Exploring the numerical performance of node-based smoothed finite elements in coupled hydro-mechanical problems

Abstract

Node-based smoothed finite element (NS-FEM) formulations for the coupled hydro-mechanical problem are now becoming popular in soil mechanics, but there has been limited comparative study of their performance. In this work, a node-based formulation is developed for the coupled hydro-mechanical problem (u−pw formulation) using low-order, equal-order interpolants and an implicit time marching scheme for the global problem. The numerical properties of the resulting formulation are then compared to different implementations of classical finite elements. The use of nodal smoothing does not render by itself the solution stable at the undrained limit, on the contrary, the range of undrained instability is increased. Stabilizing terms previously employed in FEM are equally successful in stabilizing NS-FEM solutions, but the computational cost of the stabilized solution is much higher for NS-FEM. It is also shown that NS-FEM does not present by itself any particular advantage in terms of mesh dependency over classic FEM: when strain localization is present the solution obtained is strongly dependent on mesh size.