The combined finite–discrete element method (FDEM) has proven effective for simulating crack initiation, propagation, and coalescence in brittle solids. However, existing FDEM frameworks remain limited to constant-strain elements, leading to restricted capability in representing complex stress fields, pronounced sensitivity to shear and volumetric locking, and a strong tendency toward numerical dispersion in dynamic problems. To overcome these limitations, this study develops a high order element-based framework incorporating a novel quadratic cohesive element to enhance model accuracy and continuity. The proposed quadratic cohesive element ensures uniform traction distribution along edges, avoiding the mid-node stress concentrations that typically lead to mesh incompatibility and artificial strength reduction. Three quasi-static loading tests and one wave propagation test are performed to compare quadratic and linear models. The results show that the quadratic model consistently outperforms the linear counterpart in stress path, crack propagation, and mitigating numerical dispersion. In quasi-static loading, the new quadratic model exhibits a lower error in stress, predicts a more precise crack initiation load, and provides more reliable crack path predictions compared with previous models. In dynamic conditions, it can effectively mitigate the numerical dispersion of high-frequency wave components that low-order elements struggle with and provide more stable wave propagation simulations. Moreover, the quadratic elements FDEM framework offers an economical alternative for enhancing the fidelity of crack simulations: compared to mesh refinement, quadratic elements achieve comparable accuracy in crack initiation load prediction with only 50–60% of the computational cost.
Bai et al. (2026) studied this question.