A novel strain gradient multiscale fracture model for brittle materials with random distribution of microcracks

Microcrack propagation represents a critical mechanism in material fracture, with random distributions introducing significant uncertainty into the fracture process. Addressing limitations in existing methods for characterizing microcrack spatial distribution, this study proposes a multiscale strain gradient fracture model based on two-scale asymptotic expansion theory. Through an improved Cartesian coordinate transformation approach, we have developed a macro–micro coupled fracture framework for brittle materials that effectively addresses randomly distributed microcrack problems. Our research reveals the intrinsic relationship between energy release rate and macroscopic strain, strain gradient, microcrack spacing, and length. Building on this foundation, we have extended the classical Griffith criterion to propose a two-scale fracture criterion that comprehensively considers microcrack spacing, macroscopic strain, and strain gradient effects. Through quasi-static uniaxial tensile numerical simulations using PMMA as the research subject, we found that the strain gradient effect has a certain inhibitory influence on crack propagation, effectively slowing down the crack growth. Additionally, the model also reveals the impact of randomly distributed microcracks on the macroscopic fracture behavior of brittle materials.