Numerical Simulation of Shear Band Formation with a Polar Hypoplastic Constitutive Model

Shear band formation in dry sand during biaxial compression tests is investigated with a polar hypoplastic model. The model is of the rate type and incrementally non-linear. It is established within the framework of a Cosserat continuum. It takes into account Cosserat rotations and couple stresses using the mean grain diameter as a characteristic length. The calculations of biaxial tests with a finite element method are performed for two different meshes and two different mean grain diameters. Initiation of shear bands is triggered by a small inhomogeneity in the initial material properties. From the presence of a characteristic length the calculated thickness of shear zones is almost independent of the spatial discretisation if the size of finite elements is not greater than five characteristic lengths. The numerical results show that the polar effect manifested by the appearance of grain rotations is significant in a shear zone. A quantitative comparison between the numerical calculations and the experimental results shows satisfying agreement.