Interdependent evolution of robustness, force transmission and damage in a heterogeneous quasi-brittle granular material: from suppressed to cascading failure

Abstract

A heterogeneous quasi-brittle granular material can withstand certain levels of internal damage before global failure. This robustness depends not just on the bond strengths but also on the topology and redundancy of the bonded contact network, through which forces and damage propagate. Despite extensive studies on quasi-brittle failure, there still lacks a unified framework that can quantify the interdependent evolution of robustness, damage and force transmission. Here we develop a framework to do so. It is data-driven, multiscale and relies solely on the contact strengths and topology of the contact network for material properties. Using data derived from discrete element simulations of concrete specimens under uniaxial tension, we uncover evidence of an optimized force transmission, characterized by two novel transmission patterns that predict and explain damage propagation from the microstructural to the macroscopic level. The first comprises the optimized flow routes: shortest possible paths that can transmit the global transmission capacity. These paths reliably predict tensile force chains. The second are the force bottlenecks.These provide an early and accurate prediction of the ultimate pattern, location and interaction of macrocracks. A two-pronged cooperative mechanism among bottlenecks, enabled by redundancies in transmission pathways, underlies robustness in the pre-failure regime. Bottlenecks take turns in accommodating damage, while member contacts spread the forces to confine damage to low capacity contacts which leave behind a web of strong contacts to support and curtail the failure of tensile force chains in the region. This cooperative behavior, while serving to minimize the inevitable reduction in global transmission capacity, progressively heightens the interdependency among these contacts and elicits the opposite effect. Ultimately, the dominant bottleneck becomes predisposed to cascading failure which, in turn, triggers abrupt and catastrophic failure of the system.

Forecasting failure locations in 2-dimensional disordered lattices

“…They performed numerical experiments on the tensile fracture of deformed square and kagome lattices, demonstrating that stress and fracture concentrate on self-stress domain walls, even in the presence of damage that is introduced elsewhere in the system. In another recent paper, Tordesillas et al [20] studied damage locations in discrete-element simulations of concrete samples under uniaxial tension. From a network-flow analysis of the contact-network topology and contact capacities of a specimen, the authors determined the location of the principal interacting macrocracks.…”

“…As discussed by Smart et al [32], it is appealing to investigate what insights network analysis and associated topics (e.g., graph theory and algebraic topology) can yield on novel physical systems, especially in comparison to traditional approaches. For example, this perspective was adopted by Tordesillas et al [20] to study quasi-brittle failure using network flow. Such approaches have also been useful for the study of mesoscale structures, such as dense communities of nodes, in granular systems [33].…”