Shock waves in granular materials: Discrete and continuum comparisons

Abstract

Small amplitude compression and shock waves in granular materials were examined from the point of view of an analytical model and discrete element simulations. The barotropic behaviour of granular materials was discussed in terms of the mechanisms behind the formation of shock fronts. This discussion leads to the development of a one dimensional continuum model which was used together with the method of characteristics to describe the nature of shock waves. The model provides a relationship between the states of the material on either side of a shock and an equation that defines the velocity of shock waves. Discrete Element Modelling was used to demonstrate the shock forming process in granular materials and to confirm the predictions of the analytical model. During this process it is demonstrated that an assembly based on a linear contact model does not show any barotropy and consequently cannot describe dynamics of granular materials in terms of shock forming mechanisms. This observation may have important consequences in the application of the linear contact model to dynamic systems. The Hertz–Mindlin contact model did not suffer from this issue and was able to demonstrate both barotropy and shock formation. The DEM assemblies were characterised in terms of the material properties of the analytical model which allowed direct comparisons to be made. In all respects the analytical model performed well, predicting the change in state of the material and the shock wave speed with a good deal of accuracy.