Determination of total crack free surface area creation and failure in quasi-brittle microcracking solids using 2D GraFEA simulations

One of the long-standing problems in continuum damage mechanics is accurate prediction of damage evolution that accounts for the distribution of microstructural features. This is particularly true for microcracking solids, such as concrete, where non-uniformity in the size and spatial distribution of defects can lead to non-uniqueness in the continuum-averaged energy release rate (and free surface area creation) for cases where local microcrack growth occurs. In this work, a novel theoretical framework for quantifying the crack free surface area creation is formulated and used along with a previously developed non-local numerical technique known as Graph-based Finite Element Analysis (GraFEA). Using the 2D GraFEA approach and its implementation into a finite element code, the invariance of the crack free surface area created and the total amount of energy dissipated due to fracture was demonstrated. This research aims to honor the lifelong accomplishments of Professor Alan Needleman in computational modeling of deformation and fracture. •2D GraFEA extended to estimate free surface area creation in microcracking concrete.•Used a non-local, stochastic model with population dynamics and survival probability.•Calibrated non-local characteristic length for concrete to estimate fracture energy.•Calculated fracture energy absorbed in concrete quasi-static boundary value problems.•This approach eliminated non-uniqueness in free surface area creation in GraFEA.