---
_id: '20061'
author:
- first_name: J.C.
  full_name: Mergel, J.C.
  last_name: Mergel
- first_name: R.A.
  full_name: Sauer, R.A.
  last_name: Sauer
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  id: '16494'
  last_name: Ober-Blöbaum
citation:
  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>
  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>
  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} }'
  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>.'
  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.
date_created: 2020-10-15T15:56:20Z
date_updated: 2022-01-21T10:22:38Z
doi: 10.1002/zamm.201600062
language:
- iso: eng
page: 433-457
publication: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für
  Angewandte Mathematik und Mechanik
publication_identifier:
  issn:
  - 1521-4001
status: public
title: C1-continuous space-time discretization based on Hamilton's law of varying
  action
type: journal_article
user_id: '15694'
volume: 97(4)
year: '2017'
...
---
_id: '62791'
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>
author:
- first_name: Richard
  full_name: Ostwald, Richard
  id: '106876'
  last_name: Ostwald
  orcid: 0000-0003-2147-8444
- first_name: T.
  full_name: Bartel, T.
  last_name: Bartel
- first_name: A.
  full_name: Menzel, A.
  last_name: Menzel
citation:
  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>
  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} }'
  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>.'
  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.
date_created: 2025-12-03T13:21:33Z
date_updated: 2025-12-03T13:22:16Z
department:
- _id: '952'
- _id: '321'
doi: 10.1002/zamm.200900390
intvolume: '        90'
issue: 7-8
language:
- iso: eng
page: 605-622
publication: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für
  Angewandte Mathematik und Mechanik
publication_identifier:
  issn:
  - 0044-2267
  - 1521-4001
publication_status: published
publisher: Wiley
quality_controlled: '1'
status: public
title: A computational micro‐sphere model applied to the simulation of phase‐transformations
type: journal_article
user_id: '85414'
volume: 90
year: '2010'
...