Phase field model for mixed mode fracture in concrete

Concrete is a quasi-brittle material and generally fails in mixed mode I-II fracture. The fracture energy release in mode I and mode II during crack propagation is usually different. However, the tensile test fracture toughness has generally been considered in most of the numerical models to study fracture in concrete. In this paper, a phase field model is presented which considers the fracture energy of mode I and mode II for mixed mode I-II fracture simulation in concrete. In addition, it uses a fracture mode controlling parameter ?????? which, in a sense, controls the governing failure criterion. The post-peak material response is modeled using a cohesive zone approach. The effect of the length scale parameter, mesh size and ?????? is investigated. For validation, a single-edge notch beam with a notch at various eccentricities is considered. It is shown that the model is mesh independent for a sufficiently fine mesh in cracking region. Also, the effect of the length scale parameter on global response is insignificant. It is observed that ?????? & GE; 1 gives satisfactory results both for mode I and mixed mode I-II fracture in single edge notch concrete beam. The numerical results for the load-displacement curve are compared with the experimental data both qualitatively and quantitatively. It is concluded that the proposed phase field model can simulate mode I and mixed mode I-II fracture in concrete with sufficient accuracy.