Fracture mechanics-based meshless method for crack propagation in concrete structures

Abstract

Concrete is one of the most versatile construction materials, characterized by its high compressive strength and durability. It exhibits complex fracture behaviours in the non-linear region of the fracture process zone (FPZ) near crack tip, where micro-cracking, crack coalescence, and eventual macro-crack propagation occurs. Accurately predicting crack initiation and propagation in concrete structures is essential for ensuring their safety and performance. Traditional methods like finite element analysis (FEM) face challenges in capturing crack propagation due to the need for mesh refinement, which can be computationally expensive. This study aims to address this limitation by introducing the Element-Free Galerkin (EFG) method, which offers a more efficient approach for modelling crack behaviour in concrete beams. The maximum stress theory was used as the fracture criterion and the cohesive zone model (CZM) with a bilinear softening curve is employed to simulate the FPZ. Numerical examples of simply supported beam and cantilever beams with varying pre-notch positions and loadings were analysed. The results show that under axial and point loading, the stress intensity factor increases with crack length until unstable crack growth, leading to failure. The EFG method is found to be more accurate than FEM, particularly in regions with higher deformations, with a 13 % variation due to remeshing in FEM. Under point loading, EFG predicted deformation patterns with a 6 % variation in maximum deflection. This study demonstrates that the EFG-based model effectively predicts catastrophic failures, offering a computationally efficient solution for real-world concrete structures with pre-existing cracks or defects. © 2025 Institution of Structural Engineers