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.

In this paper, we study control problems that can be directly applied to controlling the rotational motion of eye and head. We model eye and head as a sphere, or ellipsoid, rotating about its center, or about its south pole, where the axes of rotation are physiologically constrained, as was proposed originally by Listing and Donders. The Donders' constraint is either derived from Fick gimbals or from observed rotation data of adult human head. The movement dynamics is derived on SO(3) or on a suitable submanifold of SO(3) after describing a Lagrangian. Using two forms of parametrization, the axis-angle and Tait-Bryan, the motion dynamics is described as an Euler-Lagrange's equation, which is written together with an externally applied control torque. Using the control system, so obtained, we propose a class of optimal control problem that minimizes the norm of the applied external torque vector. Our control objective is to point the eye or head, toward a stationary point target, also called the regulation problem. The optimal control problem has also been analyzed by writing the dynamical system as a Newton-Euler's equation using angular velocity as part of the state variables. In this approach, explicit parametrization of SO( 3) is not required. Finally, in the appendix, we describe a recently introduced potential control problem to address the regulation problem.

Heterogeneous quasibrittle composites like concrete, ceramics and rocks comprise grains held together by bonds. The question on whether or not the path of the crack that leads to failure can be predicted from known microstructural features, viz. bond connectivity, size, fracture surface energy and strength, remains open. Many fracture criteria exist. The most widely used are based on a postulated stress and/or energy extremal. Since force and energy share common transmission paths, their flow bottleneck may be the precursory failure mechanism to reconcile these optimality criteria in one unified framework. We explore this in the framework of network flow theory, using microstructural data from 3D discrete element models of concrete under uniaxial tension. We find the force and energy bottlenecks emerge in the same path and provide an early and accurate prediction of the ultimate macrocrack path $${\mathcal {C}}$$ C . Relative to all feasible crack paths, the Griffith’s fracture surface energy and the Francfort–Marigo energy functional are minimum in $${\mathcal {C}}$$ C ; likewise for the critical strain energy density if bonds are uniformly sized. Redundancies in transmission paths govern prefailure dynamics, and predispose $${\mathcal {C}}$$ C to cascading failure during which the concomitant energy release rate and normal (Rankine) stress become maximum along $${\mathcal {C}}$$ C .

Impending catastrophic failure of granular earth slopes manifests distinct kinematic patterns in space and time. While risk assessments of slope failure hazards have routinely relied on the monitoring of ground motion, such precursory failure patterns remain poorly understood. A key challenge is the multiplicity of spatiotemporal scales and dynamical regimes. In particular, there exist a precursory failure regime where two mesoscale mechanisms coevolve, namely, the preferred transmission paths for force and damage. Despite extensive studies, a formulation which can address their coevolution not just in laboratory tests but also in large, uncontrolled field environments has proved elusive. Here we address this problem by developing a slope stability analytics framework which uses network flow theory and mesoscience to model this coevolution and predict emergent kinematic clusters solely from surface ground motion data. We test this framework on four data sets: one at the laboratory scale using individual grain displacement data; three at the field scale using line-of-sight displacement of a slope surface, from ground-based radar in two mines and from space-borne radar for the 2017 Xinmo landslide. The dynamics of the kinematic clusters deliver an early prediction of the geometry, location and time of failure.

Abstract. Using data from discrete element simulations, we develop a data analytics approach using network flow theory to study force transmission and failure in a 'dog-bone' concrete specimen submitted to uniaxial tension. With this approach, we establish the extent to which the bottlenecks, i.e., a subset of contacts that impedes flow and are prone to becoming overloaded, can predict the location of the ultimate macro-crack. At the heart of this analysis is a capacity function that quantifies, in relative terms, the maximum force that can be transmitted through the different contacts or edges in the network. Here we set this function to be solely governed by the size of the contact area between the deformable spherical grains. During all the initial stages of the loading history, when no bonds are broken, we find the bottlenecks coincide consistently with, and therefore predict, the location of the crack that later forms in the failure regime after peak force. When bonds do start to break, they are spread throughout the specimen: in, near, and far from, the bottlenecks. In one stage leading up to peak force, bonds collectively break in the lower portion of the specimen, momentarily shifting the bottlenecks to this location. Just before and around peak force, however, the bottlenecks return to their original location and remain there until the macro-crack emerges right along the bottlenecks.