Micromechanical understanding of the macroscopic features of dense granular materials

Abstract

The prevalence of granular materials in nature (soil, beach sand, rubble pile asteroids) and in several industries (cement, food grains, pharmaceutical powders) has motivated extensive research towards understanding the mechanical properties of these materials. Various features of static and sheared media, such as stress saturation with depth in static columns, rate-independent shear stress, significant stress fluctuations, and dilation in dense slowly sheared packings, are observed in these studies. How these features emerge from grain interactions is a long-standing question. This thesis delves into the microscopic aspects of static and quasistatic granular systems, where particle contacts govern the mechanical response of the packing. We investigate stress transmission in grain networks and their rearrangement during shear to decipher the underlying physics of dense granular media using a combination of particle dynamics simulations and experiments. Contrary to the conventional assumption, our investigation reveals that the deformation of particles plays a crucial role in shaping the mechanical behavior of granular packings. In fact, the stress within the material is fundamentally related to the elastic deformation of the particles. We demonstrate that the characteristic traits of granular media persist even in the absence of inter-particle friction. However, the existence of these traits is questionable in the limit of perfect rigidity of grains. This understanding challenges the prevailing notion that frictional interactions are the primary drivers of macroscopic behavior. In the realm of static systems, we conduct simulations of isotropically compressed packings, uncovering a critical coordination number and a solid fraction that marks the transition to a stable network. This critical point, dependent solely on the inter-particle friction coefficient $\mu$, signifies an emergence of macroscopic stiffness in the material, which dictates the subsequent deformation of grain assembly with increasing pressure. To investigate stress transmission in static columns that are filled under gravity, we construct a coarse-grained representation of the force network, called ``force lines" (Krishnaraj, 2020). The force lines show that the weight is preferentially transmitted to the side walls, resulting in lateral transmission of load and, consequently, the saturation of the stress with depth. Our experiments on a two-dimensional column filled with photoelastic disks validate the findings of the simulation study. These results emphasize the relationships between the microstructure and the mechanical response of grain assemblies. The simulations of simple shear in the quasistatic limit highlight the intermittent nature of particle rearrangement, termed stick-slip motion - the contact network is stable in the stick phases and rearranges in short-lived slip phases. We propose a cascade failure mechanism that offers insight into the stability of the packing and the initiation of the slip phases. The analysis reveals a system-spanning loss of stability in the contact network during slip phases. This microscopic description of slow granular flows relates intermittent rearrangement in the network to stress fluctuations and establishes the origin of the rate-independence of shear stress. The cascade failure mechanism also helps in connecting the “fluidity” that is used in continuum models to the network topology.

Finally, we combine the insights from our simulations and experimental study to propose a linear elastic description for the macroscopic behavior of stable granular packings. A significant advantage of this description lies in its capacity to incorporate microstructural details, such as coordination number and anisotropy, into the stiffness matrix. Demonstrating its potential, the model predicts the changes in solid fraction with pressure in isotropically compressed packings. The model is then applied to elucidate the stress-strain relationship during the stick phase of quasistatic shear flows. By factoring in the anisotropy in the contact network, we derive an analytical expression for shear-induced dilation. Our investigation establishes that dilation is the response of anisotropic elastic media to imposed shear strain.