Effective toughness of disordered brittle solids: A homogenization framework

This paper addresses the question of homogenization fracture properties for three-dimensional disordered brittle solids. The effective toughness, identified as minimum elastic energy release rate required to ensure crack growth, is predicted from a semi-analytical framework inspired by both micromechanics and statistical physics, that encompasses decisive influences material disorder mechanisms interaction between heterogeneities. Theoretical predictions are compared numerical values toughness computed with fracture-mechanics-based method Lebihain et al. (2020). Based on perturbative approach Linear Elastic Fracture Mechanics, this allows efficient computation propagation under tensile Mode I loading in composite materials containing several millions inclusions, where interacts them through two : crossing, wherein penetrates inclusion, by-pass, wanders out-of-plane follows inclusion/matrix interface. We show our procedure provides an accurate prediction homogenized broad range microstructural parameters such inclusion density or shape. original theoretical constitutes powerful mean connect their growth resistance, beyond particular cases considered simulations performed. As result, it new strategies rational design optimized composites tailored properties.