A constitutive model for granular materials with evolving contact structure and contact forces\u2014Part I: framework

Abstract

This and the companion paper present a constitutive model for granular materials with evolving contact structure and contact forces, where the contact structure and contact forces are characterised by some statistics of grain-scale entities such as contact normals and contact forces. And these statistics are actually the “fabric” or “force” terms in the “stress–force–fabric” (SFF) equation. The stress–strain response is obtained by inserting the predicted “fabric” or “force” terms from evolution equations into the SFF equation. Discrete element modelling is used to verify the slightly modified SFF equation and also to obtain the data of how the contact structure and contact forces evolve in various loading paths. It is demonstrated that a normalised contact force is a better measure of the contact forces in polydisperse granular assemblies and strong contacts should be contacts with larger normalised contact forces. The modified SFF equation is shown to predict the stress accurately. The constitutive equations regarding the response of the contact structure and contact forces are presented and they along with the SFF equation form a constitutive model, which is found capable of capturing the observed phenomena correctly and predicting the mechanical response in various loading conditions. The model is shown to be an extension to the hypoplastic models with more state variables.