Hybrid discrete-continuum modeling of shear localization in granular media

Abstract

Shear localization is a frequent feature of granular materials. While the discrete element method can properly simulate such a phenomenon as long as the grain representation is accurate, it is computationally intractable when there are a large number of grains. The continuum-based finite element method is computationally tractable, yet struggles to capture many grain-scale effects, e.g., shear band thickness, because of mesh dependence, unless the constitutive model has a length scale. We propose a hybrid discrete-continuum technique that combines the speed of the continuum method with the grain-scale accuracy of the discrete method. In the case of shear localization problems, we start the simulation using the continuum-based material point method. As the simulation evolves, we monitor an adaptation oracle to identify the onset of shear bands and faithfully enrich the macroscopic continuum shear bands into the microscopic-scale grains using the discrete element method. Our algorithm then simulates the shear band region with the discrete method while continuing to simulate the rest of the domain with the continuum method so that the computational cost remains significantly cheaper than a purely discrete solution. We validate our technique in planar shear, triaxial compression, and plate indentation tests for both dry and cohesive granular media. Our method is as accurate as a purely discrete simulation but over 100 times faster than a discrete simulation that would require tens of millions of grains.