A combined XFEM phase-field computational model for crack growth without remeshing
- PDF / 3,283,201 Bytes
- 19 Pages / 595.276 x 790.866 pts Page_size
- 90 Downloads / 202 Views
ORIGINAL PAPER
A combined XFEM phase-field computational model for crack growth without remeshing Alba Muixí1 · Onofre Marco1 · Antonio Rodríguez-Ferran1 · Sonia Fernández-Méndez1 Received: 5 June 2020 / Accepted: 15 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper presents an adaptive strategy for phase-field simulations with transition to fracture. The phase-field equations are solved only in small subdomains around crack tips to determine propagation, while an extended finite element method (XFEM) discretization is used in the rest of the domain to represent sharp cracks, enabling to use a coarser discretization and therefore reducing the computational cost. Crack-tip subdomains move as cracks propagate in a fully automatic process. The same mesh is used during all the simulation, with an h-refined approximation in the elements in the crack-tip subdomains. Continuity of the displacement between the refined subdomains and the XFEM region is imposed in weak form via Nitsche’s method. The robustness of the strategy is shown for some numerical examples in 2D and 3D, including branching and coalescence tests. Keywords Phase-field modeling · Brittle fracture · Crack propagation · Continuous–discontinuous models · Adaptive refinement · Nitsche’s method · XFEM
1 Introduction Typical approaches to model brittle or quasi-brittle fracture can be classified in discontinuous and continuous models, depending on the way cracks are described. In discontinuous models, cracks are represented as discontinuities in the displacement field (sharp cracks), embedded in an elastic bulk. Specific mechanical criteria—typically based on linear elastic fracture mechanics (LEFM) concepts and based on crack-tip information—are needed to model crack inception, propagation and branching. A source of difficulty is the singularity of the strain and stress fields in classical linear elasticity at crack tips. For this reason, stress intensity factors (SIF) are often used [19]. From a computational viewpoint, two different strategies may be used to describe the displacement jump associated to a sharp discontinuity: node and edge duplication, in the spirit of the original cohesive zone model (CZM), see [25], or the extended finite element method (XFEM) and related techniques, where the crack path is not constrained to follow element edges and therefore remeshing is avoided [2,20].
B 1
Sonia Fernández-Méndez [email protected]
Together with a certain mesh-dependence of the crack path (for CZM) or geometrical complexity (for XFEM), discontinuous models offer various advantages, namely: (i) the explicit representation of the crack facilitates the modeling of crack-surface physics; (ii) the sharp discontinuity avoids any spurious interaction between the two faces of the crack; (iii) coarse discretizations may be used in the wake of the crack tip. Continuous models, usually phase-field or gradient-damage models, assume continuous displacement fields and represent cracks as damaged regions that have
Data Loading...
