A Riemann-based SPH formulation for modelling elastoplastic soil behaviour using a Drucker–Prager model

Abstract

The present paper aims at proposing and investigating a Riemann-based SPH formulation to simulate the elastoplastic behaviour of soils undergoing large deformations, using a Drucker–Prager model. Basing on the pioneer work from Parshikov and Medin (Parshikov and Medin, 2002), a Riemann solver is used to maintain regular fields while being free of tuning parameters. By contrast to the work in Parshikov and Medin (2002) where piecewise constant reconstructions were employed, piecewise linear reconstructions are preferred in this work to reduce the numerical diffusion. A Particle Shifting Technique (PST) is used to maintain regular particle distributions and consequently accurate SPH interpolations. To the best of the author's knowledge, the use of a Riemann solver specific to solid mechanics with a pressure-dependent elastoplastic Drucker–Prager yield surface to model the behaviour of the material represents a novelty with respect to the existing literature. A Boundary Integral Method (BIM) initially derived for fluid dynamics (Ferrand et al., 2013; Chiron et al., 2019) is adapted to solid mechanics in order to handle complex geometries. It allows to deal with wall treatment without using fictitious particles, and shows satisfactory results even in sharp angle regions. The ability of the proposed Riemann-based formulation to simulate accurately elastoplastic problems and its robustness are examined through several test cases in plane strain conditions. Attention is paid to the capacity of the formulation to mitigate the occurrence of Tensile Instability (TI) with respect to other schemes, for which additional treatment is required to treat this issue, such as the additional artificial stress method (Gray et al., 2001).