A volumetric locking-free stable node-based smoothed finite element method for geomechanics

It was recently found that the stable node-based smoothed finite element method (SNS-FEM) does not have the advantage of NS-FEM in avoiding volumetric locking and thus produces erroneous results at the incompressible limit. This study proposes two improved schemes for SNS-FEM to overcome volumetric locking by introducing the two-level mesh repartitioning scheme (TLMR-SNS-FEM) and the bubble point-enriched scheme (Bubble-SNS-FEM). Both schemes use the centroid of each triangle element as field interpolation nodes. This appropriately increases the degrees of freedom (DOFs) of the discrete equation and avoids volumetric locking of SNS-FEM. For elastoplastic problems, a conic programming-based constitutive integration algorithm for elastic perfect plastic materials is used for stress updating. Several numerical examples of linear elastic and elastic perfectly plastic problems are analysed to validate the effectiveness and robustness of the proposed methods. Compared with existing numerical methods, both the proposed methods can efficiently overcome volumetric locking in the SNS-FEM and are temporally stable. Furthermore, the two proposed schemes exhibit essentially the same performance and inherit the computational framework of SNS-FEM. Hence they can be implemented with only minor modifications to the code of NS-FEM or SNS-FEM.