%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Actual paper reference 
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@article{code_phasefieldx,
  author = {Castillón, M.}, 
  title = {PhaseFieldX: an open-source framework for advanced phase-field simulations}, 
  journal = {Journal of Open Source Software},
  volume = {10}, 
  number = {108}, 
  pages = {7307}, 
  year = {2025}, 
  doi = {https://doi.org/10.21105/joss.07307}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Code 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@misc{code_BarattaEtal2023,
  author    = {Baratta, I.A. and Dean, J.P. and Dokken, J.S. and Habera, M. and Hale, J.S. and Richardson, C.N. and Rognes, M.E. and Scroggs, M.W. and Sime, N. and Wells, G.N.},
  title     = {DOLFINx: the next generation FEniCS problem solving environment},
  doi       = {https://doi.org/10.5281/zenodo.10447666},
  year      = {2023}
}

@article{code_scikit_image,
  author = {van der Walt, S. and Schönberger, J.L. and Nunez-Iglesias, J. and Boulogne, F. and Warner, J.D. and Yager, N. and Gouillart, E. and Yu, T. and the scikit-image contributors},
  title = {scikit-image: image processing in Python},
  year = {2014},
  volume = {2},
  pages = {e453},
  journal = {PeerJ},
  doi = {https://doi.org/10.7717/peerj.453}
}

@article{code_skeleton_algorithm,
  author = {Zhang, T.Y. and Suen, C.Y.},
  title = {A fast parallel algorithm for thinning digital patterns},
  year = {1984},
  volume = {27},
  number = {3},
  pages = {236--239},
  doi = {https://doi.org/10.1145/357994.358023},
  journal = {Communications of the ACM}
}

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% LEFM 
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% Phase-Field Models 
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@misc{Castillon2025_arxiv,
    title={A Phase-Field Approach to Fracture and Fatigue Analysis: Bridging Theory and Simulation}, 
    author={M. Castillón and I. Romero and J. Segurado},
    year={2025},
    eprint={2509.08939},
    archivePrefix={arXiv},
    primaryClass={cond-mat.mtrl-sci},
    url={https://arxiv.org/abs/2509.08939}, 
}

@article{phase_field_Miehe2010,
  author    = {Miehe, C. and Hofacker, M. and Welschinger, F.},
  title     = {A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits},
  journal   = {Computer Methods in Applied Mechanics and Engineering},
  volume    = {199},
  number    = {45-48},
  pages     = {2765--2778},
  year      = {2010},
  doi       = {https://doi.org/10.1016/j.cma.2010.04.011}
}

@article{phase_field_FrancfortMarigo1998,
  author    = {Francfort, G.A. and Marigo, J.-J.},
  title     = {Revisiting brittle fracture as an energy minimization problem},
  journal   = {Journal of the Mechanics and Physics of Solids},
  volume    = {46},
  number    = {8},
  pages     = {1319--1342},
  year      = {1998},
  doi       = {https://doi.org/10.1016/S0022-5096(98)00034-9}
}

@article{phase_field_Bourdin2000,
  author = {Bourdin, B. and Francfort, G.A. and Marigo, J.-J.},
  title = {Numerical experiments in revisited brittle fracture},
  journal = {Journal of the Mechanics and Physics of Solids},
  volume = {48},
  number = {4},
  pages = {797--826},
  year = {2000},
  doi = {https://doi.org/10.1016/S0022-5096(99)00028-9}
}

@article{phase_field_Amor2009,
  author    = {Amor, H. and Marigo, J.-J. and Maurini, C.},
  title     = {Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments},
  journal   = {Journal of the Mechanics and Physics of Solids},
  volume    = {57},
  number    = {8},
  pages     = {1209--1229},
  year      = {2009},
  doi       = {https://doi.org/10.1016/j.jmps.2009.04.011}
}

@article{phase_field_Carrara2020,
  title     = {A framework to model the fatigue behavior of brittle materials based on a variational phase-field approach},
  author    = {Carrara, P. and Ambati, M. and Alessi, R. and De Lorenzis, L.},
  journal   = {Computer Methods in Applied Mechanics and Engineering},
  volume    = {361},
  pages     = {112731},
  year      = {2020},
  issn      = {0045-7825},
  doi       = {10.1016/j.cma.2019.112731},
  url       = {https://www.sciencedirect.com/science/article/pii/S0045782519306218},
  keywords  = {Brittle fracture, Fatigue, Modeling, Paris law, Phase-field models, Wöhler curve},
}

@incollection{phase_field_modelling_of_fracture,
    title = {Chapter One - Phase-field modeling of fracture},
    author = {Wu, Jian-Ying and Nguyen, Vinh Phu and Nguyen, Chi Thanh and Sutula, Danas and Sinaie, Sina and Bordas, Stéphane P.A.},
    editor = {Bordas, Stéphane P.A. and Balint, Daniel S.},
    booktitle = {Advances in Applied Mechanics},
    publisher = {Elsevier},
    volume = {53},
    pages = {1--183},
    year = {2020},
    isbn = {0065-2156},
    doi = {10.1016/bs.aams.2019.08.001},
    url = {https://www.sciencedirect.com/science/article/pii/S0065215619300134},
    keywords = {Computational failure mechanics, Fracture, Damage, Phase-field models, Variational approach to fracture, Cohesive zone model, Cracking}
}

@article{phase_field_degradation_function_sargado,
  title = {High-accuracy phase-field models for brittle fracture based on a new family of degradation functions},
  journal = {Journal of the Mechanics and Physics of Solids},
  volume = {111},
  pages = {458-489},
  year = {2018},
  issn = {0022-5096},
  doi = {https://doi.org/10.1016/j.jmps.2017.10.015},
  url = {https://www.sciencedirect.com/science/article/pii/S0022509617303812},
  author = {Sargado, J.M. and Keilegavlen, E. and Berre, I. and Nordbotten, J.M.},
  keywords = {Fracture, Phase-field, Degradation function, Damage}
}