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eprint = {https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1965.0216}
,
    abstract = { The crystallographic characteristics of deformation twinning are derived by considering the atomic movements which occur at the moving interface as a twin propagates. This is facilitated by making use of the notation of the tensor calculus, and general expressions, valid for all crystal structures, are obtained giving the magnitude of the twinning shear and relating the twinning elements for both type I and type II twinning. The atomic shuffles, which in general must accompany the twinning shear in both single and multiple lattice structures, are examined in detail and expressions are derived for their magnitudes and directions for the cases of the four classical orientation relationships associated with deformation twinning. The use of these expressions in predicting operative twinning modes is described and the relations between this theory and other recent theories of the crystallography of deformation twinning are discussed. }
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doi = {https://doi.org/10.1016/j.jmps.2016.12.008},
url = {https://www.sciencedirect.com/science/article/pii/S0022509616304641},
author = {Jiahao Cheng and Somnath Ghosh},
keywords = {Explicit twin evolution, Crystal plasticity finite element, Magnesium, Subcycling, Tension-compression asymmetry}}

@article{KONDO2014672,
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volume = {95},
pages = {672-683},
year = {2014},
issn = {0927-0256},
doi = {https://doi.org/10.1016/j.commatsci.2014.08.034},
url = {https://www.sciencedirect.com/science/article/pii/S092702561400576X},
author = {R. Kondo and Y. Tadano and K. Shizawa},
keywords = {Dislocations, Twinning, Crystal plasticity, Finite elements, Phase-field method}}

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title = {Deformation twinning},
journal = {Progress in Materials Science},
volume = {39},
number = {1},
pages = {1-157},
year = {1995},
issn = {0079-6425},
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url = {https://www.sciencedirect.com/science/article/pii/0079642594000077},
author = {J.W. Christian and S. Mahajan}}

@ARTICLE{Knezevic201555,
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	journal = {Acta Materialia},
	volume = {88},
	pages = {55 – 73},
	doi = {10.1016/j.actamat.2015.01.037},
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	type = {Article}
}

@article{QIN2014293,
title = {Initiation and accommodation of primary twins in high-purity titanium},
journal = {Acta Materialia},
volume = {71},
pages = {293-305},
year = {2014},
issn = {1359-6454},
doi = {https://doi.org/10.1016/j.actamat.2014.03.025},
url = {https://www.sciencedirect.com/science/article/pii/S1359645414001724},
author = {Hong Qin and John J. Jonas and Hongbing Yu and Nicolas Brodusch and Raynald Gauvin and Xiyan Zhang},
keywords = {High-purity titanium, Double differentiation, Twinning, Schmid factor, Accommodation strain}}

@article{BEYERLEIN2011988,
title = {Effect of microstructure on the nucleation of deformation twins in polycrystalline high-purity magnesium: A multi-scale modeling study},
journal = {Journal of the Mechanics and Physics of Solids},
volume = {59},
number = {5},
pages = {988-1003},
year = {2011},
issn = {0022-5096},
doi = {https://doi.org/10.1016/j.jmps.2011.02.007},
url = {https://www.sciencedirect.com/science/article/pii/S0022509611000354},
author = {I.J. Beyerlein and R.J. McCabe and C.N. Tomé},
keywords = {Twinning, Nucleation, Statistics, Magnesium, hcp}}

@article{Kelly19685,
title = {Plane-strain compression of magnesium and magnesium alloy crystals},
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number = {1},
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year = {1968},
issn = {0022-5096},
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author = {E. W. Kelley and W. F. J. R. Hosford}}

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title = {Effect of local stress fields on twin characteristics in HCP metals},
journal = {Acta Materialia},
volume = {116},
pages = {143-154},
year = {2016},
issn = {1359-6454},
doi = {https://doi.org/10.1016/j.actamat.2016.06.042},
url = {https://www.sciencedirect.com/science/article/pii/S1359645416304621},
author = {M. {Arul Kumar} and I.J. Beyerlein and C.N. Tomé},
keywords = {Plasticity, Magnesium, Zirconium, Titanium, Anisotropy}}

@misc{reference_id,
  author = {Author's Name},
  title = {Title of the Web Page},
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  howpublished = {\url{URL of the Web Page}},
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}

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AUTHOR = {Tan, Jovan and Ramakrishna, Seeram},
TITLE = {Applications of Magnesium and Its Alloys: A Review},
JOURNAL = {Applied Sciences},
VOLUME = {11},
YEAR = {2021},
NUMBER = {15},
ARTICLE-NUMBER = {6861},
URL = {https://www.mdpi.com/2076-3417/11/15/6861},
ISSN = {2076-3417},
DOI = {10.3390/app11156861}
}

@inproceedings{Feinberg10.1117/12.924271,
author = {Lee D. Feinberg and Mark Clampin and Ritva Keski-Kuha and Charlie Atkinson and Scott Texter and Mark Bergeland and Benjamin B. Gallagher},
title = {{James Webb Space Telescope optical telescope element mirror development history and results}},
volume = {8442},
booktitle = {Space Telescopes and Instrumentation 2012: Optical, Infrared, and Millimeter Wave},
editor = {Mark C. Clampin and Giovanni G. Fazio and Howard A. MacEwen and Jacobus M. Oschmann Jr.},
organization = {International Society for Optics and Photonics},
publisher = {SPIE},
pages = {84422B},
keywords = {JWST, Mirrors, OTE, Telescope, Space},
year = {2012},
doi = {10.1117/12.924271},
URL = {https://doi.org/10.1117/12.924271}
}

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  title     = {Beryllium - A Unique Material in Nuclear Applications},
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  year      = {2004},
  number    = {AC07-99ID-13727},
  address   = {San Diego, CA (United States)},
  month     = {November},
  organization = {Idaho National Laboratory INL (United States)},
  publisher = {OSTI},
  note      = {Additional Information},
  url = {https://www.osti.gov/biblio/910826},
  abstractNote = {Beryllium, due to its unique combination of structural, chemical, atomic number, and neutron absorption cross section characteristics, has been used successfully as a neutron reflector for three generations of nuclear test reactors at the Idaho National Engineering and Environmental Laboratory (INEEL). The Advanced Test Reactor (ATR), the largest test reactor in the world, has utilized five successive beryllium neutron reflectors and is scheduled for continued operation with a sixth beryllium reflector. A high radiation environment in a test reactor produces radiation damage and other changes in beryllium. These changes necessitate safety analysis of the beryllium, methods to predict performance, and appropriate surveillances. Other nuclear applications also utilize beryllium. Beryllium, given its unique atomic, physical, and chemical characteristics, is widely used as a “window” for x-rays and gamma rays. Beryllium, intimately mixed with high-energy alpha radiation emitters has been successfully used to produce neutron sources. This paper addresses operational experience and methodologies associated with the use of beryllium in nuclear test reactors and in “windows” for x-rays and gamma rays. Other nuclear applications utilizing beryllium are also discussed.},
}

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TITLE = {A Review on Capturing Twin Nucleation in Crystal Plasticity for Hexagonal Metals},
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VOLUME = {11},
YEAR = {2021},
NUMBER = {9},
ARTICLE-NUMBER = {1373},
URL = {https://www.mdpi.com/2075-4701/11/9/1373},
ISSN = {2075-4701},
DOI = {10.3390/met11091373}
}

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  title={Advanced material models for the crystal plasticity finite element method: development of a general CPFEM framework},
  author={Roters, Franz},
  year={2011},
  school={Aachen, Techn. Hochsch., Habil.-Schr., 2011}
}

@incollection{CHRISTIAN2002859,
title = {CHAPTER 20 - Deformation Twinning},
editor = {J.W. CHRISTIAN},
booktitle = {The Theory of Transformations in Metals and Alloys},
publisher = {Pergamon},
address = {Oxford},
pages = {859-960},
year = {2002},
isbn = {978-0-08-044019-4},
doi = {https://doi.org/10.1016/B978-008044019-4/50025-8},
url = {https://www.sciencedirect.com/science/article/pii/B9780080440194500258},
author = {J.W. CHRISTIAN}
}

@article{Lebensohn.2003.1212,
author = {Lebensohn, R. A.  and Liu, Y.  and Castañeda, P. Ponte },
title = {Macroscopic properties and field fluctuations in model power-law polycrystals: full-field solutions versus self-consistent estimates},
journal = {Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences},
volume = {460},
number = {2045},
pages = {1381-1405},
year = {2004},
doi = {10.1098/rspa.2003.1212},

URL = {https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2003.1212},
eprint = {https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2003.1212}}

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year = {2009},
issn = {0749-6419},
doi = {https://doi.org/10.1016/j.ijplas.2008.05.005},
url = {https://www.sciencedirect.com/science/article/pii/S074964190800079X},author = {Gwénaëlle Proust and Carlos N. Tomé and Ashutosh Jain and Sean R. Agnew},
keywords = {Twinning, Polycrystal modeling, Hardening, Hexagonal materials, Magnesium}}

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title = {A crystal plasticity model for hexagonal close packed (HCP) crystals including twinning and de-twinning mechanisms},
journal = {International Journal of Plasticity},
volume = {49},
pages = {36-52},
year = {2013},
issn = {0749-6419},
doi = {https://doi.org/10.1016/j.ijplas.2013.02.016},
url = {https://www.sciencedirect.com/science/article/pii/S0749641913000612},
author = {H. Wang and P.D. Wu and J. Wang and C.N. Tomé},
keywords = {De-twinning, Twinning, Crystal plasticity, Cyclic loading}}

@article{BARNETT2015151,
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journal = {International Journal of Plasticity},
volume = {72},
pages = {151-167},
year = {2015},
issn = {0749-6419},
doi = {https://doi.org/10.1016/j.ijplas.2015.05.003},
url = {https://www.sciencedirect.com/science/article/pii/S074964191500073X},
author = {M.R. Barnett and O. Bouaziz and L.S. Toth},
keywords = {A. Twinning, B. Metallic material, B. Constitutive behaviour, C. Analytic functions, Magnesium}}

@article{ARDELJAN2015396,
title = {Explicit incorporation of deformation twins into crystal plasticity finite element models},
journal = {Computer Methods in Applied Mechanics and Engineering},
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pages = {396-413},
year = {2015},
issn = {0045-7825},
doi = {https://doi.org/10.1016/j.cma.2015.07.003},
url = {https://www.sciencedirect.com/science/article/pii/S0045782515002157},
author = {Milan Ardeljan and Rodney J. McCabe and Irene J. Beyerlein and Marko Knezevic},
keywords = {Crystal plasticity finite element models, Stress fields, Deformation twinning, Twin formation, Twin thickening}}

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title = {Adaptive multi-time-domain subcycling for crystal plasticity FE modeling of discrete twin evolution},
journal = {Computational Mechanics},
volume = {61},
pages = {33-54},
year = {2018},
issn = {1432-0924},
doi = {https://doi.org/10.1007/s00466-017-1421-4},
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author = {Somnath Ghosh and Jiahao Cheng}}

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volume = {135},
pages = {102778},
year = {2020},
issn = {0749-6419},
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author = {Nicolò Grilli and Alan C.F. Cocks and Edmund Tarleton},
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	type = {Article},
	publication_stage = {Final},
	source = {Scopus},
	note = {Cited by: 1657}
}

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  year={2011},
  url={https://api.semanticscholar.org/CorpusID:13597028},
journal={International Journal of Research and Reviews in Applied Sciences},
vol = {6},
pages = {462-483},
number = {4}
}

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title = {Validating a polycrystal model for the elastoplastic response of magnesium alloy AZ31 using in situ neutron diffraction},
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volume = {54},
number = {18},
pages = {4841-4852},
year = {2006},
issn = {1359-6454},
doi = {https://doi.org/10.1016/j.actamat.2006.06.020},
url = {https://www.sciencedirect.com/science/article/pii/S1359645406004502},
author = {S.R. Agnew and D.W. Brown and C.N. Tomé},
keywords = {Magnesium, Texture, Plasticity, Neutron scattering, ECAP}}

@article{WANG201477,
title = {In situ observation of collective grain-scale mechanics in Mg and Mg–rare earth alloys},
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author = {F. Wang and S. Sandlöbes and M. Diehl and L. Sharma and F. Roters and D. Raabe},
keywords = {Magnesium, Shear banding, Deformation twinning, Electron channelling contrast imaging, Crystal plasticity modelling}}

@article{rogers1947high,
  title={High-intensity radiation from beryllium-window X-ray tubes},
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  journal={Radiology},
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  number={6},
  pages={594--603},
  year={1947},
  publisher={The Radiological Society of North America}
}