Phase-field fracture simulations of the Brazilian splitting test

The tensile strength of brittle and tension-sensitive materials can be determined experimentally by the Brazilian test. To complement the experimental results numerical methods are required which predict the effective properties of the material as an outcome of the calculations. Here a modified phase-field approach to fracture is presented which is able to find the position of the crack, to determine the stress distribution in the (cracking) specimen and to quantify the tensile resistance of the material. Especially we discuss the definition of the phase-field crack driving forces and show by comparison to the analytical solution of the Brazilian test that common strategies of energy splitting are not applicable. Compressive split fracture needs to be driven by the stress state and requires a driving force based on a criterion of fracture mechanics. To demonstrate the predictive capability of the presented approach numerical simulations in two and three dimensions are compared to experimentally obtained results.