Modelling unstable crack propagation in concrete by finite element method with continuous nodal stress

Abstract

Cracks in concrete will propagate unstably due to excessive shear stress, interactions at the rock-concrete interface, or sudden energy release, significantly compromising structural bearing capacity. To investigate this phenomenon, a nonlinear numerical method for modelling mixed-mode I-II crack propagation has been developed. This approach integrates dynamic equilibrium with a fictitious crack model and an initiation fracture toughness criterion. Key innovations include the incorporation of a finite element method with continuous nodal stress to enhance calculation accuracy, the utilization of kinetic energy to compensate for abrupt losses of strain energy during crack propagation, and the consideration of the deformation of the distributive beam and its interactions with specimens and supports. It was validated by modelling classic benchmarks for the dynamic initiation and propagation of brittle materials under mode I and mixed-mode I-II loading, and applied to analyse unstable crack propagation in concrete for four-point shear (FPS) beam specimens under various ratios of mode I and II stress intensity factors (K_I/K_II = 0 to 5.32) and loading rates (2 × 10^-7 m/s to 2 × 10^-3 m/s). Results indicated that the method effectively captures unstable crack propagation, with load-crack mouth shear displacement (CMSD) curves and crack propagation trajectories closely matching the experimental data. Furthermore, it was observed that when the elastic strain energy within the concrete beam exceeds the residual energy stored in the extended cracks, the crack transitions from stability to instability; conversely, if the elastic strain energy is less than or approximately equal to the residual energy, the crack decelerates and returns to stability. Additionally, parametric analyses reveal that lower distributive beam stiffness, shorter preset crack lengths, reduced concrete fracture energy, and a less robust cohesive force–displacement curve increase the likelihood of unstable crack propagation in concrete.