Modeling shear-induced solid-liquid transition of granular materials using persistent homology

Abstract

This paper investigates the transition between the solid and liquid phases of sheared granular materials from the perspective of the contact network. Tools from persistent homology are employed to quantify the dynamics of contact network during the solid-liquid transition from a global perspective, and two important topological invariants, i.e., components and loops, are mainly investigated from discrete numerical simulations. The highly heterogeneous composition of the contact network is revealed, and a rationale partition threshold for distinguishing between strong and weak contact subnetworks can be determined through the emergence and death of these topological invariants. During the shearing process, we recognize mechanical precursors forecasting the occurrence of solid-liquid transition when the assembly is still stable. Furthermore, we provide the panorama of the solid-liquid transition from the evolution of contact network and its homology groups. Finally, this study suggests that the persistent homology method is capable of quantitatively bridging the microscopic dynamics with macroscopic responses through the contact network, which paves an efficient way to further include the evolution of the contact network in the constitutive modeling of granular materials.