Particle node-based smoothed point interpolation method with stress regularisation for large deformation problems in geomechanics

Abstract

In this study, a new numerical scheme is developed for modelling large deformation problems in geomechanics. The approach is based on employing the node based smoothed point interpolation methods (NSPIMs) in the framework of the particle finite element method (PFEM). The proposed technique is particle based in the sense that all variables are computed and stored at the nodes, hence constant transformation of the information between Gauss points and nodes, which is required in the particle finite element method (PFEM), is avoided. The accuracy of the proposed technique and its possible numerical instabilities, inherited through the use of NSPIMs in the method, are investigated in details. Accordingly, two remedial techniques, one based on stress regularisation by moving least square (MLS) and the other based on an improved formulation of NSPIMs, are presented to alleviate the instability problem and improve the accuracy of the numerical solutions. The proposed techniques and measures are thoroughly examined through three numerical examples, and conclusions are drawn.