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

Abstract

AbstractThe 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.