Updated Lagrangian nonlocal general particle dynamics for large deformation problems

Abstract

The traditional general particle dynamics (GPD) has been successfully applied in modeling fracture propagation, frictional contact and stick–slip problems in rocks. In this study, the updated Lagrangian nonlocal general particle dynamics (UL-NGPD) method is proposed to solve large deformation problems. In the UL-NGPD, the continuity equation and momentum equation are reformulated in the integro-differential formulation by introducing nonlocal theories in the updated Lagrangian framework. The artificial viscosity and artificial force state are utilized to enhance the numerical stability and accuracy in modeling large deformation. The nonlocal velocity gradient in the deformed configuration is used to update the Cauchy stress rate from the Drucker-Prager elasto-plastic constitutive model with strain-softening behaviour for solids. The UL-NGPD paradigm is numerically implemented through an explicit Predictor-Corrector scheme for high-performance computing. The stability and accuracy of the UL-NGPD are verified by numerical tests on compression test, slope stability analysis and aluminum bar collapse experiment. Thereafter, simulations of granular soil collapse and retrogressive landslide in sensitive clays are presented to demonstrate its efficacy and robustness in modeling challenging geotechnical problems involving large deformation. The numerical results show that the proposed UL-NGPD is powerful and suitable for analyzing large deformation problems in geotechnical engineering.