Phase field approach for managing multi-fragment interactions in load-bearing fractured media

This work introduces a novel approach for characterizing the residual load bearing capacity of fractured components based on the Phase Field fracture model. The underlying idea involves exploiting this well-established framework for fracturing materials and applying it to mechanically loaded domains in which fracture has already occurred. Hence, the continuous phase field here portrays the smeared representation of known crack patterns, based on which the unilateral contact interactions between the crack lips are enforced through a suitable strain energy decomposition. This allows for a theoretically robust and implicit treatment of the originally discontinuous problem while remaining in a continuum framework. As such, the proposed approach avoids the numerically challenging definition and management of conventional contact pairs, thus proving to be especially promising for its application to domains with multiple fragments. Besides presenting the theoretical foundation and algorithmic convenience of the approach, its accuracy and representativeness are proven against theoretical predictions and numerical results from Finite Element models featuring conventional contact interactions.