Injecting Particle Scale Physics into Continuum Models of Granular Materials for Large-Scale Applications

Models of granular materials that incorporate grain scale behaviour can be developed using a "bottom-up" approach known as micromechanics. Typically these models are derived from laws introduced to represent inter-particle contact behaviour. Here models based on two separate contact laws are compared. The first law is based on a binary contact interaction governed by spring-slider systems similar to those used in discrete element methods. In the second model, an effective contact law is introduced that is based on the observed behaviour of particle clusters. While the model based on the binary contact law can reproduce some aspects of granular behaviour, it is not capable of predicting both strain softening and dilatant behaviour under biaxial compression. In contrast, the effective contact law is able to reproduce not only the correct stress-strain response, but also the observed microstructural evolution in the two cases examined: uniform deformation and strain localisation. It has the additional advantage that it is able to simulate granular assemblies where the numbers of particles involved would make discrete element methods impractical. To demonstrate this ability results from a finite element simulation of an assembly consisting of over half a million particles are presented. These results suggest that the contact laws used in micromechanical models must account for physical mechanisms occurring in at least two length scales: at the contacts and within particle clusters.