A constitutive model for granular materials with evolving contact structure and contact forces\u2014part II: constitutive equations

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. In the model, the critical state is characterised by two fitting equations and three critical state parameters. A semi-mechanistic analysis is conducted about the change of the contact number and the obtained results are combined with observed phenomena in DEM virtual experiments to give the constitutive equations for the “fabric” terms. The change of fabric anisotropy is related to the strain rate, current fabric anisotropy and also contact forces. The change of coordination number is induced by two terms related to volumetric and shear deformations, and also an additional term related to the change of fabric anisotropy. The constitutive equations regarding the “force” terms are also proposed. All the “fabric” or “force” terms are modelled to tend toward their critial state value, which agrees with Li and Dafalias’s (J Eng Mech 138(3):263–275, 2012. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000324) basic philosophy in their evolution equation for the fabric tensor. These equations along with the SFF equation form a constitutive model.