A topological approach to crack path detection and crack opening displacement calculation in phase-field models of fracture

Date

2026-08-15

Author

Babaoğlu, Muhittin
Kaynar, Ozan Özgür
Göktepe, Serdar

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As opposed to discrete approaches, the crack topology is approximated in a smeared manner in phase-field fracture models (PFMs) through a continuous order variable. Although this allows for avoiding the additional intricate algorithms for tracking and controlling the crack initiation, propagation, and branching in complex fracture problems, the diffusive nature of crack in PFMs hinders the determination of the exact crack path and the estimation of the crack opening displacement (COD). The latter plays a central role in many practical engineering problems such as the modeling of fluid flow in hydraulic fracture, the heat conduction and advection in thermal cracking, and the phase-field modeling of cohesive fracture. Therefore, this contribution deals with the development of an efficient and robust computational tool for calculating COD. To this end, we consider a progressively propagating crack whose backbone is represented by multiple segments, each of which is fitted by a cubic spline. The set of points belonging to a segment is then decomposed into two sets, separated by the spline. The components of the displacement vectors normal to the spline are fitted by two planes separately for the two sets. The COD is then obtained by subtracting these two planes from one another. The originality of the proposed crack reconstruction method lies in the novel calculation of COD by displacement-fitted planes based on explicitly determined crack path within the PFM. The excellent performance of the proposed tool is demonstrated through representative numerical examples with basic to complex crack profiles.

Subject Keywords

Crack opening displacement, Displacement jump, Phase-field fracture

URI

https://hdl.handle.net/11511/119301

Collections

Department of Civil Engineering, Article