In this paper, we study the size effect of the macroscopic mechanical behavior of quasi-brittle materials such as concrete and mortar by applying the method of multi-scale analysis to take into account the generation and propagation of micro-cracks. For micro-scale analyses, the cohesive crack model is used to characterize the quasi-brittle softening behavior in conjunction with the discrete crack model for representing the generation and propagation of microscopic fractured surfaces. After reviewing the two-scale boundary value problems based on the homogenization method and the modeling of quasi-brittle fracture in micro-scale, we perform two numerical experiments to reveal the predominant factor of the size effect and to clarify its mechanism. One is for a comparative study to evaluate the effect of the amount of micro-crack formation on the macroscopic fracture energy. The other is to point out the importance of distinguishing between the microscopic size effect due to the micro-scale heterogeneity and the macroscopic size effect as energy balance in the overall structure.
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