Quasi-static cylindrical cavity expansion in an elastoplastic compressible Mises solid

The self-similar elastoplastic field induced by quasi-static expansion of a pressurized cylindrical cavity is investigated for Mises solids under the assumption of plane-strain. Material behavior is modeled by the elastoplastic J2 flow theory with the standard hypoelastic version. The theory accounts for elastic-compressibility and allows for arbitrary strain-hardening (or softening) in the plastic range. A formulation of the exact governing equations is presented and analyzed in detail for the remote elastic field and for asymptotic plastic behavior near the cavity wall, along with numerical investigations for the entire deformation zone. An analytical solution was obtained under the axially-hydrostatic assumption (axial stress coincides with hydrostatic stress) within an error of about 2% or less as compared to the exact, numerically evaluated, value of cavitation pressure. Two ad-hoc compressibility approximations for cavitation pressure are suggested. These relations, which give very accurate results, appear to provide tight lower and upper bounds on the exact value of cavitation pressure within an error of less than 0.5%.