A temporal stable smoothed particle finite element method for large deformation problems in geomechanics

In this study, a stabilized smoothed particle finite element method (SPFEM) for modeling nonlinear, large deformation dynamic problems in geomechanics is presented. The stabilization is introduced to the weak form formulations through a strain gradient of the smoothing cell, which helps eliminate the spurious zero -energy modes in SPFEM and achieve a temporal stable solution. Compared to the existing strain gradient stabilization approaches in SPFEM, the proposed stabilized SPFEM approach is computationally less intensive, free of artificial penalty parameters and free of volumetric locking. The performance of the proposed stabilized SPFEM is demonstrated by the studies of two numerical benchmark examples, the results of which show excellent agreement with the analytical reference solutions. This stabilization technique is also found to help improve the computation accuracy in terms of displacement and strain energy in comparison with results from the standard SPFEM. In addition, the proposed stabilized SPFEM is found to be temporal stable and free of volumetric locking. Finally, two numerical applications of the stabilized SPFEM to the large deformation soil flow and slope failure are discussed.