A unified analytical solution for elastic–plastic stress analysis of a cylindrical cavity in Mohr–Coulomb materials under biaxial in situ stresses

Abstract

This paper presents a unified analytical solution for elastoplastic stress analysis around a cylindrical cavity under biaxial in situ stresses during both loading and unloading. The two-dimensional solution is obtained by assuming that the connected plastic zone is statically determinate and using the complex variable theory in the elastic analysis. It is shown that the biaxial state of initial stresses applies significant influences on the stress distribution around the inner cavity. Under biaxial far-field stresses, the asymptotic conformal mapping function predicts that the outer boundary of the statically determinate plastic zone is in oval shape in Mohr–Coulomb materials. The major axis of the elastic–plastic interface lies in the direction of the greatest far-field compression pressure during loading, whereas it is along the perpendicular direction during unloading. The loading and unloading solutions are validated by comparing with the results of numerical simulation and other analytical solutions. In the assumed states, the new solution provides an accurate analytical method to capture the biaxial in situ stress effect in the prediction of the plastic failure zone and calculations of the static stress field and the elastic displacement field around a cylindrical cavity within an infinite medium.