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

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 [Formula: see text]. Relative to all feasible crack paths, the Griffith's fracture surface energy and the Francfort-Marigo energy functional are minimum in [Formula: see text]; likewise for the critical strain energy density if bonds are uniformly sized. Redundancies in transmission paths govern prefailure dynamics, and predispose [Formula: see text] to cascading failure during which the concomitant energy release rate and normal (Rankine) stress become maximum along [Formula: see text].