Numerical modeling of concrete fracture and size effect using position-based high aspect ratio solid elements

Abstract The size effect, defined as the reduction in nominal structural strength with increasing size, is a critical phenomenon in concrete and other quasi-brittle materials, governed by fracture processes such as crack initiation, propagation, and localization within the fracture process zone (FPZ). As the structural size increases, the relative influence of the FPZ diminishes, resulting in more brittle behavior. Although several numerical approaches have advanced the understanding of size effects, challenges still remain in accurately and efficiently capturing fracture processes and size-dependent behavior. In this context, the present study applies a recently developed approach, namely the position-based mesh fragmentation technique, which employs high-aspect-ratio solid elements to explicitly simulate concrete fracture. The study investigates size effects in concrete beams subjected to three-point bending under both pure Mode I and mixed-mode loading conditions, considering unnotched and notched specimens with different notch-to-depth ratios. The numerical results are complemented by a comprehensive statistical analysis, including quality indicators that provide a benchmark reference for future comparisons. Average computational times are also reported, providing benchmark values for efficiency comparisons that are rarely addressed in the literature. Moreover, the study provides insights into the influence of the FPZ and boundary conditions on structural strength and failure modes, establishing an efficient and statistically validated numerical framework for predicting size effects in concrete structures. Additionally, the numerical and experimental results are compared using Bažant’s size effect law, allowing the assessment of the numerical framework in terms of its capability to reproduce the scaling behavior of nominal strength with increasing structural size.