Phase-field modeling of brittle fracture in heterogeneous bars

We investigate phase-field modeling of brittle fracture in a one-dimensional bar featuring continuous variation elastic and/or properties along its axis. Our main goal is to quantitatively assess how the heterogeneity and material influences observed behavior bar, as obtained from approach. The results clarify limit stress, peak stress toughness heterogeneous relate those reference homogeneous what are parameters affecting these relationships. Overall, effect shown be strictly tied non-local nature regularization. Finally, we show that this non-locality may amend ill-posedness sharp-crack problem bars where multiple points compete locations.