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

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. Further-more, 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 re-sponses through the contact network, which paves an efficient way to further include the evo-lution of the contact network in the constitutive modeling of granular materials.

Automated summary

This paper investigates the transition between the solid and liquid phases of sheared granular materials from the perspective of the contact network. Persistent homology tools are used to quantify the dynamics of the contact network, and two important topological invariants, components and loops, are analyzed through numerical simulations. The study reveals the heterogeneous composition of the contact network and suggests a partition threshold for distinguishing strong and weak contact subnetworks. Mechanical precursors of the solid-liquid transition are identified during the shearing process. The study demonstrates the capability of the persistent homology method in bridging microscopic dynamics with macroscopic responses through the contact network.