Abstract
Based on a two-scale asymptotic analysis procedure, we rigorously derive a new macroscopic brittle fracture model for materials with micro-cracks inside. Strain gradient effects are naturally involved in the model in the absence of any phenomenological assumptions. Coefficients of the fracture criterion are expressed in form of derivatives of the fourth- and sixth-order effective elastic tensors that are explicitly related to solutions of the first order unit cell problems. The model is numerically implemented into a finite element code. Abilities of the model to predict microstructure size effects and strain gradient effects on macro fracture behaviors are confirmed by numerical simulations. The model is also validated against experimental measurements.
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