Hypoplastic constitutive model in SPH

The Smoothed Particle Hydrodynamics (SPH) is a pure Lagrangian method mainly used in Astrophysics and Computational Fluid Dynamics (CFD). Owing to features it poses, SPH is an attractive method for analyzing large deformation problems in Geotechnical Engineering if the physical process can be modeled correctly, which calls for appropriate constitutive models. In this paper, the feasibility of implementing hypoplastic model in SPH is investigated. A simple hypoplastic model is employed to simulate the non-linear stress-strain behaviour of geomaterials. Instead of using equation of state, in this study stresses are computed directly through hypoplastic constitutive equation, thus giving rise to decoupling of density and stress computation. Strain rate needed by the constitutive model is evaluated using SPH integral interpolation. The discretized governing equations are solved marching forward in time by Verlet integration. The problem of a column of sand subjected to gravity is simulated to check the capability of the proposed SPH application in geomechanics.