[{"language":[{"iso":"eng"}],"_id":"20061","user_id":"15694","status":"public","type":"journal_article","publication":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","title":"C1-continuous space-time discretization based on Hamilton's law of varying action","doi":"10.1002/zamm.201600062","date_updated":"2022-01-21T10:22:38Z","date_created":"2020-10-15T15:56:20Z","author":[{"first_name":"J.C.","full_name":"Mergel, J.C.","last_name":"Mergel"},{"first_name":"R.A.","last_name":"Sauer","full_name":"Sauer, R.A."},{"last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"}],"volume":"97(4)","year":"2017","citation":{"bibtex":"@article{Mergel_Sauer_Ober-Blöbaum_2017, title={C1-continuous space-time discretization based on Hamilton’s law of varying action}, volume={97(4)}, DOI={<a href=\"https://doi.org/10.1002/zamm.201600062\">10.1002/zamm.201600062</a>}, journal={ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik}, author={Mergel, J.C. and Sauer, R.A. and Ober-Blöbaum, Sina}, year={2017}, pages={433–457} }","mla":"Mergel, J. C., et al. “C1-Continuous Space-Time Discretization Based on Hamilton’s Law of Varying Action.” <i>ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift Für Angewandte Mathematik Und Mechanik</i>, vol. 97(4), 2017, pp. 433–57, doi:<a href=\"https://doi.org/10.1002/zamm.201600062\">10.1002/zamm.201600062</a>.","short":"J.C. Mergel, R.A. Sauer, S. Ober-Blöbaum, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift Für Angewandte Mathematik Und Mechanik 97(4) (2017) 433–457.","apa":"Mergel, J. C., Sauer, R. A., &#38; Ober-Blöbaum, S. (2017). C1-continuous space-time discretization based on Hamilton’s law of varying action. <i>ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift Für Angewandte Mathematik Und Mechanik</i>, <i>97(4)</i>, 433–457. <a href=\"https://doi.org/10.1002/zamm.201600062\">https://doi.org/10.1002/zamm.201600062</a>","ama":"Mergel JC, Sauer RA, Ober-Blöbaum S. C1-continuous space-time discretization based on Hamilton’s law of varying action. <i>ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik</i>. 2017;97(4):433-457. doi:<a href=\"https://doi.org/10.1002/zamm.201600062\">10.1002/zamm.201600062</a>","chicago":"Mergel, J.C., R.A. Sauer, and Sina Ober-Blöbaum. “C1-Continuous Space-Time Discretization Based on Hamilton’s Law of Varying Action.” <i>ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift Für Angewandte Mathematik Und Mechanik</i> 97(4) (2017): 433–57. <a href=\"https://doi.org/10.1002/zamm.201600062\">https://doi.org/10.1002/zamm.201600062</a>.","ieee":"J. C. Mergel, R. A. Sauer, and S. Ober-Blöbaum, “C1-continuous space-time discretization based on Hamilton’s law of varying action,” <i>ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik</i>, vol. 97(4), pp. 433–457, 2017, doi: <a href=\"https://doi.org/10.1002/zamm.201600062\">10.1002/zamm.201600062</a>."},"page":"433-457","publication_identifier":{"issn":["1521-4001"]}},{"publication_identifier":{"issn":["0044-2267","1521-4001"]},"publication_status":"published","page":"605-622","intvolume":"        90","citation":{"apa":"Ostwald, R., Bartel, T., &#38; Menzel, A. (2010). A computational micro‐sphere model applied to the simulation of phase‐transformations. <i>ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift Für Angewandte Mathematik Und Mechanik</i>, <i>90</i>(7–8), 605–622. <a href=\"https://doi.org/10.1002/zamm.200900390\">https://doi.org/10.1002/zamm.200900390</a>","bibtex":"@article{Ostwald_Bartel_Menzel_2010, title={A computational micro‐sphere model applied to the simulation of phase‐transformations}, volume={90}, DOI={<a href=\"https://doi.org/10.1002/zamm.200900390\">10.1002/zamm.200900390</a>}, number={7–8}, journal={ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik}, publisher={Wiley}, author={Ostwald, Richard and Bartel, T. and Menzel, A.}, year={2010}, pages={605–622} }","mla":"Ostwald, Richard, et al. “A Computational Micro‐sphere Model Applied to the Simulation of Phase‐transformations.” <i>ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift Für Angewandte Mathematik Und Mechanik</i>, vol. 90, no. 7–8, Wiley, 2010, pp. 605–22, doi:<a href=\"https://doi.org/10.1002/zamm.200900390\">10.1002/zamm.200900390</a>.","short":"R. Ostwald, T. Bartel, A. Menzel, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift Für Angewandte Mathematik Und Mechanik 90 (2010) 605–622.","chicago":"Ostwald, Richard, T. Bartel, and A. Menzel. “A Computational Micro‐sphere Model Applied to the Simulation of Phase‐transformations.” <i>ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift Für Angewandte Mathematik Und Mechanik</i> 90, no. 7–8 (2010): 605–22. <a href=\"https://doi.org/10.1002/zamm.200900390\">https://doi.org/10.1002/zamm.200900390</a>.","ieee":"R. Ostwald, T. Bartel, and A. Menzel, “A computational micro‐sphere model applied to the simulation of phase‐transformations,” <i>ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik</i>, vol. 90, no. 7–8, pp. 605–622, 2010, doi: <a href=\"https://doi.org/10.1002/zamm.200900390\">10.1002/zamm.200900390</a>.","ama":"Ostwald R, Bartel T, Menzel A. A computational micro‐sphere model applied to the simulation of phase‐transformations. <i>ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik</i>. 2010;90(7-8):605-622. doi:<a href=\"https://doi.org/10.1002/zamm.200900390\">10.1002/zamm.200900390</a>"},"volume":90,"author":[{"full_name":"Ostwald, Richard","id":"106876","orcid":"0000-0003-2147-8444","last_name":"Ostwald","first_name":"Richard"},{"last_name":"Bartel","full_name":"Bartel, T.","first_name":"T."},{"first_name":"A.","full_name":"Menzel, A.","last_name":"Menzel"}],"date_updated":"2025-12-03T13:22:16Z","doi":"10.1002/zamm.200900390","type":"journal_article","status":"public","department":[{"_id":"952"},{"_id":"321"}],"user_id":"85414","_id":"62791","issue":"7-8","quality_controlled":"1","year":"2010","date_created":"2025-12-03T13:21:33Z","publisher":"Wiley","title":"A computational micro‐sphere model applied to the simulation of phase‐transformations","publication":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>We present an efficient model for the simulation of polycrystalline materials undergoing solid to solid phase transformations. As a basis, we use a one‐dimensional, thermodynamically consistent phase‐transformation model. This model is embedded into a micro‐sphere formulation in order to simulate three‐dimensional boundary value problems. To solve the underlying evolution equations, we use a newly developed explicit integration scheme which could be proved to be unconditionally A‐stable. Besides the investigation of homogeneous deformation states, representative finite element examples are discussed. It is shown that the model nicely reflects the overall behaviour.</jats:p>"}],"language":[{"iso":"eng"}]}]