A blended shifted‐fracture/phase‐field framework for sharp/diffuse crack modeling

The shifted fracture method (SFM) is an embedded method that enables sharp crack representations while using mesh‐fitted data structures. In the SFM, the true crack is embedded in the computational grid, but the crack interface conditions are approximated by, or shifted to, a surrogate crack composed of element boundaries (i.e., edges/faces in two/three dimensions). This avoids enriched degrees‐of‐freedom and cut elements, so that data structures and geometrical treatment are much simpler, while still maintaining mesh‐independent and accurate crack approximations. This article presents a continuous‐discontinuous model of fracture based on blending a phase‐field (PF) model with the SFM. The PF tracks the evolution of cracks inside a numerical fracture processing zone: diffuse cracks initiate, propagate, branch, and merge according to the field equations of energy minimization; no ad‐hoc criteria are needed. The PF damage variable is then used to define the geometry of the true crack. With computational efficiency in mind, the PF model is only solved in subdomains where additional crack growth is expected and the SFM representation is used elsewhere. The efficiency and accuracy of the proposed approach in capturing complex crack patterns are illustrated by a representative set of two‐dimensional numerical examples.