FE-studies of a Deterministic and Statistical Size Effect in Granular Bodies Including Shear Localization

The numerical investigations of size effects in granular bodies during a quasi-static plane strain compression test are performed. To describe a mechanical behaviour of a cohesionless granular material during a monotonous deformation path in a plane strain compression test, a micro-polar hypoplastic constitutive model was used. It includes particle rotations, curvatures, non-symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. In the paper, deterministic and statistical size effects in geometrically similar granular specimens are analysed. The deterministic calculations were carried out with a uniform distribution of the initial void ratio. To investigate a statistical size effect, in order to reduce the number of realizations without loosing the accuracy of the calculations, a Latin hypercube method was applied to generate symmetric Gaussian truncated random fields in a granular specimen. The results show that the statistical size effect is significantly stronger than the deterministic one. The shear resistance decreases and the rate of softening increases with increasing specimen size. The effect of the boundary roughness on shear localization is pronounced.