“…At macroscopic scale, concrete could be regarded as a homogeneous material, while at mesoscopic scale it is treated as consisting of coarse aggregates and mortar matrix (Wriggers and Moftah, 2006). Many concrete nonlinear fracture models (Bažant and Jirasek, 2002; Jirasek and Zimmermann, 2001a, 2001b; Majewski et al., 2008; Pijaudier-Cabot et al., 2004; Skarżyński et al., 2011; Syroka-Korol, 2014, 2015; Yılmaz and Molinari, 2017), based on the theory of fracture mechanics and the nonlocal theory, have been established at macro-scale. The macroscopic computational models in the literatures are able to describe the nonlinear mechanical properties and the size effect behavior of concrete by including a characteristic length of microstructure.…”