An inclusion model for predicting granular elasticity incorporating force chain mechanics

Abstract

Granular media is ubiquitous, playing a vital role in a diverse set of applications. The complex microstructure of granular media results from assorted particle shapes, morphologies, and packings, make it difficult to predict its macroscopic behavior. Under compression, these complex microstructures enable highly anisotropic and heterogenous behaviors, including creation of highly-loaded particles (i.e. force chains) supported by clusters of minimally-loaded particles. While many existing constitutive models relate state variables describing microscale behavior to continuum properties, these models do not generally consider the mesoscale interactions between the force chain network and minimally-loaded particles. Here, we develop a micromechanics model that connects micro-scale force chain mechanics to macro-scale mechanical behavior through explicit consideration of the interaction between force chains and minimally-loaded particles. We first examine the elastic behavior of a force chain using a spring model, explicitly considering the mesoscale interactions between the force-chains and surrounding regions. We then construct an equivalent inclusion problem to calculate macroscopic mechanical response as analytical functions of microscopic properties, with proper consideration of mesoscale interactions. We present our calibration and validation approaches, showing the model’s predictive abilities. Finally, we examine the effect of relevant microscopic quantities on macroscopic response, demonstrating the importance of these mesoscale interactions on bulk deviatoric behavior.