A simple method to model crack propagation in concrete

Crack analysis is vital to explain behavior of concrete structures. In the present study, an interface element with softening spring is used to simulate cohesive zone model (CZM) in beam to accurately explain the propagation for mixed-mode crack. Modified crack closure integral method is implemented to model propagation of fracture process zone (FPZ) and stress-free region. An element stiffness matrix is used to derive forces in nodes due to normal and shear stress in the FPZ. Size effects such as depth of the beam, effective crack and initial notch are considered in calculation of the FPZ length and crack extension. By using this model, energy release rate is calculated directly by virtual crack closure technique (VCCT) by considering the variation of work done by external loads. The model decreases computational time and complexity for discrete cracks and provides accuracy as compared to other previous research.