A localizing gradient enhanced isotropic damage model with Ottosen equivalent strain for the mixed-mode fracture of concrete

•Proposed a new equivalent strain measure, which enabled the simplest form of damage model to give good predictions for mixed mode fracture of concrete.•Compared to other commonly used equivalent strain measures, the proposed strain measure is shown to give the best results for complicated loading cases.•Captured the development of secondary horizontal cracks for the smallest specimens in the double edge notch tests by Nooru Mohamed (1992).•Captured the crack profile correctly for the single edge notch test by Carpiuc-Prisacari (2015). [Display omitted] Standard isotropic damage models are simple to implement, but they may be inadequate for the mixed-mode fracture of concrete. A new equivalent strain based on the four-parameter failure criterion by Ottosen [1] is proposed here for incorporation into a standard isotropic damage model for mixed-mode fracture, and its performance benchmarked against three other commonly used equivalent strain definitions (Mazars, modified von Mises, Rankine). Departing from the original approach [1], shear failure is utilized here as one of the states for the determination of the four parameters. Numerically, mesh sensitivity is resolved by adopting the localizing gradient enhancement to obtain sharp damage profiles at failure [2]. For the numerical analysis, a series of tests done on Double-Edge-Notched (DEN) specimens of different sizes [3] and the interactive test with multi axial loadings for Single-Edge-Notched (SEN) specimen [4] are considered. These examples illustrate that a simple isotropic damage model in conjunction with new equivalent strain measure is able to capture mixed-mode fracture accurately.