Stabilized node integration in the smoothed particle finite element method: verification and application

  • Yuan, Wei-Hai (Hohai University)
  • Liu, Ming (Hohai University)
  • Zhang, Wei (South China Agricultural University)

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The Particle Finite Element Method (PFEM) is an effective framework for the analysis of large deformations. To enrich this powerful method, we first proposed the Smoothed Particle Finite Element Method (SPFEM)[1,2] by introducing the nodal integration technique based on strain smoothing into the PFEM framework. In SPFEM, the numerical integration of the weak form is performed at nodes instead of Gauss points, and the state variables are tracked only at nodes, completely avoiding the mapping of these variables between the old and new meshes after each re-meshing, which is necessary for conventional PFEM. Compared to conventional PFEM, SPFEM is free of volumetric locking and has higher computational efficiency due to the use of lower-order elements with fewer integration points. Even though the SPFEM with nodal integration has many successful applications, it still suffers from spurious low-energy instability, which often compromises stress accuracy due to the under-integration of the weak form. This instability is due to under-integration, which only uses nodes to carry out numerical integration of weak form. In nodal integration, the derivatives of the shape functions vanish at the nodes, resulting in zero or near-zero strain at the nodes. As a result, the interior nodes have little or no internal energy contribution to the system which finally leads to a spurious numerical oscillation in dynamic problems. Aiming to solve this deficiency, we proposed a stable method to stabilize the numerical instability in SPFEM. The performance of the proposed stabilized method is demonstrated by two numerical benchmark examples, and we also found that this stabilized method can improve the computational accuracy compared to the results of the standard SPFEM. Moreover, some applications such as large deformation of soil flow, slope stability analysis and progressive failure are carried out using the stabilized SPFEM.