Investigation of driving forces in a phase field approach to mixed mode fracture of concrete

Concrete, with its heterogeneous internal structure of cement mortar and grains, exhibits complex quasi-brittle cracking where a gradual decrease in the material integrity is observed. In practical engineering, concrete structures are commonly under loading conditions that cause complex mixed mode fracture patterns. Hence, the prediction of failure mechanisms and patterns in concrete is a demanding task. In the past decades, computational fracture modeling of concrete has proven to be a suitable substitute for costly experimental testing. Among many fracture models, the phase field approach, owing to its ability to capture various crack phenomena without a need for ad hoc criteria, has gained significant attention. Although there exist phase field models applied to various failure mechanisms ranging from brittle to ductile fractures, only a limited number of them deal with the quasi-brittle cracking observed in concrete. Hence, in this work, a thermodynamically consistent phase field approach for quasi-brittle fracture is presented, and its performance for capturing the mixed mode failure patterns of concrete is investigated. Starting from a purely geometric approach, the evolution of fracture is associated with a constitutive crack driving functional. The crack driving force is related to an equivalent effective stress measure leading to a simple, yet versatile, framework in which various failure criteria can be implicitly incorporated into the framework. In particular, equivalent effective stresses based on the Rankine, Drucker-Prager, modified von Mises, and three-parameter failure criteria are derived. A unified form of the equivalent effective stress encompassing all the models is also proposed, which offers flexibility in choosing an appropriate driving force, and allows a simple implementation into a finite element framework. Utilizing this unified form, the effectiveness of the aforementioned driving forces in capturing complex mixed mode cracking in concrete is investigated by comparing the results obtained from computational simulations to existing experimental data. In particular, the load-displacement curves and the crack propagation paths are compared with the corresponding experimental observations, and a systematic study of the performance of different driving forces is detailed in this study.