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.
This is the peer reviewed version of the following article: Li, K.; Rodriguez-Ferran, A.; Scovazzi, G. A blended shifted-fracture/phase-field framework for sharp/diffuse crack modeling. "International journal for numerical methods in engineering", 28 Febrer 2023, vol. 124, núm. 4, p. 998-1030, which has been published in final form at https://onlinelibrary.wiley.com/doi/10.1002/nme.7152. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.
