Corpus ID: 235458109

A posteriori estimator for the adaptive solution of a quasi-static fracture phase-field model with irreversibility constraints

@article{Walloth2021APE,
  title={A posteriori estimator for the adaptive solution of a quasi-static fracture phase-field model with irreversibility constraints},
  author={M. Walloth and W. Wollner},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.09469}
}
Within this article, we develop a residual type a posteriori error estimator for a time discrete quasi-static phase-field fracture model. Particular emphasize is given to the robustness of the error estimator for the variational inequality governing the phase-field evolution with respect to the phase-field regularization parameter . The article concludes with numerical examples highlighting the performance of the proposed a posteriori error estimators on three standard test cases; the single… Expand

References

SHOWING 1-10 OF 37 REFERENCES
Mesh adaptivity for quasi-static phase-field fractures based on a residual-type a posteriori error estimator
In this work, we consider adaptive mesh refinement for a monolithic phase-field description for fractures in brittle materials. Our approach is based on an a posteriori error estimator for theExpand
A phase-field description of dynamic brittle fracture
Abstract In contrast to discrete descriptions of fracture, phase-field descriptions do not require numerical tracking of discontinuities in the displacement field. This greatly reduces implementationExpand
An Adaptive Finite Element Approximation of a Variational Model of Brittle Fracture
TLDR
This work formulate and analyze two adaptive finite element algorithms for the computation of its (local) minimizers and presents two theoretical results which demonstrate convergence of these algorithms to local minimizers of the Ambrosio-Tortorelli functional. Expand
Goal functional evaluations for phase-field fracture using PU-based DWR mesh adaptivity
In this study, a posteriori error estimation and goal-oriented mesh adaptivity are developed for phase-field fracture propagation. Goal functionals are computed with the dual-weighted residual (DWR)Expand
Phase Field Approximation of Dynamic Brittle Fracture
The numerical assessment of fracture has gained importance in fields like the safety analysis of technical structures or the hydraulic fracturing process. The modelling technique discussed in thisExpand
A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework
Phase-field models based on the variational formulation for brittle fracture have recently been gaining popularity. These models have proven capable of accurately and robustly predicting complexExpand
Anisotropic Mesh Adaptation for Crack Detection In Brittle Materials
TLDR
A modification of this variational model includes additional constraints via penalty terms to enforce the irreversibility of the fracture as well as the applied displacement field to numerically compute the time-evolving minimizing solution. Expand
A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits
The computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies. This can be overcome by aExpand
Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations
The computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies. This can be overcome by aExpand
Phase-field modeling of ductile fracture
Phase-field modeling of brittle fracture in elastic solids is a well-established framework that overcomes the limitations of the classical Griffith theory in the prediction of crack nucleation and inExpand
...
1
2
3
4
...