R. Masri). 1 This work is based on a part of a PhD thesis to be submitted to the Technion. 0997-7538/$ – see front matter  2007 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.euromechsol.2006.12.003