New article: A correction method for crack area overestimation in phase-field fracture
New article: Castillón, M., Segurado, J. and Romero, I. (2026). A correction method for crack area overestimation in phase-field fracture, Computational Mechanics. (link).
Phase-field fracture models systematically overestimate the crack area, a consequence of the diffuse crack representation and of numerical artifacts such as strain localization, where the phase-field variable saturates artificially across finite elements. In this article we propose a correction framework built on the principle of energy equipartition: as the length-scale parameter vanishes, the contributions of the phase field and of its gradient to the fracture energy become equal. Since the numerical artifacts affect mainly the phase-field term while leaving the gradient term largely unperturbed, the crack area can be approximated as twice the gradient-dependent energy. The resulting estimate is mesh-independent, applies to the whole domain, and extends naturally to three dimensions. The method is validated against benchmarks with analytical solutions, compared with skeletonization algorithms, and applied to complex geometries with curvilinear crack paths and to a three-dimensional simulation.