Large deformation analysis of geomaterials using stabilized total Lagrangian smoothed particle hydrodynamics

Abstract

Smoothed particle hydrodynamics (SPH) based on Eulerian kernels is widely-used in large deformation analysis of geomaterials. Despite being popular, it has tensile instability and rank-deficiency; thus, it needs several numerical treatments to be stable. In this work, a stabilized total Lagrangian SPH method is presented, which is inherently free of tensile instability. A stiffness-based hourglass control algorithm is employed to cure the instability caused by rank-deficiency. Periodic update of reference configuration is employed to allow the modeling of large deformation. Numerical examples are presented to show the performance of the method. The comparison between the presented method and the conventional smoothed particle hydrodynamics are discussed. The influences of hourglass control and configuration update are also investigated. It is found that the presented method is robust and can model large deformation and plastic flows in geomaterials. Particularly, the stabilized method delivers better stress results.