Coupled Evolution of Preferential Paths for Force and Damage in the Pre-failure Regime in Disordered and Heterogeneous, Quasi-Brittle Granular Materials

Abstract

A disordered and 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 quantitatively characterize and model the interdependent evolution of 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. The discrete element method (DEM) was used to directly simulate quasi-brittle materials like concrete under uniaxial tension. Concrete was modeled as a random heterogeneous 2-phase and 3-phase material composed of aggregate particles, cement matrix and interfacial transitional zones with experimental-based meso-structure from X-ray micro-CT-images of real concrete. We uncover evidence of an optimized force transmission, characterized by two novel transmission patterns that predict and explain the coupled evolution of force and damage pathways from the microstructural to the macroscopic level. The first comprises the shortest possible percolating paths that can transmit the global force transmission capacity. These paths reliably predict tensile force chains. The second pattern is the flow bottleneck, a path in the optimized route that is prone to congestion and is where the macrocrack emerges. The cooperative evolution of preferential pathways for damage and force casts light on why sites of highest concentrations of stress and damage in the nascent stages of pre-failure regime do not provide a reliable indicator of the ultimate location of the macrocrack.

Early prediction of macrocrack location in concrete, rocks and other granular composite materials

“…Flow bottlenecks are a fundamental concept of network resilience and have been considered as precursors for cascading failure in various cyber, transport and infrastructure systems 23 . Prior evidence also demonstrate that these emergent structures can reliably predict, early in the prefailure regime, the ultimate locale of cascading failure for various natural and synthetic granular media 16,[17][18][19][20] . Second, the problem of finding where the flow bottleneck emerges and how this path is influenced by heterogeneities in transmission pathways can be expressed in terms of an optimization problem.…”

“…To achieve this, we break with the tradition of modeling fracture propagation and attendant energy and force transmission as flows in a continuum 1,6,15 . Instead, we model these as flows in a network [15][16][17][18][19][20] . To the best of our knowledge, this is the first study that: (i) delivers a method for early and accurate prediction of the ultimate macrocrack location from known microstructural bond properties (i.e., fracture strength and surface energy, size), disorder in the network connectivity (an effect of packing and grain size distribution), and stage of loading; and (ii) reconciles and consolidates, in a single framework, the precursory failure mechanism of energy and force flow bottlenecks with widely used fracture criteria.…”

“…Heterogeneity in transmission pathways has major implications for the spread of failure in a broad range of networked systems 21,22 . In quasibrittle granular composites, this was recently investigated with respect to the coupled evolution of force and damage propagation in the framework of network flow theory 16 . It showed that the majority of force chains develop in the most direct (shortest possible) routes for force transmission, while the ultimate macrocrack emerged in the recurrent force bottleneck that persisted from the nascent stages of the prefailure regime.…”

“…It showed that the majority of force chains develop in the most direct (shortest possible) routes for force transmission, while the ultimate macrocrack emerged in the recurrent force bottleneck that persisted from the nascent stages of the prefailure regime. Different from the work in 16 , here we study the general case of energy, force and their residual transmission processes; the endmost deals with the proximity to breakage of bonds, viz. the amount of energy or force flow that each bond could still transmit given its capacity and current flow.…”

“…We consider two types of flow: (i) energy flow, (ii) tensile force flow. These flows can be reasonably assumed to obey the above two conditions for flow 16 .…”