A refined augmented finite element formulation with coupled cohesive law for fracture analysis

Conventional Augmented Finite Element Methods (A-FEM) often suffer from non-physical crack paths and numerical instabilities in mixed-mode fracture, primarily due to the uncoupled assumptions in cohesive constitutive relations and coarse stress integration. This study proposes a refined A-FEM formulation that incorporates physically-consistent coupled cohesive laws to capture the intricate interactions between opening and sliding modes within the fracture process zone. To resolve the long-standing issue of spurious “load-jumps” during crack-tip transition, an adaptive stress integration algorithm (IM-GI) is developed. This scheme explicitly tracks the instantaneous evolution of strong discontinuities, thereby ensuring local equilibrium and energy consistency during the fracture process. Numerical benchmarks, from element-level mixed-mode tests to complex dual-crack interactions, demonstrate that the proposed formulation eliminates spurious crack patterns by rigorously accounting for inter-mode coupling. Notably, the refined framework achieves the high-fidelity of standard cohesive zone models while preserving the computational efficiency of enriched methods. The formulation's robustness is further validated through wedge splitting and structural-scale concrete beam failure tests, which confirm its mesh-independence even on relatively coarse grids. The results underscore that the synergy between coupled constitutive modeling and refined integration is indispensable for the high-fidelity simulation of complex fracture mechanisms in engineering structures.