Asymptotic behaviour of granular materials

The concept of the asymptotic behaviour of particulate materials is described, including its enhancement by considering asymptotic states in extension. A 3D discrete element model with elastic spherical particles and the granulometry of a real sand is set up. The numerical sample is stretched from different initial states, and the influence of the strain rate direction on the final state is studied within the stress ratio, void ratio and mean stress space. Asymptotic behaviour is clearly observed, although the grains remain intact (no grain crushing is considered). The extension asymptotic states were observed, and the notion of a normal extension line is introduced. The extension asymptotic states coincide with the peak states observed in the shear tests with constant stress path direction in dense samples.