A stable node-based smoothed PFEM for solving geotechnical large deformation 2D problems

The strain smoothed nodal integration particle finite element method (NS-PFEM) has a high level of computational efficiency. However, it suffers from the ‘overly soft’ problem. This study presents the development of a stable nodal integration PFEM for solving geotechnical large deformation problems. A node-based strain smoothing (SNS) PFEM is developed by combining a 3-node triangular element-based PFEM and a stable nodal integration method with strain gradient in the smooth domain for single solid phase. Its performance is examined by simulating two benchmark tests on elastic material (i.e., cantilever beam and infinite plate with a circular hole) and three cases on elastoplastic material (i.e., cavity expansion, penetration of a rigid footing in soft soil and progressive failure of slope). Results show that the integration of stabilisation term gives the SNS-PFEM ‘close to exact’ stiffness, thereby resolving the ‘overly soft’ and temporal instability issues seen with the NS-PFEM. The proposed method is powerful and easily extensible for analysing large deformation problems in geotechnical engineering.