A stabilized total-Lagrangian SPH method for large deformation and failure in geomaterials

Abstract: Conventional smoothed particle hydrodynamics based on Eulerian kernels (CESPH) is widely-used in large deformation analysis in geomaterials. Despite being popular, it suffers from tensile instability and rank-deficiency; thus, it needs several numerical treatments to be stable. In this work, we present a stabilized total-Lagrangian SPH method (TLSPH), which is inherently free of tensile instability. A stiffness-based hourglass control algorithm is employed to cure the hourglass mode caused by rank-deficiency. Periodic update of reference configuration is used in simulations to allow TLSPH to model large deformation and post-failure flow in geomaterials. Several numerical examples are presented to show the performance of the stabilized TLSPH method. The comparison between TLSPH and CESPH are discussed. The influences of hourglass control and configuration update are also discussed and shown in the numerical examples. It is found that the presented stabilized TLSPH is robust and can model large deformation and plastic flows in geomaterials. Particularly, the stabilized TLSPH delivers accurate and smooth stress results.