Scaling theory for quasibrittle structural failure

This inaugural article has a twofold purpose: (i) to present a simpler and more general justification of the fundamental scaling laws of quasibrittle fracture, bridging the asymptotic behaviors of plasticity, linear elastic fracture mechanics, and Weibull statistical theory of brittle failure, and (ii) to give a broad but succinct overview of various applications and ramifications covering many fields, many kinds of quasibrittle materials, and many scales (from 10^-8 to 10⁶ m). The justification rests on developing a method to combine dimensional analysis of cohesive fracture with second-order accurate asymptotic matching. This method exploits the recently established general asymptotic properties of the cohesive crack model and nonlocal Weibull statistical model. The key idea is to select the dimensionless variables in such a way that, in each asymptotic case, all of them vanish except one. The minimal nature of the hypotheses made explains the surprisingly broad applicability of the scaling laws.