Stable axisymmetric SPH formulation with no axis singularity

Abstract

SummaryThe axisymmetric formulation of the governing equations for geomechanics in the framework of smoothed particle hydrodynamics (SPH) is presented in this study. Two forms of SPH discretization for the motion equations, which are labeled as form I and form II, are proposed, and the methods to compute the hoop stress and strain terms including hoop strain rate and the acceleration introduced by the hoop stress are compared. To avoid possible singularity problem near the axis of symmetry, a perfectly smooth contact along with ghost particles are applied to prevent the real particles from overly approaching the axis of symmetry to remove this potential singularity. In addition, the Mohr–Coulomb constitutive model is implemented into the SPH formulation in describing soil behavior. Four numerical tests are carried out to validate and compare the accuracy and stability of the proposed algorithms, and their results are compared with analytical solutions and results from FEM analysis. The performance in these comparisons suggests that SPH II with hoop terms computed through direct hoop method is more stable than the others, and the adoption of contact for the symmetric axis is efficient in eliminating the singularity problem. Copyright © 2015 John Wiley & Sons, Ltd.