An improved updated Lagrangian SPH method for structural modelling

Abstract

This paper presents a set of novel refined schemes to enhance the accuracy and stability of the updated Lagrangian SPH (ULSPH) for structural modelling. The original ULSPH structure model was first proposed by Gray et al. (Comput Methods Appl Mech Eng 190:6641–6662, 2001) and has been utilised for a wide range of structural analyses including metal, soil, rubber, ice, etc., although the model often faces several drawbacks including unphysical numerical damping, high-frequency noise in reproduced stress fields, presence of several artificial terms requiring ad hoc tunings and numerical instability in the presence of tensile stresses. In these regards, this study presents a set of enhanced schemes corresponding to (1) consistency correction on discretisation schemes for differential operators, (2) a numerical diffusive term incorporated in the continuity or the density rate equation, (3) tuning-free stabilising term based on Riemann solution and (4) careful control/switch of stress divergence differential operator model under tensile stresses. Qualitative/quantitative validations are conducted through several well-known benchmark tests.