---
_id: '42165'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>Composite materials, such as fiber
    reinforced polymers, become increasingly important due to their excellent mechanical
    and lightweight properties. In this respect, this paper reports the characterization
    of a unidirectional carbon fiber reinforced polymer composite material. Particularly,
    the mechanical behavior of the overall composite and of the individual constituents
    of the composite is investigated. To this end, tensile and shear tests are performed
    for the composite. As a result, statistics for five transversely isotropic material
    parameters can be established for the composite. For the description of the mechanical
    properties of the constituents, tensile tests for the carbon fiber as well as
    for the polymer matrix are carried out. In addition, the volume fraction of fibers
    in the matrix is determined experimentally using an ashing technique and Archimedes’
    principle. For the Young’s modulus of the fiber, the Young’s modulus and transverse
    contraction of the matrix, as well as the volume fraction of the constituents,
    statistics can be concluded. The resulting mechanical properties on both scales
    are useful for the application and validation of different material models and
    homogenization methods. Finally, in order to validate the obtained properties
    in the future, inhomogeneous tests were performed, once a flat plate with a hole
    and a flat plate with semicircular notches.</jats:p>
author:
- first_name: Eduard
  full_name: Penner, Eduard
  last_name: Penner
- first_name: Ismail
  full_name: Caylak, Ismail
  id: '75'
  last_name: Caylak
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
citation:
  ama: Penner E, Caylak I, Mahnken R. Experimental Investigations of Carbon Fiber
    Reinforced Polymer Composites and Their Constituents to Determine Their Elastic
    Material Properties and Complementary Inhomogeneous Experiments with Local Strain
    Considerations. <i>Fibers and Polymers</i>. Published online 2023. doi:<a href="https://doi.org/10.1007/s12221-023-00122-x">10.1007/s12221-023-00122-x</a>
  apa: Penner, E., Caylak, I., &#38; Mahnken, R. (2023). Experimental Investigations
    of Carbon Fiber Reinforced Polymer Composites and Their Constituents to Determine
    Their Elastic Material Properties and Complementary Inhomogeneous Experiments
    with Local Strain Considerations. <i>Fibers and Polymers</i>. <a href="https://doi.org/10.1007/s12221-023-00122-x">https://doi.org/10.1007/s12221-023-00122-x</a>
  bibtex: '@article{Penner_Caylak_Mahnken_2023, title={Experimental Investigations
    of Carbon Fiber Reinforced Polymer Composites and Their Constituents to Determine
    Their Elastic Material Properties and Complementary Inhomogeneous Experiments
    with Local Strain Considerations}, DOI={<a href="https://doi.org/10.1007/s12221-023-00122-x">10.1007/s12221-023-00122-x</a>},
    journal={Fibers and Polymers}, publisher={Springer Science and Business Media
    LLC}, author={Penner, Eduard and Caylak, Ismail and Mahnken, Rolf}, year={2023}
    }'
  chicago: Penner, Eduard, Ismail Caylak, and Rolf Mahnken. “Experimental Investigations
    of Carbon Fiber Reinforced Polymer Composites and Their Constituents to Determine
    Their Elastic Material Properties and Complementary Inhomogeneous Experiments
    with Local Strain Considerations.” <i>Fibers and Polymers</i>, 2023. <a href="https://doi.org/10.1007/s12221-023-00122-x">https://doi.org/10.1007/s12221-023-00122-x</a>.
  ieee: 'E. Penner, I. Caylak, and R. Mahnken, “Experimental Investigations of Carbon
    Fiber Reinforced Polymer Composites and Their Constituents to Determine Their
    Elastic Material Properties and Complementary Inhomogeneous Experiments with Local
    Strain Considerations,” <i>Fibers and Polymers</i>, 2023, doi: <a href="https://doi.org/10.1007/s12221-023-00122-x">10.1007/s12221-023-00122-x</a>.'
  mla: Penner, Eduard, et al. “Experimental Investigations of Carbon Fiber Reinforced
    Polymer Composites and Their Constituents to Determine Their Elastic Material
    Properties and Complementary Inhomogeneous Experiments with Local Strain Considerations.”
    <i>Fibers and Polymers</i>, Springer Science and Business Media LLC, 2023, doi:<a
    href="https://doi.org/10.1007/s12221-023-00122-x">10.1007/s12221-023-00122-x</a>.
  short: E. Penner, I. Caylak, R. Mahnken, Fibers and Polymers (2023).
date_created: 2023-02-16T12:37:11Z
date_updated: 2023-03-24T08:42:33Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.1007/s12221-023-00122-x
keyword:
- Polymers and Plastics
- General Chemical Engineering
- General Chemistry
language:
- iso: eng
publication: Fibers and Polymers
publication_identifier:
  issn:
  - 1229-9197
  - 1875-0052
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Experimental Investigations of Carbon Fiber Reinforced Polymer Composites and
  Their Constituents to Determine Their Elastic Material Properties and Complementary
  Inhomogeneous Experiments with Local Strain Considerations
type: journal_article
user_id: '335'
year: '2023'
...
---
_id: '43095'
article_number: '116911'
author:
- first_name: Peter
  full_name: Lenz, Peter
  last_name: Lenz
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
citation:
  ama: Lenz P, Mahnken R. Non-local integral-type damage combined to mean-field homogenization
    methods for composites and its parallel implementation. <i>Composite Structures</i>.
    Published online 2023. doi:<a href="https://doi.org/10.1016/j.compstruct.2023.116911">10.1016/j.compstruct.2023.116911</a>
  apa: Lenz, P., &#38; Mahnken, R. (2023). Non-local integral-type damage combined
    to mean-field homogenization methods for composites and its parallel implementation.
    <i>Composite Structures</i>, Article 116911. <a href="https://doi.org/10.1016/j.compstruct.2023.116911">https://doi.org/10.1016/j.compstruct.2023.116911</a>
  bibtex: '@article{Lenz_Mahnken_2023, title={Non-local integral-type damage combined
    to mean-field homogenization methods for composites and its parallel implementation},
    DOI={<a href="https://doi.org/10.1016/j.compstruct.2023.116911">10.1016/j.compstruct.2023.116911</a>},
    number={116911}, journal={Composite Structures}, publisher={Elsevier BV}, author={Lenz,
    Peter and Mahnken, Rolf}, year={2023} }'
  chicago: Lenz, Peter, and Rolf Mahnken. “Non-Local Integral-Type Damage Combined
    to Mean-Field Homogenization Methods for Composites and Its Parallel Implementation.”
    <i>Composite Structures</i>, 2023. <a href="https://doi.org/10.1016/j.compstruct.2023.116911">https://doi.org/10.1016/j.compstruct.2023.116911</a>.
  ieee: 'P. Lenz and R. Mahnken, “Non-local integral-type damage combined to mean-field
    homogenization methods for composites and its parallel implementation,” <i>Composite
    Structures</i>, Art. no. 116911, 2023, doi: <a href="https://doi.org/10.1016/j.compstruct.2023.116911">10.1016/j.compstruct.2023.116911</a>.'
  mla: Lenz, Peter, and Rolf Mahnken. “Non-Local Integral-Type Damage Combined to
    Mean-Field Homogenization Methods for Composites and Its Parallel Implementation.”
    <i>Composite Structures</i>, 116911, Elsevier BV, 2023, doi:<a href="https://doi.org/10.1016/j.compstruct.2023.116911">10.1016/j.compstruct.2023.116911</a>.
  short: P. Lenz, R. Mahnken, Composite Structures (2023).
date_created: 2023-03-24T08:35:59Z
date_updated: 2023-03-24T08:45:42Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.1016/j.compstruct.2023.116911
keyword:
- Civil and Structural Engineering
- Ceramics and Composites
language:
- iso: eng
publication: Composite Structures
publication_identifier:
  issn:
  - 0263-8223
publication_status: published
publisher: Elsevier BV
status: public
title: Non-local integral-type damage combined to mean-field homogenization methods
  for composites and its parallel implementation
type: journal_article
user_id: '335'
year: '2023'
...
---
_id: '44888'
author:
- first_name: Peter
  full_name: Lenz, Peter
  last_name: Lenz
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
citation:
  ama: Lenz P, Mahnken R. Thermo‐chemo‐mechanical modelling of a curing process combined
    with mean‐field homogenization methods at large strains. <i>PAMM</i>. 2023;22(1).
    doi:<a href="https://doi.org/10.1002/pamm.202200214">10.1002/pamm.202200214</a>
  apa: Lenz, P., &#38; Mahnken, R. (2023). Thermo‐chemo‐mechanical modelling of a
    curing process combined with mean‐field homogenization methods at large strains.
    <i>PAMM</i>, <i>22</i>(1). <a href="https://doi.org/10.1002/pamm.202200214">https://doi.org/10.1002/pamm.202200214</a>
  bibtex: '@article{Lenz_Mahnken_2023, title={Thermo‐chemo‐mechanical modelling of
    a curing process combined with mean‐field homogenization methods at large strains},
    volume={22}, DOI={<a href="https://doi.org/10.1002/pamm.202200214">10.1002/pamm.202200214</a>},
    number={1}, journal={PAMM}, publisher={Wiley}, author={Lenz, Peter and Mahnken,
    Rolf}, year={2023} }'
  chicago: Lenz, Peter, and Rolf Mahnken. “Thermo‐chemo‐mechanical Modelling of a
    Curing Process Combined with Mean‐field Homogenization Methods at Large Strains.”
    <i>PAMM</i> 22, no. 1 (2023). <a href="https://doi.org/10.1002/pamm.202200214">https://doi.org/10.1002/pamm.202200214</a>.
  ieee: 'P. Lenz and R. Mahnken, “Thermo‐chemo‐mechanical modelling of a curing process
    combined with mean‐field homogenization methods at large strains,” <i>PAMM</i>,
    vol. 22, no. 1, 2023, doi: <a href="https://doi.org/10.1002/pamm.202200214">10.1002/pamm.202200214</a>.'
  mla: Lenz, Peter, and Rolf Mahnken. “Thermo‐chemo‐mechanical Modelling of a Curing
    Process Combined with Mean‐field Homogenization Methods at Large Strains.” <i>PAMM</i>,
    vol. 22, no. 1, Wiley, 2023, doi:<a href="https://doi.org/10.1002/pamm.202200214">10.1002/pamm.202200214</a>.
  short: P. Lenz, R. Mahnken, PAMM 22 (2023).
date_created: 2023-05-16T12:15:44Z
date_updated: 2023-05-16T12:17:50Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.1002/pamm.202200214
intvolume: '        22'
issue: '1'
keyword:
- Electrical and Electronic Engineering
- Atomic and Molecular Physics
- and Optics
language:
- iso: eng
publication: PAMM
publication_identifier:
  issn:
  - 1617-7061
  - 1617-7061
publication_status: published
publisher: Wiley
quality_controlled: '1'
status: public
title: Thermo‐chemo‐mechanical modelling of a curing process combined with mean‐field
  homogenization methods at large strains
type: journal_article
user_id: '335'
volume: 22
year: '2023'
...
---
_id: '44887'
author:
- first_name: Chun
  full_name: Cheng, Chun
  last_name: Cheng
- first_name: Chunlei
  full_name: Song, Chunlei
  last_name: Song
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
- first_name: Zhipeng
  full_name: Yuan, Zhipeng
  last_name: Yuan
- first_name: Liang
  full_name: Yu, Liang
  last_name: Yu
- first_name: Xiaozhe
  full_name: Ju, Xiaozhe
  last_name: Ju
citation:
  ama: Cheng C, Song C, Mahnken R, Yuan Z, Yu L, Ju X. A Non-Linear Mean-Field Debonding
    Model at Large Strains for the Analysis of Fibre Kinking in Ud Composites. Published
    online 2023.
  apa: Cheng, C., Song, C., Mahnken, R., Yuan, Z., Yu, L., &#38; Ju, X. (2023). <i>A
    Non-Linear Mean-Field Debonding Model at Large Strains for the Analysis of Fibre
    Kinking in Ud Composites</i>. Elsevier BV.
  bibtex: '@article{Cheng_Song_Mahnken_Yuan_Yu_Ju_2023, title={A Non-Linear Mean-Field
    Debonding Model at Large Strains for the Analysis of Fibre Kinking in Ud Composites},
    publisher={Elsevier BV}, author={Cheng, Chun and Song, Chunlei and Mahnken, Rolf
    and Yuan, Zhipeng and Yu, Liang and Ju, Xiaozhe}, year={2023} }'
  chicago: Cheng, Chun, Chunlei Song, Rolf Mahnken, Zhipeng Yuan, Liang Yu, and Xiaozhe
    Ju. “A Non-Linear Mean-Field Debonding Model at Large Strains for the Analysis
    of Fibre Kinking in Ud Composites.” Elsevier BV, 2023.
  ieee: C. Cheng, C. Song, R. Mahnken, Z. Yuan, L. Yu, and X. Ju, “A Non-Linear Mean-Field
    Debonding Model at Large Strains for the Analysis of Fibre Kinking in Ud Composites.”
    Elsevier BV, 2023.
  mla: Cheng, Chun, et al. <i>A Non-Linear Mean-Field Debonding Model at Large Strains
    for the Analysis of Fibre Kinking in Ud Composites</i>. Elsevier BV, 2023.
  short: C. Cheng, C. Song, R. Mahnken, Z. Yuan, L. Yu, X. Ju, (2023).
date_created: 2023-05-16T12:10:06Z
date_updated: 2023-05-16T12:17:43Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
language:
- iso: eng
publication_status: published
publisher: Elsevier BV
status: public
title: A Non-Linear Mean-Field Debonding Model at Large Strains for the Analysis of
  Fibre Kinking in Ud Composites
type: preprint
user_id: '335'
year: '2023'
...
---
_id: '44891'
author:
- first_name: Hendrik
  full_name: Westermann, Hendrik
  id: '60816'
  last_name: Westermann
  orcid: 0000-0002-5034-9708
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
citation:
  ama: Westermann H, Mahnken R. A thermodynamic framework for the phase‐field approach
    considering carbide precipitation during phase transformations. <i>PAMM</i>. 2023;22(1).
    doi:<a href="https://doi.org/10.1002/pamm.202200080">10.1002/pamm.202200080</a>
  apa: Westermann, H., &#38; Mahnken, R. (2023). A thermodynamic framework for the
    phase‐field approach considering carbide precipitation during phase transformations.
    <i>PAMM</i>, <i>22</i>(1). <a href="https://doi.org/10.1002/pamm.202200080">https://doi.org/10.1002/pamm.202200080</a>
  bibtex: '@article{Westermann_Mahnken_2023, title={A thermodynamic framework for
    the phase‐field approach considering carbide precipitation during phase transformations},
    volume={22}, DOI={<a href="https://doi.org/10.1002/pamm.202200080">10.1002/pamm.202200080</a>},
    number={1}, journal={PAMM}, publisher={Wiley}, author={Westermann, Hendrik and
    Mahnken, Rolf}, year={2023} }'
  chicago: Westermann, Hendrik, and Rolf Mahnken. “A Thermodynamic Framework for the
    Phase‐field Approach Considering Carbide Precipitation during Phase Transformations.”
    <i>PAMM</i> 22, no. 1 (2023). <a href="https://doi.org/10.1002/pamm.202200080">https://doi.org/10.1002/pamm.202200080</a>.
  ieee: 'H. Westermann and R. Mahnken, “A thermodynamic framework for the phase‐field
    approach considering carbide precipitation during phase transformations,” <i>PAMM</i>,
    vol. 22, no. 1, 2023, doi: <a href="https://doi.org/10.1002/pamm.202200080">10.1002/pamm.202200080</a>.'
  mla: Westermann, Hendrik, and Rolf Mahnken. “A Thermodynamic Framework for the Phase‐field
    Approach Considering Carbide Precipitation during Phase Transformations.” <i>PAMM</i>,
    vol. 22, no. 1, Wiley, 2023, doi:<a href="https://doi.org/10.1002/pamm.202200080">10.1002/pamm.202200080</a>.
  short: H. Westermann, R. Mahnken, PAMM 22 (2023).
date_created: 2023-05-16T12:20:19Z
date_updated: 2023-05-16T12:21:15Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.1002/pamm.202200080
intvolume: '        22'
issue: '1'
keyword:
- Electrical and Electronic Engineering
- Atomic and Molecular Physics
- and Optics
language:
- iso: eng
publication: PAMM
publication_identifier:
  issn:
  - 1617-7061
  - 1617-7061
publication_status: published
publisher: Wiley
quality_controlled: '1'
status: public
title: A thermodynamic framework for the phase‐field approach considering carbide
  precipitation during phase transformations
type: journal_article
user_id: '335'
volume: 22
year: '2023'
...
---
_id: '44892'
author:
- first_name: Ayoub
  full_name: Hamdoun, Ayoub
  last_name: Hamdoun
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
citation:
  ama: Hamdoun A, Mahnken R. A finite strain gradient theory for viscoplasticity by
    means of micromorphic regularization. <i>PAMM</i>. 2023;22(1). doi:<a href="https://doi.org/10.1002/pamm.202200074">10.1002/pamm.202200074</a>
  apa: Hamdoun, A., &#38; Mahnken, R. (2023). A finite strain gradient theory for
    viscoplasticity by means of micromorphic regularization. <i>PAMM</i>, <i>22</i>(1).
    <a href="https://doi.org/10.1002/pamm.202200074">https://doi.org/10.1002/pamm.202200074</a>
  bibtex: '@article{Hamdoun_Mahnken_2023, title={A finite strain gradient theory for
    viscoplasticity by means of micromorphic regularization}, volume={22}, DOI={<a
    href="https://doi.org/10.1002/pamm.202200074">10.1002/pamm.202200074</a>}, number={1},
    journal={PAMM}, publisher={Wiley}, author={Hamdoun, Ayoub and Mahnken, Rolf},
    year={2023} }'
  chicago: Hamdoun, Ayoub, and Rolf Mahnken. “A Finite Strain Gradient Theory for
    Viscoplasticity by Means of Micromorphic Regularization.” <i>PAMM</i> 22, no.
    1 (2023). <a href="https://doi.org/10.1002/pamm.202200074">https://doi.org/10.1002/pamm.202200074</a>.
  ieee: 'A. Hamdoun and R. Mahnken, “A finite strain gradient theory for viscoplasticity
    by means of micromorphic regularization,” <i>PAMM</i>, vol. 22, no. 1, 2023, doi:
    <a href="https://doi.org/10.1002/pamm.202200074">10.1002/pamm.202200074</a>.'
  mla: Hamdoun, Ayoub, and Rolf Mahnken. “A Finite Strain Gradient Theory for Viscoplasticity
    by Means of Micromorphic Regularization.” <i>PAMM</i>, vol. 22, no. 1, Wiley,
    2023, doi:<a href="https://doi.org/10.1002/pamm.202200074">10.1002/pamm.202200074</a>.
  short: A. Hamdoun, R. Mahnken, PAMM 22 (2023).
date_created: 2023-05-16T12:21:32Z
date_updated: 2023-05-16T12:23:15Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.1002/pamm.202200074
intvolume: '        22'
issue: '1'
keyword:
- Electrical and Electronic Engineering
- Atomic and Molecular Physics
- and Optics
language:
- iso: eng
publication: PAMM
publication_identifier:
  issn:
  - 1617-7061
  - 1617-7061
publication_status: published
publisher: Wiley
quality_controlled: '1'
status: public
title: A finite strain gradient theory for viscoplasticity by means of micromorphic
  regularization
type: journal_article
user_id: '335'
volume: 22
year: '2023'
...
---
_id: '44890'
author:
- first_name: Arnold
  full_name: Tchomgue Simeu, Arnold
  id: '83075'
  last_name: Tchomgue Simeu
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
citation:
  ama: Tchomgue Simeu A, Mahnken R. Goal‐oriented adaptivity based on a model hierarchy
    of mean‐field and full‐field homogenization methods in elasto‐plasticity. <i>PAMM</i>.
    2023;22(1). doi:<a href="https://doi.org/10.1002/pamm.202200053">10.1002/pamm.202200053</a>
  apa: Tchomgue Simeu, A., &#38; Mahnken, R. (2023). Goal‐oriented adaptivity based
    on a model hierarchy of mean‐field and full‐field homogenization methods in elasto‐plasticity.
    <i>PAMM</i>, <i>22</i>(1). <a href="https://doi.org/10.1002/pamm.202200053">https://doi.org/10.1002/pamm.202200053</a>
  bibtex: '@article{Tchomgue Simeu_Mahnken_2023, title={Goal‐oriented adaptivity based
    on a model hierarchy of mean‐field and full‐field homogenization methods in elasto‐plasticity},
    volume={22}, DOI={<a href="https://doi.org/10.1002/pamm.202200053">10.1002/pamm.202200053</a>},
    number={1}, journal={PAMM}, publisher={Wiley}, author={Tchomgue Simeu, Arnold
    and Mahnken, Rolf}, year={2023} }'
  chicago: Tchomgue Simeu, Arnold, and Rolf Mahnken. “Goal‐oriented Adaptivity Based
    on a Model Hierarchy of Mean‐field and Full‐field Homogenization Methods in Elasto‐plasticity.”
    <i>PAMM</i> 22, no. 1 (2023). <a href="https://doi.org/10.1002/pamm.202200053">https://doi.org/10.1002/pamm.202200053</a>.
  ieee: 'A. Tchomgue Simeu and R. Mahnken, “Goal‐oriented adaptivity based on a model
    hierarchy of mean‐field and full‐field homogenization methods in elasto‐plasticity,”
    <i>PAMM</i>, vol. 22, no. 1, 2023, doi: <a href="https://doi.org/10.1002/pamm.202200053">10.1002/pamm.202200053</a>.'
  mla: Tchomgue Simeu, Arnold, and Rolf Mahnken. “Goal‐oriented Adaptivity Based on
    a Model Hierarchy of Mean‐field and Full‐field Homogenization Methods in Elasto‐plasticity.”
    <i>PAMM</i>, vol. 22, no. 1, Wiley, 2023, doi:<a href="https://doi.org/10.1002/pamm.202200053">10.1002/pamm.202200053</a>.
  short: A. Tchomgue Simeu, R. Mahnken, PAMM 22 (2023).
date_created: 2023-05-16T12:18:15Z
date_updated: 2023-05-25T10:02:34Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.1002/pamm.202200053
intvolume: '        22'
issue: '1'
keyword:
- Electrical and Electronic Engineering
- Atomic and Molecular Physics
- and Optics
language:
- iso: eng
publication: PAMM
publication_identifier:
  issn:
  - 1617-7061
  - 1617-7061
publication_status: published
publisher: Wiley
quality_controlled: '1'
status: public
title: Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field
  homogenization methods in elasto‐plasticity
type: journal_article
user_id: '335'
volume: 22
year: '2023'
...
---
_id: '45757'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title><jats:p>Three prominent low order implicit
    time integration schemes are the first order implicit Euler-method, the second
    order trapezoidal rule and the second order Ellsiepen method. Its advantages are
    stability and comparatively low computational cost, however, they require the
    solution of a nonlinear system of equations. This paper presents a general approach
    for the construction of third order Runge–Kutta methods by embedding the above
    mentioned implicit schemes into the class of ELDIRK-methods. These will be defined
    to have an <jats:italic>Explicit Last</jats:italic> stage in the general Butcher
    array of <jats:italic>Diagonal Implicit Runge–Kutta</jats:italic> (DIRK) methods,
    with the consequence, that no additional system of equations must be solved. The
    main results—valid also for non-linear ordinary differential equations—are as
    follows: Two extra function calculations are required in order to embed the implicit
    Euler-method and one extra function calculation is required for the trapezoidal-rule
    and the Ellsiepen method, in order to obtain the third order properties, respectively.
    Two numerical examples are concerned with a parachute with viscous damping and
    a two-dimensional laser beam simulation. Here, we verify the higher order convergence
    behaviours of the proposed new ELDIRK-methods, and its successful performances
    for asymptotically exact global error estimation of so-called reversed embedded
    RK-method are shown.\r\n</jats:p>"
author:
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
citation:
  ama: Mahnken R. Derivation of third order Runge–Kutta methods (ELDIRK) by embedding
    of lower order implicit time integration schemes for local and global error estimation.
    <i>Computational Mechanics</i>. Published online 2023. doi:<a href="https://doi.org/10.1007/s00466-023-02347-2">10.1007/s00466-023-02347-2</a>
  apa: Mahnken, R. (2023). Derivation of third order Runge–Kutta methods (ELDIRK)
    by embedding of lower order implicit time integration schemes for local and global
    error estimation. <i>Computational Mechanics</i>. <a href="https://doi.org/10.1007/s00466-023-02347-2">https://doi.org/10.1007/s00466-023-02347-2</a>
  bibtex: '@article{Mahnken_2023, title={Derivation of third order Runge–Kutta methods
    (ELDIRK) by embedding of lower order implicit time integration schemes for local
    and global error estimation}, DOI={<a href="https://doi.org/10.1007/s00466-023-02347-2">10.1007/s00466-023-02347-2</a>},
    journal={Computational Mechanics}, publisher={Springer Science and Business Media
    LLC}, author={Mahnken, Rolf}, year={2023} }'
  chicago: Mahnken, Rolf. “Derivation of Third Order Runge–Kutta Methods (ELDIRK)
    by Embedding of Lower Order Implicit Time Integration Schemes for Local and Global
    Error Estimation.” <i>Computational Mechanics</i>, 2023. <a href="https://doi.org/10.1007/s00466-023-02347-2">https://doi.org/10.1007/s00466-023-02347-2</a>.
  ieee: 'R. Mahnken, “Derivation of third order Runge–Kutta methods (ELDIRK) by embedding
    of lower order implicit time integration schemes for local and global error estimation,”
    <i>Computational Mechanics</i>, 2023, doi: <a href="https://doi.org/10.1007/s00466-023-02347-2">10.1007/s00466-023-02347-2</a>.'
  mla: Mahnken, Rolf. “Derivation of Third Order Runge–Kutta Methods (ELDIRK) by Embedding
    of Lower Order Implicit Time Integration Schemes for Local and Global Error Estimation.”
    <i>Computational Mechanics</i>, Springer Science and Business Media LLC, 2023,
    doi:<a href="https://doi.org/10.1007/s00466-023-02347-2">10.1007/s00466-023-02347-2</a>.
  short: R. Mahnken, Computational Mechanics (2023).
date_created: 2023-06-23T06:47:36Z
date_updated: 2023-06-23T06:48:42Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.1007/s00466-023-02347-2
keyword:
- Applied Mathematics
- Computational Mathematics
- Computational Theory and Mathematics
- Mechanical Engineering
- Ocean Engineering
- Computational Mechanics
language:
- iso: eng
publication: Computational Mechanics
publication_identifier:
  issn:
  - 0178-7675
  - 1432-0924
publication_status: published
publisher: Springer Science and Business Media LLC
quality_controlled: '1'
status: public
title: Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower
  order implicit time integration schemes for local and global error estimation
type: journal_article
user_id: '335'
year: '2023'
...
---
_id: '46762'
author:
- first_name: Arnold
  full_name: Tchomgue Simeu, Arnold
  id: '83075'
  last_name: Tchomgue Simeu
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
citation:
  ama: 'Tchomgue Simeu A, Mahnken R. Mesh- and model adaptivity for elasto-plastic
    mean-field and full-field homogenization based on downwind  and upwind approximations.
    In: <i>XI International Conference on Adaptive Modeling and Simulation</i>. CIMNE;
    2023. doi:<a href="https://doi.org/10.23967/admos.2023.054">10.23967/admos.2023.054</a>'
  apa: Tchomgue Simeu, A., &#38; Mahnken, R. (2023). Mesh- and model adaptivity for
    elasto-plastic mean-field and full-field homogenization based on downwind  and
    upwind approximations. <i>XI International Conference on Adaptive Modeling and
    Simulation</i>. <a href="https://doi.org/10.23967/admos.2023.054">https://doi.org/10.23967/admos.2023.054</a>
  bibtex: '@inproceedings{Tchomgue Simeu_Mahnken_2023, title={Mesh- and model adaptivity
    for elasto-plastic mean-field and full-field homogenization based on downwind 
    and upwind approximations}, DOI={<a href="https://doi.org/10.23967/admos.2023.054">10.23967/admos.2023.054</a>},
    booktitle={XI International Conference on Adaptive Modeling and Simulation}, publisher={CIMNE},
    author={Tchomgue Simeu, Arnold and Mahnken, Rolf}, year={2023} }'
  chicago: Tchomgue Simeu, Arnold, and Rolf Mahnken. “Mesh- and Model Adaptivity for
    Elasto-Plastic Mean-Field and Full-Field Homogenization Based on Downwind  and
    Upwind Approximations.” In <i>XI International Conference on Adaptive Modeling
    and Simulation</i>. CIMNE, 2023. <a href="https://doi.org/10.23967/admos.2023.054">https://doi.org/10.23967/admos.2023.054</a>.
  ieee: 'A. Tchomgue Simeu and R. Mahnken, “Mesh- and model adaptivity for elasto-plastic
    mean-field and full-field homogenization based on downwind  and upwind approximations,”
    2023, doi: <a href="https://doi.org/10.23967/admos.2023.054">10.23967/admos.2023.054</a>.'
  mla: Tchomgue Simeu, Arnold, and Rolf Mahnken. “Mesh- and Model Adaptivity for Elasto-Plastic
    Mean-Field and Full-Field Homogenization Based on Downwind  and Upwind Approximations.”
    <i>XI International Conference on Adaptive Modeling and Simulation</i>, CIMNE,
    2023, doi:<a href="https://doi.org/10.23967/admos.2023.054">10.23967/admos.2023.054</a>.
  short: 'A. Tchomgue Simeu, R. Mahnken, in: XI International Conference on Adaptive
    Modeling and Simulation, CIMNE, 2023.'
date_created: 2023-09-01T07:52:20Z
date_updated: 2023-09-01T07:54:31Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.23967/admos.2023.054
language:
- iso: eng
publication: XI International Conference on Adaptive Modeling and Simulation
publication_status: published
publisher: CIMNE
quality_controlled: '1'
status: public
title: Mesh- and model adaptivity for elasto-plastic mean-field and full-field homogenization
  based on downwind  and upwind approximations
type: conference
user_id: '335'
year: '2023'
...
---
_id: '31185'
article_number: '115699'
author:
- first_name: Xiaozhe
  full_name: Ju, Xiaozhe
  last_name: Ju
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
- first_name: Yangjian
  full_name: Xu, Yangjian
  last_name: Xu
- first_name: Lihua
  full_name: Liang, Lihua
  last_name: Liang
- first_name: Chun
  full_name: Cheng, Chun
  last_name: Cheng
- first_name: Wangmin
  full_name: Zhou, Wangmin
  last_name: Zhou
citation:
  ama: Ju X, Mahnken R, Xu Y, Liang L, Cheng C, Zhou W. Multiscale analysis of composite
    structures with goal-oriented mesh adaptivity and reduced order homogenization.
    <i>Composite Structures</i>. Published online 2022. doi:<a href="https://doi.org/10.1016/j.compstruct.2022.115699">10.1016/j.compstruct.2022.115699</a>
  apa: Ju, X., Mahnken, R., Xu, Y., Liang, L., Cheng, C., &#38; Zhou, W. (2022). Multiscale
    analysis of composite structures with goal-oriented mesh adaptivity and reduced
    order homogenization. <i>Composite Structures</i>, Article 115699. <a href="https://doi.org/10.1016/j.compstruct.2022.115699">https://doi.org/10.1016/j.compstruct.2022.115699</a>
  bibtex: '@article{Ju_Mahnken_Xu_Liang_Cheng_Zhou_2022, title={Multiscale analysis
    of composite structures with goal-oriented mesh adaptivity and reduced order homogenization},
    DOI={<a href="https://doi.org/10.1016/j.compstruct.2022.115699">10.1016/j.compstruct.2022.115699</a>},
    number={115699}, journal={Composite Structures}, publisher={Elsevier BV}, author={Ju,
    Xiaozhe and Mahnken, Rolf and Xu, Yangjian and Liang, Lihua and Cheng, Chun and
    Zhou, Wangmin}, year={2022} }'
  chicago: Ju, Xiaozhe, Rolf Mahnken, Yangjian Xu, Lihua Liang, Chun Cheng, and Wangmin
    Zhou. “Multiscale Analysis of Composite Structures with Goal-Oriented Mesh Adaptivity
    and Reduced Order Homogenization.” <i>Composite Structures</i>, 2022. <a href="https://doi.org/10.1016/j.compstruct.2022.115699">https://doi.org/10.1016/j.compstruct.2022.115699</a>.
  ieee: 'X. Ju, R. Mahnken, Y. Xu, L. Liang, C. Cheng, and W. Zhou, “Multiscale analysis
    of composite structures with goal-oriented mesh adaptivity and reduced order homogenization,”
    <i>Composite Structures</i>, Art. no. 115699, 2022, doi: <a href="https://doi.org/10.1016/j.compstruct.2022.115699">10.1016/j.compstruct.2022.115699</a>.'
  mla: Ju, Xiaozhe, et al. “Multiscale Analysis of Composite Structures with Goal-Oriented
    Mesh Adaptivity and Reduced Order Homogenization.” <i>Composite Structures</i>,
    115699, Elsevier BV, 2022, doi:<a href="https://doi.org/10.1016/j.compstruct.2022.115699">10.1016/j.compstruct.2022.115699</a>.
  short: X. Ju, R. Mahnken, Y. Xu, L. Liang, C. Cheng, W. Zhou, Composite Structures
    (2022).
date_created: 2022-05-10T11:18:45Z
date_updated: 2023-01-24T13:11:40Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.1016/j.compstruct.2022.115699
keyword:
- Civil and Structural Engineering
- Ceramics and Composites
language:
- iso: eng
publication: Composite Structures
publication_identifier:
  issn:
  - 0263-8223
publication_status: published
publisher: Elsevier BV
quality_controlled: '1'
status: public
title: Multiscale analysis of composite structures with goal-oriented mesh adaptivity
  and reduced order homogenization
type: journal_article
user_id: '335'
year: '2022'
...
---
_id: '30656'
abstract:
- lang: eng
  text: '<jats:title>Abstract</jats:title><jats:p>Optimized material parameters obtained
    from parameter identification for verification wrt a certain loading scenario
    are amenable to two deficiencies: Firstly, they may lack a general validity for
    different loading scenarios. Secondly, they may be prone to instability, such
    that a small perturbation of experimental data may ensue a large perturbation
    for the material parameters. This paper presents a framework for extension of
    hyperelastic models for rubber-like materials accounting for both deficiencies.
    To this end, an additive decomposition of the strain energy function is assumed
    into a sum of weighted strain mode related quantities. We propose a practical
    guide for model development accounting for the criteria of verification, validation
    and stability by means of the strain mode-dependent weighting functions and techniques
    of model reduction. The approach is successfully applied for 13 hyperelastic models
    with regard to the classical experimental data on vulcanized rubber published
    by Treloar (Trans Faraday Soc 40:59–70, 1944), showing both excellent fitting
    capabilties and stable material parameters.</jats:p>'
author:
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
citation:
  ama: Mahnken R. Strain mode-dependent weighting functions in hyperelasticity accounting
    for verification, validation, and stability of material parameters. <i>Archive
    of Applied Mechanics</i>. 2022;92(3):713-754. doi:<a href="https://doi.org/10.1007/s00419-021-02069-y">10.1007/s00419-021-02069-y</a>
  apa: Mahnken, R. (2022). Strain mode-dependent weighting functions in hyperelasticity
    accounting for verification, validation, and stability of material parameters.
    <i>Archive of Applied Mechanics</i>, <i>92</i>(3), 713–754. <a href="https://doi.org/10.1007/s00419-021-02069-y">https://doi.org/10.1007/s00419-021-02069-y</a>
  bibtex: '@article{Mahnken_2022, title={Strain mode-dependent weighting functions
    in hyperelasticity accounting for verification, validation, and stability of material
    parameters}, volume={92}, DOI={<a href="https://doi.org/10.1007/s00419-021-02069-y">10.1007/s00419-021-02069-y</a>},
    number={3}, journal={Archive of Applied Mechanics}, publisher={Springer Science
    and Business Media LLC}, author={Mahnken, Rolf}, year={2022}, pages={713–754}
    }'
  chicago: 'Mahnken, Rolf. “Strain Mode-Dependent Weighting Functions in Hyperelasticity
    Accounting for Verification, Validation, and Stability of Material Parameters.”
    <i>Archive of Applied Mechanics</i> 92, no. 3 (2022): 713–54. <a href="https://doi.org/10.1007/s00419-021-02069-y">https://doi.org/10.1007/s00419-021-02069-y</a>.'
  ieee: 'R. Mahnken, “Strain mode-dependent weighting functions in hyperelasticity
    accounting for verification, validation, and stability of material parameters,”
    <i>Archive of Applied Mechanics</i>, vol. 92, no. 3, pp. 713–754, 2022, doi: <a
    href="https://doi.org/10.1007/s00419-021-02069-y">10.1007/s00419-021-02069-y</a>.'
  mla: Mahnken, Rolf. “Strain Mode-Dependent Weighting Functions in Hyperelasticity
    Accounting for Verification, Validation, and Stability of Material Parameters.”
    <i>Archive of Applied Mechanics</i>, vol. 92, no. 3, Springer Science and Business
    Media LLC, 2022, pp. 713–54, doi:<a href="https://doi.org/10.1007/s00419-021-02069-y">10.1007/s00419-021-02069-y</a>.
  short: R. Mahnken, Archive of Applied Mechanics 92 (2022) 713–754.
date_created: 2022-03-28T13:24:07Z
date_updated: 2023-01-24T13:10:27Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.1007/s00419-021-02069-y
intvolume: '        92'
issue: '3'
keyword:
- Mechanical Engineering
language:
- iso: eng
page: 713-754
publication: Archive of Applied Mechanics
publication_identifier:
  issn:
  - 0939-1533
  - 1432-0681
publication_status: published
publisher: Springer Science and Business Media LLC
quality_controlled: '1'
status: public
title: Strain mode-dependent weighting functions in hyperelasticity accounting for
  verification, validation, and stability of material parameters
type: journal_article
user_id: '335'
volume: 92
year: '2022'
...
---
_id: '30655'
author:
- first_name: Xiaozhe
  full_name: Ju, Xiaozhe
  last_name: Ju
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
- first_name: Yangjian
  full_name: Xu, Yangjian
  last_name: Xu
- first_name: Lihua
  full_name: Liang, Lihua
  last_name: Liang
citation:
  ama: Ju X, Mahnken R, Xu Y, Liang L. Goal-oriented error estimation and h-adaptive
    finite elements for hyperelastic micromorphic continua. <i>Computational Mechanics</i>.
    2022;69(3):847-863. doi:<a href="https://doi.org/10.1007/s00466-021-02117-y">10.1007/s00466-021-02117-y</a>
  apa: Ju, X., Mahnken, R., Xu, Y., &#38; Liang, L. (2022). Goal-oriented error estimation
    and h-adaptive finite elements for hyperelastic micromorphic continua. <i>Computational
    Mechanics</i>, <i>69</i>(3), 847–863. <a href="https://doi.org/10.1007/s00466-021-02117-y">https://doi.org/10.1007/s00466-021-02117-y</a>
  bibtex: '@article{Ju_Mahnken_Xu_Liang_2022, title={Goal-oriented error estimation
    and h-adaptive finite elements for hyperelastic micromorphic continua}, volume={69},
    DOI={<a href="https://doi.org/10.1007/s00466-021-02117-y">10.1007/s00466-021-02117-y</a>},
    number={3}, journal={Computational Mechanics}, publisher={Springer Science and
    Business Media LLC}, author={Ju, Xiaozhe and Mahnken, Rolf and Xu, Yangjian and
    Liang, Lihua}, year={2022}, pages={847–863} }'
  chicago: 'Ju, Xiaozhe, Rolf Mahnken, Yangjian Xu, and Lihua Liang. “Goal-Oriented
    Error Estimation and h-Adaptive Finite Elements for Hyperelastic Micromorphic
    Continua.” <i>Computational Mechanics</i> 69, no. 3 (2022): 847–63. <a href="https://doi.org/10.1007/s00466-021-02117-y">https://doi.org/10.1007/s00466-021-02117-y</a>.'
  ieee: 'X. Ju, R. Mahnken, Y. Xu, and L. Liang, “Goal-oriented error estimation and
    h-adaptive finite elements for hyperelastic micromorphic continua,” <i>Computational
    Mechanics</i>, vol. 69, no. 3, pp. 847–863, 2022, doi: <a href="https://doi.org/10.1007/s00466-021-02117-y">10.1007/s00466-021-02117-y</a>.'
  mla: Ju, Xiaozhe, et al. “Goal-Oriented Error Estimation and h-Adaptive Finite Elements
    for Hyperelastic Micromorphic Continua.” <i>Computational Mechanics</i>, vol.
    69, no. 3, Springer Science and Business Media LLC, 2022, pp. 847–63, doi:<a href="https://doi.org/10.1007/s00466-021-02117-y">10.1007/s00466-021-02117-y</a>.
  short: X. Ju, R. Mahnken, Y. Xu, L. Liang, Computational Mechanics 69 (2022) 847–863.
date_created: 2022-03-28T13:23:17Z
date_updated: 2023-01-24T13:10:56Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.1007/s00466-021-02117-y
intvolume: '        69'
issue: '3'
keyword:
- Applied Mathematics
- Computational Mathematics
- Computational Theory and Mathematics
- Mechanical Engineering
- Ocean Engineering
- Computational Mechanics
language:
- iso: eng
page: 847-863
publication: Computational Mechanics
publication_identifier:
  issn:
  - 0178-7675
  - 1432-0924
publication_status: published
publisher: Springer Science and Business Media LLC
quality_controlled: '1'
status: public
title: Goal-oriented error estimation and h-adaptive finite elements for hyperelastic
  micromorphic continua
type: journal_article
user_id: '335'
volume: 69
year: '2022'
...
---
_id: '30657'
article_number: '114790'
author:
- first_name: Alexander
  full_name: Henkes, Alexander
  last_name: Henkes
- first_name: Henning
  full_name: Wessels, Henning
  last_name: Wessels
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
citation:
  ama: Henkes A, Wessels H, Mahnken R. Physics informed neural networks for continuum
    micromechanics. <i>Computer Methods in Applied Mechanics and Engineering</i>.
    2022;393. doi:<a href="https://doi.org/10.1016/j.cma.2022.114790">10.1016/j.cma.2022.114790</a>
  apa: Henkes, A., Wessels, H., &#38; Mahnken, R. (2022). Physics informed neural
    networks for continuum micromechanics. <i>Computer Methods in Applied Mechanics
    and Engineering</i>, <i>393</i>, Article 114790. <a href="https://doi.org/10.1016/j.cma.2022.114790">https://doi.org/10.1016/j.cma.2022.114790</a>
  bibtex: '@article{Henkes_Wessels_Mahnken_2022, title={Physics informed neural networks
    for continuum micromechanics}, volume={393}, DOI={<a href="https://doi.org/10.1016/j.cma.2022.114790">10.1016/j.cma.2022.114790</a>},
    number={114790}, journal={Computer Methods in Applied Mechanics and Engineering},
    publisher={Elsevier BV}, author={Henkes, Alexander and Wessels, Henning and Mahnken,
    Rolf}, year={2022} }'
  chicago: Henkes, Alexander, Henning Wessels, and Rolf Mahnken. “Physics Informed
    Neural Networks for Continuum Micromechanics.” <i>Computer Methods in Applied
    Mechanics and Engineering</i> 393 (2022). <a href="https://doi.org/10.1016/j.cma.2022.114790">https://doi.org/10.1016/j.cma.2022.114790</a>.
  ieee: 'A. Henkes, H. Wessels, and R. Mahnken, “Physics informed neural networks
    for continuum micromechanics,” <i>Computer Methods in Applied Mechanics and Engineering</i>,
    vol. 393, Art. no. 114790, 2022, doi: <a href="https://doi.org/10.1016/j.cma.2022.114790">10.1016/j.cma.2022.114790</a>.'
  mla: Henkes, Alexander, et al. “Physics Informed Neural Networks for Continuum Micromechanics.”
    <i>Computer Methods in Applied Mechanics and Engineering</i>, vol. 393, 114790,
    Elsevier BV, 2022, doi:<a href="https://doi.org/10.1016/j.cma.2022.114790">10.1016/j.cma.2022.114790</a>.
  short: A. Henkes, H. Wessels, R. Mahnken, Computer Methods in Applied Mechanics
    and Engineering 393 (2022).
date_created: 2022-03-28T13:24:32Z
date_updated: 2023-01-24T13:09:40Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.1016/j.cma.2022.114790
intvolume: '       393'
keyword:
- Computer Science Applications
- General Physics and Astronomy
- Mechanical Engineering
- Mechanics of Materials
- Computational Mechanics
language:
- iso: eng
publication: Computer Methods in Applied Mechanics and Engineering
publication_identifier:
  issn:
  - 0045-7825
publication_status: published
publisher: Elsevier BV
quality_controlled: '1'
status: public
title: Physics informed neural networks for continuum micromechanics
type: journal_article
user_id: '335'
volume: 393
year: '2022'
...
---
_id: '34074'
author:
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
- first_name: Jamil
  full_name: Mirzapour, Jamil
  last_name: Mirzapour
citation:
  ama: Mahnken R, Mirzapour J. A statistically based strain energy function for polymer
    chains in rubber elasticity. <i>Archive of Applied Mechanics</i>. 2022;92(11):3295-3323.
    doi:<a href="https://doi.org/10.1007/s00419-022-02237-8">10.1007/s00419-022-02237-8</a>
  apa: Mahnken, R., &#38; Mirzapour, J. (2022). A statistically based strain energy
    function for polymer chains in rubber elasticity. <i>Archive of Applied Mechanics</i>,
    <i>92</i>(11), 3295–3323. <a href="https://doi.org/10.1007/s00419-022-02237-8">https://doi.org/10.1007/s00419-022-02237-8</a>
  bibtex: '@article{Mahnken_Mirzapour_2022, title={A statistically based strain energy
    function for polymer chains in rubber elasticity}, volume={92}, DOI={<a href="https://doi.org/10.1007/s00419-022-02237-8">10.1007/s00419-022-02237-8</a>},
    number={11}, journal={Archive of Applied Mechanics}, publisher={Springer Science
    and Business Media LLC}, author={Mahnken, Rolf and Mirzapour, Jamil}, year={2022},
    pages={3295–3323} }'
  chicago: 'Mahnken, Rolf, and Jamil Mirzapour. “A Statistically Based Strain Energy
    Function for Polymer Chains in Rubber Elasticity.” <i>Archive of Applied Mechanics</i>
    92, no. 11 (2022): 3295–3323. <a href="https://doi.org/10.1007/s00419-022-02237-8">https://doi.org/10.1007/s00419-022-02237-8</a>.'
  ieee: 'R. Mahnken and J. Mirzapour, “A statistically based strain energy function
    for polymer chains in rubber elasticity,” <i>Archive of Applied Mechanics</i>,
    vol. 92, no. 11, pp. 3295–3323, 2022, doi: <a href="https://doi.org/10.1007/s00419-022-02237-8">10.1007/s00419-022-02237-8</a>.'
  mla: Mahnken, Rolf, and Jamil Mirzapour. “A Statistically Based Strain Energy Function
    for Polymer Chains in Rubber Elasticity.” <i>Archive of Applied Mechanics</i>,
    vol. 92, no. 11, Springer Science and Business Media LLC, 2022, pp. 3295–323,
    doi:<a href="https://doi.org/10.1007/s00419-022-02237-8">10.1007/s00419-022-02237-8</a>.
  short: R. Mahnken, J. Mirzapour, Archive of Applied Mechanics 92 (2022) 3295–3323.
date_created: 2022-11-14T12:51:05Z
date_updated: 2023-04-27T10:07:20Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.1007/s00419-022-02237-8
intvolume: '        92'
issue: '11'
keyword:
- Mechanical Engineering
language:
- iso: eng
page: 3295-3323
publication: Archive of Applied Mechanics
publication_identifier:
  issn:
  - 0939-1533
  - 1432-0681
publication_status: published
publisher: Springer Science and Business Media LLC
quality_controlled: '1'
status: public
title: A statistically based strain energy function for polymer chains in rubber elasticity
type: journal_article
user_id: '335'
volume: 92
year: '2022'
...
---
_id: '41485'
author:
- first_name: Robin
  full_name: Clemens, Robin
  last_name: Clemens
- first_name: Enrico
  full_name: Barth, Enrico
  last_name: Barth
- first_name: Eckart
  full_name: Uhlmann, Eckart
  last_name: Uhlmann
- first_name: Yingjie
  full_name: Zhan, Yingjie
  last_name: Zhan
- first_name: Ismail
  full_name: Caylak, Ismail
  id: '75'
  last_name: Caylak
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
citation:
  ama: Clemens R, Barth E, Uhlmann E, Zhan Y, Caylak I, Mahnken R. Effects on Process
    Forces of Individual Milling Tool Edges Depending on the Cutting Angle and Cutting
    Speed When Milling Cfrp. <i>SSRN Electronic Journal</i>. Published online 2022.
    doi:<a href="https://doi.org/10.2139/ssrn.4259246">10.2139/ssrn.4259246</a>
  apa: Clemens, R., Barth, E., Uhlmann, E., Zhan, Y., Caylak, I., &#38; Mahnken, R.
    (2022). Effects on Process Forces of Individual Milling Tool Edges Depending on
    the Cutting Angle and Cutting Speed When Milling Cfrp. <i>SSRN Electronic Journal</i>.
    <a href="https://doi.org/10.2139/ssrn.4259246">https://doi.org/10.2139/ssrn.4259246</a>
  bibtex: '@article{Clemens_Barth_Uhlmann_Zhan_Caylak_Mahnken_2022, title={Effects
    on Process Forces of Individual Milling Tool Edges Depending on the Cutting Angle
    and Cutting Speed When Milling Cfrp}, DOI={<a href="https://doi.org/10.2139/ssrn.4259246">10.2139/ssrn.4259246</a>},
    journal={SSRN Electronic Journal}, publisher={Elsevier BV}, author={Clemens, Robin
    and Barth, Enrico and Uhlmann, Eckart and Zhan, Yingjie and Caylak, Ismail and
    Mahnken, Rolf}, year={2022} }'
  chicago: Clemens, Robin, Enrico Barth, Eckart Uhlmann, Yingjie Zhan, Ismail Caylak,
    and Rolf Mahnken. “Effects on Process Forces of Individual Milling Tool Edges
    Depending on the Cutting Angle and Cutting Speed When Milling Cfrp.” <i>SSRN Electronic
    Journal</i>, 2022. <a href="https://doi.org/10.2139/ssrn.4259246">https://doi.org/10.2139/ssrn.4259246</a>.
  ieee: 'R. Clemens, E. Barth, E. Uhlmann, Y. Zhan, I. Caylak, and R. Mahnken, “Effects
    on Process Forces of Individual Milling Tool Edges Depending on the Cutting Angle
    and Cutting Speed When Milling Cfrp,” <i>SSRN Electronic Journal</i>, 2022, doi:
    <a href="https://doi.org/10.2139/ssrn.4259246">10.2139/ssrn.4259246</a>.'
  mla: Clemens, Robin, et al. “Effects on Process Forces of Individual Milling Tool
    Edges Depending on the Cutting Angle and Cutting Speed When Milling Cfrp.” <i>SSRN
    Electronic Journal</i>, Elsevier BV, 2022, doi:<a href="https://doi.org/10.2139/ssrn.4259246">10.2139/ssrn.4259246</a>.
  short: R. Clemens, E. Barth, E. Uhlmann, Y. Zhan, I. Caylak, R. Mahnken, SSRN Electronic
    Journal (2022).
date_created: 2023-02-02T12:49:43Z
date_updated: 2023-04-27T10:08:09Z
department:
- _id: '9'
- _id: '154'
doi: 10.2139/ssrn.4259246
keyword:
- General Earth and Planetary Sciences
- General Environmental Science
language:
- iso: eng
publication: SSRN Electronic Journal
publication_identifier:
  issn:
  - 1556-5068
publication_status: published
publisher: Elsevier BV
quality_controlled: '1'
status: public
title: Effects on Process Forces of Individual Milling Tool Edges Depending on the
  Cutting Angle and Cutting Speed When Milling Cfrp
type: journal_article
user_id: '335'
year: '2022'
...
---
_id: '32592'
article_number: '115199'
author:
- first_name: X.
  full_name: Ju, X.
  last_name: Ju
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
- first_name: Y.
  full_name: Xu, Y.
  last_name: Xu
- first_name: L.
  full_name: Liang, L.
  last_name: Liang
citation:
  ama: Ju X, Mahnken R, Xu Y, Liang L. NTFA-enabled goal-oriented adaptive space–time
    finite elements for micro-heterogeneous elastoplasticity problems. <i>Computer
    Methods in Applied Mechanics and Engineering</i>. 2022;398. doi:<a href="https://doi.org/10.1016/j.cma.2022.115199">10.1016/j.cma.2022.115199</a>
  apa: Ju, X., Mahnken, R., Xu, Y., &#38; Liang, L. (2022). NTFA-enabled goal-oriented
    adaptive space–time finite elements for micro-heterogeneous elastoplasticity problems.
    <i>Computer Methods in Applied Mechanics and Engineering</i>, <i>398</i>, Article
    115199. <a href="https://doi.org/10.1016/j.cma.2022.115199">https://doi.org/10.1016/j.cma.2022.115199</a>
  bibtex: '@article{Ju_Mahnken_Xu_Liang_2022, title={NTFA-enabled goal-oriented adaptive
    space–time finite elements for micro-heterogeneous elastoplasticity problems},
    volume={398}, DOI={<a href="https://doi.org/10.1016/j.cma.2022.115199">10.1016/j.cma.2022.115199</a>},
    number={115199}, journal={Computer Methods in Applied Mechanics and Engineering},
    publisher={Elsevier BV}, author={Ju, X. and Mahnken, Rolf and Xu, Y. and Liang,
    L.}, year={2022} }'
  chicago: Ju, X., Rolf Mahnken, Y. Xu, and L. Liang. “NTFA-Enabled Goal-Oriented
    Adaptive Space–Time Finite Elements for Micro-Heterogeneous Elastoplasticity Problems.”
    <i>Computer Methods in Applied Mechanics and Engineering</i> 398 (2022). <a href="https://doi.org/10.1016/j.cma.2022.115199">https://doi.org/10.1016/j.cma.2022.115199</a>.
  ieee: 'X. Ju, R. Mahnken, Y. Xu, and L. Liang, “NTFA-enabled goal-oriented adaptive
    space–time finite elements for micro-heterogeneous elastoplasticity problems,”
    <i>Computer Methods in Applied Mechanics and Engineering</i>, vol. 398, Art. no.
    115199, 2022, doi: <a href="https://doi.org/10.1016/j.cma.2022.115199">10.1016/j.cma.2022.115199</a>.'
  mla: Ju, X., et al. “NTFA-Enabled Goal-Oriented Adaptive Space–Time Finite Elements
    for Micro-Heterogeneous Elastoplasticity Problems.” <i>Computer Methods in Applied
    Mechanics and Engineering</i>, vol. 398, 115199, Elsevier BV, 2022, doi:<a href="https://doi.org/10.1016/j.cma.2022.115199">10.1016/j.cma.2022.115199</a>.
  short: X. Ju, R. Mahnken, Y. Xu, L. Liang, Computer Methods in Applied Mechanics
    and Engineering 398 (2022).
date_created: 2022-08-08T13:09:53Z
date_updated: 2023-04-27T10:04:01Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.1016/j.cma.2022.115199
intvolume: '       398'
keyword:
- Computer Science Applications
- General Physics and Astronomy
- Mechanical Engineering
- Mechanics of Materials
- Computational Mechanics
language:
- iso: eng
publication: Computer Methods in Applied Mechanics and Engineering
publication_identifier:
  issn:
  - 0045-7825
publication_status: published
publisher: Elsevier BV
quality_controlled: '1'
status: public
title: NTFA-enabled goal-oriented adaptive space–time finite elements for micro-heterogeneous
  elastoplasticity problems
type: journal_article
user_id: '335'
volume: 398
year: '2022'
...
---
_id: '34075'
author:
- first_name: Eduard
  full_name: Penner, Eduard
  last_name: Penner
- first_name: Ismail
  full_name: Caylak, Ismail
  id: '75'
  last_name: Caylak
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
citation:
  ama: Penner E, Caylak I, Mahnken R. A polymorphic uncertainty model for the curing
    process of transversely fiber-reinforced plastics. <i>Mathematics and Mechanics
    of Complex Systems</i>. 2022;10(1):21-50. doi:<a href="https://doi.org/10.2140/memocs.2022.10.21">10.2140/memocs.2022.10.21</a>
  apa: Penner, E., Caylak, I., &#38; Mahnken, R. (2022). A polymorphic uncertainty
    model for the curing process of transversely fiber-reinforced plastics. <i>Mathematics
    and Mechanics of Complex Systems</i>, <i>10</i>(1), 21–50. <a href="https://doi.org/10.2140/memocs.2022.10.21">https://doi.org/10.2140/memocs.2022.10.21</a>
  bibtex: '@article{Penner_Caylak_Mahnken_2022, title={A polymorphic uncertainty model
    for the curing process of transversely fiber-reinforced plastics}, volume={10},
    DOI={<a href="https://doi.org/10.2140/memocs.2022.10.21">10.2140/memocs.2022.10.21</a>},
    number={1}, journal={Mathematics and Mechanics of Complex Systems}, publisher={Mathematical
    Sciences Publishers}, author={Penner, Eduard and Caylak, Ismail and Mahnken, Rolf},
    year={2022}, pages={21–50} }'
  chicago: 'Penner, Eduard, Ismail Caylak, and Rolf Mahnken. “A Polymorphic Uncertainty
    Model for the Curing Process of Transversely Fiber-Reinforced Plastics.” <i>Mathematics
    and Mechanics of Complex Systems</i> 10, no. 1 (2022): 21–50. <a href="https://doi.org/10.2140/memocs.2022.10.21">https://doi.org/10.2140/memocs.2022.10.21</a>.'
  ieee: 'E. Penner, I. Caylak, and R. Mahnken, “A polymorphic uncertainty model for
    the curing process of transversely fiber-reinforced plastics,” <i>Mathematics
    and Mechanics of Complex Systems</i>, vol. 10, no. 1, pp. 21–50, 2022, doi: <a
    href="https://doi.org/10.2140/memocs.2022.10.21">10.2140/memocs.2022.10.21</a>.'
  mla: Penner, Eduard, et al. “A Polymorphic Uncertainty Model for the Curing Process
    of Transversely Fiber-Reinforced Plastics.” <i>Mathematics and Mechanics of Complex
    Systems</i>, vol. 10, no. 1, Mathematical Sciences Publishers, 2022, pp. 21–50,
    doi:<a href="https://doi.org/10.2140/memocs.2022.10.21">10.2140/memocs.2022.10.21</a>.
  short: E. Penner, I. Caylak, R. Mahnken, Mathematics and Mechanics of Complex Systems
    10 (2022) 21–50.
date_created: 2022-11-14T12:55:22Z
date_updated: 2023-04-27T10:04:44Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.2140/memocs.2022.10.21
intvolume: '        10'
issue: '1'
keyword:
- Computational Mathematics
- Numerical Analysis
- Civil and Structural Engineering
language:
- iso: eng
page: 21-50
publication: Mathematics and Mechanics of Complex Systems
publication_identifier:
  issn:
  - 2325-3444
  - 2326-7186
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
status: public
title: A polymorphic uncertainty model for the curing process of transversely fiber-reinforced
  plastics
type: journal_article
user_id: '335'
volume: 10
year: '2022'
...
---
_id: '33801'
article_number: '115553'
author:
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
citation:
  ama: Mahnken R. New low order Runge–Kutta schemes for asymptotically exact global
    error estimation of embedded methods without order reduction. <i>Computer Methods
    in Applied Mechanics and Engineering</i>. 2022;401. doi:<a href="https://doi.org/10.1016/j.cma.2022.115553">10.1016/j.cma.2022.115553</a>
  apa: Mahnken, R. (2022). New low order Runge–Kutta schemes for asymptotically exact
    global error estimation of embedded methods without order reduction. <i>Computer
    Methods in Applied Mechanics and Engineering</i>, <i>401</i>, Article 115553.
    <a href="https://doi.org/10.1016/j.cma.2022.115553">https://doi.org/10.1016/j.cma.2022.115553</a>
  bibtex: '@article{Mahnken_2022, title={New low order Runge–Kutta schemes for asymptotically
    exact global error estimation of embedded methods without order reduction}, volume={401},
    DOI={<a href="https://doi.org/10.1016/j.cma.2022.115553">10.1016/j.cma.2022.115553</a>},
    number={115553}, journal={Computer Methods in Applied Mechanics and Engineering},
    publisher={Elsevier BV}, author={Mahnken, Rolf}, year={2022} }'
  chicago: Mahnken, Rolf. “New Low Order Runge–Kutta Schemes for Asymptotically Exact
    Global Error Estimation of Embedded Methods without Order Reduction.” <i>Computer
    Methods in Applied Mechanics and Engineering</i> 401 (2022). <a href="https://doi.org/10.1016/j.cma.2022.115553">https://doi.org/10.1016/j.cma.2022.115553</a>.
  ieee: 'R. Mahnken, “New low order Runge–Kutta schemes for asymptotically exact global
    error estimation of embedded methods without order reduction,” <i>Computer Methods
    in Applied Mechanics and Engineering</i>, vol. 401, Art. no. 115553, 2022, doi:
    <a href="https://doi.org/10.1016/j.cma.2022.115553">10.1016/j.cma.2022.115553</a>.'
  mla: Mahnken, Rolf. “New Low Order Runge–Kutta Schemes for Asymptotically Exact
    Global Error Estimation of Embedded Methods without Order Reduction.” <i>Computer
    Methods in Applied Mechanics and Engineering</i>, vol. 401, 115553, Elsevier BV,
    2022, doi:<a href="https://doi.org/10.1016/j.cma.2022.115553">10.1016/j.cma.2022.115553</a>.
  short: R. Mahnken, Computer Methods in Applied Mechanics and Engineering 401 (2022).
date_created: 2022-10-17T13:42:12Z
date_updated: 2023-04-27T10:05:16Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.1016/j.cma.2022.115553
intvolume: '       401'
keyword:
- Computer Science Applications
- General Physics and Astronomy
- Mechanical Engineering
- Mechanics of Materials
- Computational Mechanics
language:
- iso: eng
publication: Computer Methods in Applied Mechanics and Engineering
publication_identifier:
  issn:
  - 0045-7825
publication_status: published
publisher: Elsevier BV
quality_controlled: '1'
status: public
title: New low order Runge–Kutta schemes for asymptotically exact global error estimation
  of embedded methods without order reduction
type: journal_article
user_id: '335'
volume: 401
year: '2022'
...
---
_id: '23794'
author:
- first_name: Hendrik
  full_name: Westermann, Hendrik
  id: '60816'
  last_name: Westermann
  orcid: 0000-0002-5034-9708
- first_name: Alexander
  full_name: Reitz, Alexander
  id: '24803'
  last_name: Reitz
  orcid: 0000-0001-9047-467X
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
- first_name: Mirko
  full_name: Schaper, Mirko
  id: '43720'
  last_name: Schaper
- first_name: Olexandr
  full_name: Grydin, Olexandr
  id: '43822'
  last_name: Grydin
citation:
  ama: Westermann H, Reitz A, Mahnken R, Schaper M, Grydin O. Microstructure transformations
    in a press hardening steel during tailored thermo‐mechanical processing. <i>steel
    research international</i>. Published online 2022. doi:<a href="https://doi.org/10.1002/srin.202100346">10.1002/srin.202100346</a>
  apa: Westermann, H., Reitz, A., Mahnken, R., Schaper, M., &#38; Grydin, O. (2022).
    Microstructure transformations in a press hardening steel during tailored thermo‐mechanical
    processing. <i>Steel Research International</i>. <a href="https://doi.org/10.1002/srin.202100346">https://doi.org/10.1002/srin.202100346</a>
  bibtex: '@article{Westermann_Reitz_Mahnken_Schaper_Grydin_2022, title={Microstructure
    transformations in a press hardening steel during tailored thermo‐mechanical processing},
    DOI={<a href="https://doi.org/10.1002/srin.202100346">10.1002/srin.202100346</a>},
    journal={steel research international}, author={Westermann, Hendrik and Reitz,
    Alexander and Mahnken, Rolf and Schaper, Mirko and Grydin, Olexandr}, year={2022}
    }'
  chicago: Westermann, Hendrik, Alexander Reitz, Rolf Mahnken, Mirko Schaper, and
    Olexandr Grydin. “Microstructure Transformations in a Press Hardening Steel during
    Tailored Thermo‐mechanical Processing.” <i>Steel Research International</i>, 2022.
    <a href="https://doi.org/10.1002/srin.202100346">https://doi.org/10.1002/srin.202100346</a>.
  ieee: 'H. Westermann, A. Reitz, R. Mahnken, M. Schaper, and O. Grydin, “Microstructure
    transformations in a press hardening steel during tailored thermo‐mechanical processing,”
    <i>steel research international</i>, 2022, doi: <a href="https://doi.org/10.1002/srin.202100346">10.1002/srin.202100346</a>.'
  mla: Westermann, Hendrik, et al. “Microstructure Transformations in a Press Hardening
    Steel during Tailored Thermo‐mechanical Processing.” <i>Steel Research International</i>,
    2022, doi:<a href="https://doi.org/10.1002/srin.202100346">10.1002/srin.202100346</a>.
  short: H. Westermann, A. Reitz, R. Mahnken, M. Schaper, O. Grydin, Steel Research
    International (2022).
date_created: 2021-09-06T12:00:55Z
date_updated: 2023-04-27T16:39:38Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
- _id: '158'
doi: 10.1002/srin.202100346
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: 'https://doi.org/10.1002/srin.202100346 [Titel anhand dieser DOI in Citavi-Projekt
    übernehmen] '
oa: '1'
publication: steel research international
publication_identifier:
  issn:
  - 1611-3683
  - 1869-344X
publication_status: published
quality_controlled: '1'
status: public
title: Microstructure transformations in a press hardening steel during tailored thermo‐mechanical
  processing
type: journal_article
user_id: '43720'
year: '2022'
...
---
_id: '29089'
author:
- first_name: Hendrik
  full_name: Westermann, Hendrik
  id: '60816'
  last_name: Westermann
  orcid: 0000-0002-5034-9708
- first_name: Alexander
  full_name: Reitz, Alexander
  id: '24803'
  last_name: Reitz
  orcid: 0000-0001-9047-467X
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
- first_name: Olexandr
  full_name: Grydin, Olexandr
  id: '43822'
  last_name: Grydin
- first_name: Mirko
  full_name: Schaper, Mirko
  id: '43720'
  last_name: Schaper
citation:
  ama: Westermann H, Reitz A, Mahnken R, Grydin O, Schaper M. Constitutive modeling
    of viscoplasticity including phase transformations for graded thermo‐mechanical
    processing. <i>PAMM</i>. Published online 2021. doi:<a href="https://doi.org/10.1002/pamm.202100041">10.1002/pamm.202100041</a>
  apa: Westermann, H., Reitz, A., Mahnken, R., Grydin, O., &#38; Schaper, M. (2021).
    Constitutive modeling of viscoplasticity including phase transformations for graded
    thermo‐mechanical processing. <i>PAMM</i>. <a href="https://doi.org/10.1002/pamm.202100041">https://doi.org/10.1002/pamm.202100041</a>
  bibtex: '@article{Westermann_Reitz_Mahnken_Grydin_Schaper_2021, title={Constitutive
    modeling of viscoplasticity including phase transformations for graded thermo‐mechanical
    processing}, DOI={<a href="https://doi.org/10.1002/pamm.202100041">10.1002/pamm.202100041</a>},
    journal={PAMM}, author={Westermann, Hendrik and Reitz, Alexander and Mahnken,
    Rolf and Grydin, Olexandr and Schaper, Mirko}, year={2021} }'
  chicago: Westermann, Hendrik, Alexander Reitz, Rolf Mahnken, Olexandr Grydin, and
    Mirko Schaper. “Constitutive Modeling of Viscoplasticity Including Phase Transformations
    for Graded Thermo‐mechanical Processing.” <i>PAMM</i>, 2021. <a href="https://doi.org/10.1002/pamm.202100041">https://doi.org/10.1002/pamm.202100041</a>.
  ieee: 'H. Westermann, A. Reitz, R. Mahnken, O. Grydin, and M. Schaper, “Constitutive
    modeling of viscoplasticity including phase transformations for graded thermo‐mechanical
    processing,” <i>PAMM</i>, 2021, doi: <a href="https://doi.org/10.1002/pamm.202100041">10.1002/pamm.202100041</a>.'
  mla: Westermann, Hendrik, et al. “Constitutive Modeling of Viscoplasticity Including
    Phase Transformations for Graded Thermo‐mechanical Processing.” <i>PAMM</i>, 2021,
    doi:<a href="https://doi.org/10.1002/pamm.202100041">10.1002/pamm.202100041</a>.
  short: H. Westermann, A. Reitz, R. Mahnken, O. Grydin, M. Schaper, PAMM (2021).
date_created: 2021-12-22T12:41:34Z
date_updated: 2023-01-24T12:54:26Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.1002/pamm.202100041
language:
- iso: eng
publication: PAMM
publication_identifier:
  issn:
  - 1617-7061
  - 1617-7061
publication_status: published
status: public
title: Constitutive modeling of viscoplasticity including phase transformations for
  graded thermo‐mechanical processing
type: journal_article
user_id: '335'
year: '2021'
...