Efficient Fracture Modeling in Beam–Column Structures Using a Variational Damage Model

Traditional fracture modeling in structural mechanics (e.g., beams, bars/columns) often relies on solid elements, leading to computationally intensive simulations. In this study, we present a variational damage model specifically designed for structural mechanics to enhance the efficiency of fracture simulations in beam–column structures. The model accounts for the coupling effects of in-plane and bending deformations on damage evolution through a new mixed fracture energy density formulation. For the numerical implementation, Hermite elements are employed for beam structures in both 2D and 3D to ensure [Formula: see text] continuity. The proposed formulation accurately captures the evolution of fractures in structures and demonstrates low sensitivity to mesh discretization. In addition, the proposed model significantly reduces computational cost by using fewer elements compared to solid-based fracture simulations. The effectiveness of the model is illustrated through representative 2D and 3D numerical examples that showcase its capability in structural fracture simulations.