Overcoming volumetric locking in stable node-based smoothed particle finite element method with cubic bubble function and selective integration

The stable node-based smoothed particle finite element method (SNS-PFEM) reduces spatial numerical oscillation from direct nodal integration in NS-PFEM but leads to a severe volumetric locking effect when modeling nearly incompressible materials-related boundary value problems. This study proposes an improved locking-free SNS-PFEM to investigate the performance of the bubble function and selective integration scheme in circumventing volumetric locking. Three locking-free variants of SNS-PFEM: (1) SNS-PFEM with a cubic bubble function (bSNS-PFEM), (2) SNS-PFEM with a selective integration scheme (selective SNS-PFEM), and (3) SNS-PFEM with a cubic bubble function and selective integration scheme (selective bSNS-PFEM)—were gradually developed for comparison. The performance of these three approaches was first successively examined using two examples with elastic materials, that is, an infinite plate with a circular hole and Cook's membrane. The comparisons show that the cubic bubble function and selective integration scheme are both necessary as a locking-free approach for modeling nearly incompressible materials, and the proposed selective bSNS-PFEM performs best among the three variants in terms of accuracy and convergence. Two examples of slope stability analysis and footing penetration on elastoplastic materials were then conducted by SNS-PFEM and the proposed selective bSNS-PFEM. The results indicate that the proposed selective bSNS-PFEM is stable and accurate, even when accompanied by significant deformation. All obtained results indicate that the locking-free selective bSNS-PFEM is a powerful approach for modeling nearly incompressible materials with both material and geometric nonlinearity.