Smoothed Particle Finite-Element Method for Large-Deformation Problems in Geomechanics

This study presents a novel smoothed particle FEM (SPFEM) for large-deformation problems in geomechanics. Within the framework of the particle FEM (PFEM), a strain smoothing technique for nodal integration is incorporated. The problem domain is divided into strain smoothing cells associated with particles, and the equilibrium of the continuum medium is achieved at these strain smoothing cells. The corresponding computational formulations and numerical procedure are given. Compared with the original PFEM, the SPFEM possesses the following advantages: (1) all the field variables are calculated and stored at the particles, and the frequent information transfer between Gauss points and particles, which inevitably introduces error and adds considerable complexity to solution procedures, is avoided; (2) the SPFEM possesses the upper bound property, providing a conservative estimation for problems in geomechanics; and (3) linear elements can be used directly without suffering from the volumetric locking, so special treatment to bypass the volumetric locking is not required. By solving two benchmark examples, the SPFEM has been verified to be a promising numerical method for analyzing large-deformation problems in geomechanics.