---
_id: '52233'
abstract:
- lang: eng
  text: ELDIRK methods are 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>
    methods, with the consequence, that no additional system of equations must be
    solved, compared to the embedded RK method. Two general formulations for second-
    and third-order ELDIRK methods have been obtained recently in Mahnken [21] with
    specific schemes,  e.g. for the embedded implicit Euler method, the embedded trapezoidal-rule
    and the embedded Ellsiepen method. In the first part of this paper, we investigate
    some general stability characteristics of ELDIRK methods, and it will be shown
    that the above specific RK schemes are not A-stable. Therefore, in the second
    part, the above-mentioned general formulations are used for further stability
    investigations, with the aim to construct new second- and third-order ELDIRK methods
    which simultaneously are A-stable. Two numerical examples are concerned with the
    curing for a thermosetting material and phase-field RVE modeling for crystallinity
    and orientation. The numerical results confirm the theoretical results on convergence
    order and stability.
author:
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
- first_name: Hendrik
  full_name: Westermann, Hendrik
  id: '60816'
  last_name: Westermann
  orcid: 0000-0002-5034-9708
citation:
  ama: Mahnken R, Westermann H. Construction of A-stable explicit last-stage diagonal
    implicit Runge–Kutta (ELDIRK) methods. <i>Computational Mechanics</i>. Published
    online 2024. doi:<a href="https://doi.org/10.1007/s00466-024-02442-y">10.1007/s00466-024-02442-y</a>
  apa: Mahnken, R., &#38; Westermann, H. (2024). Construction of A-stable explicit
    last-stage diagonal implicit Runge–Kutta (ELDIRK) methods. <i>Computational Mechanics</i>.
    <a href="https://doi.org/10.1007/s00466-024-02442-y">https://doi.org/10.1007/s00466-024-02442-y</a>
  bibtex: '@article{Mahnken_Westermann_2024, title={Construction of A-stable explicit
    last-stage diagonal implicit Runge–Kutta (ELDIRK) methods}, DOI={<a href="https://doi.org/10.1007/s00466-024-02442-y">10.1007/s00466-024-02442-y</a>},
    journal={Computational Mechanics}, publisher={Springer Science and Business Media
    LLC}, author={Mahnken, Rolf and Westermann, Hendrik}, year={2024} }'
  chicago: Mahnken, Rolf, and Hendrik Westermann. “Construction of A-Stable Explicit
    Last-Stage Diagonal Implicit Runge–Kutta (ELDIRK) Methods.” <i>Computational Mechanics</i>,
    2024. <a href="https://doi.org/10.1007/s00466-024-02442-y">https://doi.org/10.1007/s00466-024-02442-y</a>.
  ieee: 'R. Mahnken and H. Westermann, “Construction of A-stable explicit last-stage
    diagonal implicit Runge–Kutta (ELDIRK) methods,” <i>Computational Mechanics</i>,
    2024, doi: <a href="https://doi.org/10.1007/s00466-024-02442-y">10.1007/s00466-024-02442-y</a>.'
  mla: Mahnken, Rolf, and Hendrik Westermann. “Construction of A-Stable Explicit Last-Stage
    Diagonal Implicit Runge–Kutta (ELDIRK) Methods.” <i>Computational Mechanics</i>,
    Springer Science and Business Media LLC, 2024, doi:<a href="https://doi.org/10.1007/s00466-024-02442-y">10.1007/s00466-024-02442-y</a>.
  short: R. Mahnken, H. Westermann, Computational Mechanics (2024).
date_created: 2024-03-03T13:23:28Z
date_updated: 2024-03-19T12:14:07Z
department:
- _id: '154'
- _id: '321'
doi: 10.1007/s00466-024-02442-y
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: Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta
  (ELDIRK) methods
type: journal_article
user_id: '335'
year: '2024'
...
---
_id: '48465'
article_number: '116545'
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. On the accuracy, stability and computational efficiency
    of explicit last-stage diagonally implicit Runge–Kutta methods (ELDIRK) for the
    adaptive solution of phase-field problems. <i>Computer Methods in Applied Mechanics
    and Engineering</i>. 2023;418. doi:<a href="https://doi.org/10.1016/j.cma.2023.116545">10.1016/j.cma.2023.116545</a>
  apa: Westermann, H., &#38; Mahnken, R. (2023). On the accuracy, stability and computational
    efficiency of explicit last-stage diagonally implicit Runge–Kutta methods (ELDIRK)
    for the adaptive solution of phase-field problems. <i>Computer Methods in Applied
    Mechanics and Engineering</i>, <i>418</i>, Article 116545. <a href="https://doi.org/10.1016/j.cma.2023.116545">https://doi.org/10.1016/j.cma.2023.116545</a>
  bibtex: '@article{Westermann_Mahnken_2023, title={On the accuracy, stability and
    computational efficiency of explicit last-stage diagonally implicit Runge–Kutta
    methods (ELDIRK) for the adaptive solution of phase-field problems}, volume={418},
    DOI={<a href="https://doi.org/10.1016/j.cma.2023.116545">10.1016/j.cma.2023.116545</a>},
    number={116545}, journal={Computer Methods in Applied Mechanics and Engineering},
    publisher={Elsevier BV}, author={Westermann, Hendrik and Mahnken, Rolf}, year={2023}
    }'
  chicago: Westermann, Hendrik, and Rolf Mahnken. “On the Accuracy, Stability and
    Computational Efficiency of Explicit Last-Stage Diagonally Implicit Runge–Kutta
    Methods (ELDIRK) for the Adaptive Solution of Phase-Field Problems.” <i>Computer
    Methods in Applied Mechanics and Engineering</i> 418 (2023). <a href="https://doi.org/10.1016/j.cma.2023.116545">https://doi.org/10.1016/j.cma.2023.116545</a>.
  ieee: 'H. Westermann and R. Mahnken, “On the accuracy, stability and computational
    efficiency of explicit last-stage diagonally implicit Runge–Kutta methods (ELDIRK)
    for the adaptive solution of phase-field problems,” <i>Computer Methods in Applied
    Mechanics and Engineering</i>, vol. 418, Art. no. 116545, 2023, doi: <a href="https://doi.org/10.1016/j.cma.2023.116545">10.1016/j.cma.2023.116545</a>.'
  mla: Westermann, Hendrik, and Rolf Mahnken. “On the Accuracy, Stability and Computational
    Efficiency of Explicit Last-Stage Diagonally Implicit Runge–Kutta Methods (ELDIRK)
    for the Adaptive Solution of Phase-Field Problems.” <i>Computer Methods in Applied
    Mechanics and Engineering</i>, vol. 418, 116545, Elsevier BV, 2023, doi:<a href="https://doi.org/10.1016/j.cma.2023.116545">10.1016/j.cma.2023.116545</a>.
  short: H. Westermann, R. Mahnken, Computer Methods in Applied Mechanics and Engineering
    418 (2023).
date_created: 2023-10-25T10:47:23Z
date_updated: 2023-11-07T14:34:56Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.1016/j.cma.2023.116545
intvolume: '       418'
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: On the accuracy, stability and computational efficiency of explicit last-stage
  diagonally implicit Runge–Kutta methods (ELDIRK) for the adaptive solution of phase-field
  problems
type: journal_article
user_id: '335'
volume: 418
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: '34257'
abstract:
- lang: eng
  text: Galvanic corrosion is a destructive process between dissimilar metals. The
    present paper presents a constructed numerical test case to simulate galvanic
    corrosion of two dissimilar metals. This test case is used to study the accuracy
    of different implementations to track the dissolving anode boundary. One technique
    is to numerically simulate a mesh displacement based on the prescribed displacement
    at the anode boundary. The second method is to adjust only the boundary elements.
    Re-meshing after a certain number of time steps is applied to both implementations.
    They produce similar results for an electrical and electrochemical field problem.
    This work shows that mesh smoothing does not result in higher accuracy when modeling
    a moving anode front. Adjusting only the boundary elements is sufficient when
    frequent re-meshing is used.
author:
- first_name: Sven
  full_name: Harzheim, Sven
  last_name: Harzheim
- first_name: Martin
  full_name: Hofmann, Martin
  last_name: Hofmann
- first_name: Thomas
  full_name: Wallmersperger, Thomas
  last_name: Wallmersperger
citation:
  ama: Harzheim S, Hofmann M, Wallmersperger T. Comparison of two mesh-moving techniques
    for finite element simulations of galvanic corrosion. <i>Acta Mechanica</i>. 2022;233(11):4427-4439.
    doi:<a href="https://doi.org/10.1007/s00707-022-03326-z">10.1007/s00707-022-03326-z</a>
  apa: Harzheim, S., Hofmann, M., &#38; Wallmersperger, T. (2022). Comparison of two
    mesh-moving techniques for finite element simulations of galvanic corrosion. <i>Acta
    Mechanica</i>, <i>233</i>(11), 4427–4439. <a href="https://doi.org/10.1007/s00707-022-03326-z">https://doi.org/10.1007/s00707-022-03326-z</a>
  bibtex: '@article{Harzheim_Hofmann_Wallmersperger_2022, title={Comparison of two
    mesh-moving techniques for finite element simulations of galvanic corrosion},
    volume={233}, DOI={<a href="https://doi.org/10.1007/s00707-022-03326-z">10.1007/s00707-022-03326-z</a>},
    number={11}, journal={Acta Mechanica}, publisher={Springer Science and Business
    Media LLC}, author={Harzheim, Sven and Hofmann, Martin and Wallmersperger, Thomas},
    year={2022}, pages={4427–4439} }'
  chicago: 'Harzheim, Sven, Martin Hofmann, and Thomas Wallmersperger. “Comparison
    of Two Mesh-Moving Techniques for Finite Element Simulations of Galvanic Corrosion.”
    <i>Acta Mechanica</i> 233, no. 11 (2022): 4427–39. <a href="https://doi.org/10.1007/s00707-022-03326-z">https://doi.org/10.1007/s00707-022-03326-z</a>.'
  ieee: 'S. Harzheim, M. Hofmann, and T. Wallmersperger, “Comparison of two mesh-moving
    techniques for finite element simulations of galvanic corrosion,” <i>Acta Mechanica</i>,
    vol. 233, no. 11, pp. 4427–4439, 2022, doi: <a href="https://doi.org/10.1007/s00707-022-03326-z">10.1007/s00707-022-03326-z</a>.'
  mla: Harzheim, Sven, et al. “Comparison of Two Mesh-Moving Techniques for Finite
    Element Simulations of Galvanic Corrosion.” <i>Acta Mechanica</i>, vol. 233, no.
    11, Springer Science and Business Media LLC, 2022, pp. 4427–39, doi:<a href="https://doi.org/10.1007/s00707-022-03326-z">10.1007/s00707-022-03326-z</a>.
  short: S. Harzheim, M. Hofmann, T. Wallmersperger, Acta Mechanica 233 (2022) 4427–4439.
date_created: 2022-12-06T20:47:16Z
date_updated: 2023-01-02T11:07:28Z
department:
- _id: '630'
doi: 10.1007/s00707-022-03326-z
intvolume: '       233'
issue: '11'
keyword:
- Mechanical Engineering
- Computational Mechanics
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://link.springer.com/article/10.1007/s00707-022-03326-z
oa: '1'
page: 4427-4439
project:
- _id: '130'
  grant_number: '418701707'
  name: 'TRR 285: TRR 285'
- _id: '142'
  name: 'TRR 285 – B03: TRR 285 - Subproject B03'
publication: Acta Mechanica
publication_identifier:
  issn:
  - 0001-5970
  - 1619-6937
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Comparison of two mesh-moving techniques for finite element simulations of
  galvanic corrosion
type: journal_article
user_id: '14931'
volume: 233
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: '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: '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: '45420'
author:
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
- first_name: P.
  full_name: Steinmann, P.
  last_name: Steinmann
citation:
  ama: Mahnken R, Steinmann P. Parameter Identification of Constitutive Models for
    Fluidsaturated Porous Media within an FE-Setting. <i>ZAMM - Journal of Applied
    Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik</i>.
    2011;80(S1):161-164. doi:<a href="https://doi.org/10.1002/zamm.20000801341">10.1002/zamm.20000801341</a>
  apa: Mahnken, R., &#38; Steinmann, P. (2011). Parameter Identification of Constitutive
    Models for Fluidsaturated Porous Media within an FE-Setting. <i>ZAMM - Journal
    of Applied Mathematics and Mechanics / Zeitschrift Für Angewandte Mathematik Und
    Mechanik</i>, <i>80</i>(S1), 161–164. <a href="https://doi.org/10.1002/zamm.20000801341">https://doi.org/10.1002/zamm.20000801341</a>
  bibtex: '@article{Mahnken_Steinmann_2011, title={Parameter Identification of Constitutive
    Models for Fluidsaturated Porous Media within an FE-Setting}, volume={80}, DOI={<a
    href="https://doi.org/10.1002/zamm.20000801341">10.1002/zamm.20000801341</a>},
    number={S1}, journal={ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift
    für Angewandte Mathematik und Mechanik}, publisher={Wiley}, author={Mahnken, Rolf
    and Steinmann, P.}, year={2011}, pages={161–164} }'
  chicago: 'Mahnken, Rolf, and P. Steinmann. “Parameter Identification of Constitutive
    Models for Fluidsaturated Porous Media within an FE-Setting.” <i>ZAMM - Journal
    of Applied Mathematics and Mechanics / Zeitschrift Für Angewandte Mathematik Und
    Mechanik</i> 80, no. S1 (2011): 161–64. <a href="https://doi.org/10.1002/zamm.20000801341">https://doi.org/10.1002/zamm.20000801341</a>.'
  ieee: 'R. Mahnken and P. Steinmann, “Parameter Identification of Constitutive Models
    for Fluidsaturated Porous Media within an FE-Setting,” <i>ZAMM - Journal of Applied
    Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik</i>,
    vol. 80, no. S1, pp. 161–164, 2011, doi: <a href="https://doi.org/10.1002/zamm.20000801341">10.1002/zamm.20000801341</a>.'
  mla: Mahnken, Rolf, and P. Steinmann. “Parameter Identification of Constitutive
    Models for Fluidsaturated Porous Media within an FE-Setting.” <i>ZAMM - Journal
    of Applied Mathematics and Mechanics / Zeitschrift Für Angewandte Mathematik Und
    Mechanik</i>, vol. 80, no. S1, Wiley, 2011, pp. 161–64, doi:<a href="https://doi.org/10.1002/zamm.20000801341">10.1002/zamm.20000801341</a>.
  short: R. Mahnken, P. Steinmann, ZAMM - Journal of Applied Mathematics and Mechanics
    / Zeitschrift Für Angewandte Mathematik Und Mechanik 80 (2011) 161–164.
date_created: 2023-05-31T12:09:05Z
date_updated: 2023-05-31T12:09:41Z
department:
- _id: '9'
- _id: '154'
doi: 10.1002/zamm.20000801341
intvolume: '        80'
issue: S1
keyword:
- Applied Mathematics
- Computational Mechanics
language:
- iso: eng
page: 161-164
publication: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für
  Angewandte Mathematik und Mechanik
publication_identifier:
  issn:
  - 0044-2267
publication_status: published
publisher: Wiley
quality_controlled: '1'
status: public
title: Parameter Identification of Constitutive Models for Fluidsaturated Porous Media
  within an FE-Setting
type: journal_article
user_id: '335'
volume: 80
year: '2011'
...
---
_id: '45421'
author:
- first_name: C.
  full_name: Döbert, C.
  last_name: Döbert
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
- first_name: E.
  full_name: Stein, E.
  last_name: Stein
citation:
  ama: Döbert C, Mahnken R, Stein E. Numerical Simulation of Interface Debonding during
    Fibre Pull-Out Tests. <i>ZAMM - Journal of Applied Mathematics and Mechanics /
    Zeitschrift für Angewandte Mathematik und Mechanik</i>. 2011;80(S2):467-468. doi:<a
    href="https://doi.org/10.1002/zamm.200008014105">10.1002/zamm.200008014105</a>
  apa: Döbert, C., Mahnken, R., &#38; Stein, E. (2011). Numerical Simulation of Interface
    Debonding during Fibre Pull-Out Tests. <i>ZAMM - Journal of Applied Mathematics
    and Mechanics / Zeitschrift Für Angewandte Mathematik Und Mechanik</i>, <i>80</i>(S2),
    467–468. <a href="https://doi.org/10.1002/zamm.200008014105">https://doi.org/10.1002/zamm.200008014105</a>
  bibtex: '@article{Döbert_Mahnken_Stein_2011, title={Numerical Simulation of Interface
    Debonding during Fibre Pull-Out Tests}, volume={80}, DOI={<a href="https://doi.org/10.1002/zamm.200008014105">10.1002/zamm.200008014105</a>},
    number={S2}, journal={ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift
    für Angewandte Mathematik und Mechanik}, publisher={Wiley}, author={Döbert, C.
    and Mahnken, Rolf and Stein, E.}, year={2011}, pages={467–468} }'
  chicago: 'Döbert, C., Rolf Mahnken, and E. Stein. “Numerical Simulation of Interface
    Debonding during Fibre Pull-Out Tests.” <i>ZAMM - Journal of Applied Mathematics
    and Mechanics / Zeitschrift Für Angewandte Mathematik Und Mechanik</i> 80, no.
    S2 (2011): 467–68. <a href="https://doi.org/10.1002/zamm.200008014105">https://doi.org/10.1002/zamm.200008014105</a>.'
  ieee: 'C. Döbert, R. Mahnken, and E. Stein, “Numerical Simulation of Interface Debonding
    during Fibre Pull-Out Tests,” <i>ZAMM - Journal of Applied Mathematics and Mechanics
    / Zeitschrift für Angewandte Mathematik und Mechanik</i>, vol. 80, no. S2, pp.
    467–468, 2011, doi: <a href="https://doi.org/10.1002/zamm.200008014105">10.1002/zamm.200008014105</a>.'
  mla: Döbert, C., et al. “Numerical Simulation of Interface Debonding during Fibre
    Pull-Out Tests.” <i>ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift
    Für Angewandte Mathematik Und Mechanik</i>, vol. 80, no. S2, Wiley, 2011, pp.
    467–68, doi:<a href="https://doi.org/10.1002/zamm.200008014105">10.1002/zamm.200008014105</a>.
  short: C. Döbert, R. Mahnken, E. Stein, ZAMM - Journal of Applied Mathematics and
    Mechanics / Zeitschrift Für Angewandte Mathematik Und Mechanik 80 (2011) 467–468.
date_created: 2023-05-31T12:10:26Z
date_updated: 2023-05-31T12:11:07Z
department:
- _id: '9'
- _id: '154'
doi: 10.1002/zamm.200008014105
intvolume: '        80'
issue: S2
keyword:
- Applied Mathematics
- Computational Mechanics
language:
- iso: eng
page: 467-468
publication: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für
  Angewandte Mathematik und Mechanik
publication_identifier:
  issn:
  - 0044-2267
publication_status: published
publisher: Wiley
quality_controlled: '1'
status: public
title: Numerical Simulation of Interface Debonding during Fibre Pull-Out Tests
type: journal_article
user_id: '335'
volume: 80
year: '2011'
...
---
_id: '45419'
author:
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
citation:
  ama: Mahnken R. Improvements for finite-element implementation of the Gurson Model.
    <i>ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte
    Mathematik und Mechanik</i>. 2011;80(S2):481-482. doi:<a href="https://doi.org/10.1002/zamm.200008014112">10.1002/zamm.200008014112</a>
  apa: Mahnken, R. (2011). Improvements for finite-element implementation of the Gurson
    Model. <i>ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift Für
    Angewandte Mathematik Und Mechanik</i>, <i>80</i>(S2), 481–482. <a href="https://doi.org/10.1002/zamm.200008014112">https://doi.org/10.1002/zamm.200008014112</a>
  bibtex: '@article{Mahnken_2011, title={Improvements for finite-element implementation
    of the Gurson Model}, volume={80}, DOI={<a href="https://doi.org/10.1002/zamm.200008014112">10.1002/zamm.200008014112</a>},
    number={S2}, journal={ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift
    für Angewandte Mathematik und Mechanik}, publisher={Wiley}, author={Mahnken, Rolf},
    year={2011}, pages={481–482} }'
  chicago: 'Mahnken, Rolf. “Improvements for Finite-Element Implementation of the
    Gurson Model.” <i>ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift
    Für Angewandte Mathematik Und Mechanik</i> 80, no. S2 (2011): 481–82. <a href="https://doi.org/10.1002/zamm.200008014112">https://doi.org/10.1002/zamm.200008014112</a>.'
  ieee: 'R. Mahnken, “Improvements for finite-element implementation of the Gurson
    Model,” <i>ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für
    Angewandte Mathematik und Mechanik</i>, vol. 80, no. S2, pp. 481–482, 2011, doi:
    <a href="https://doi.org/10.1002/zamm.200008014112">10.1002/zamm.200008014112</a>.'
  mla: Mahnken, Rolf. “Improvements for Finite-Element Implementation of the Gurson
    Model.” <i>ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift Für
    Angewandte Mathematik Und Mechanik</i>, vol. 80, no. S2, Wiley, 2011, pp. 481–82,
    doi:<a href="https://doi.org/10.1002/zamm.200008014112">10.1002/zamm.200008014112</a>.
  short: R. Mahnken, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift
    Für Angewandte Mathematik Und Mechanik 80 (2011) 481–482.
date_created: 2023-05-31T12:07:05Z
date_updated: 2023-05-31T12:07:53Z
department:
- _id: '9'
- _id: '154'
doi: 10.1002/zamm.200008014112
intvolume: '        80'
issue: S2
keyword:
- Applied Mathematics
- Computational Mechanics
language:
- iso: eng
page: 481-482
publication: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für
  Angewandte Mathematik und Mechanik
publication_identifier:
  issn:
  - 0044-2267
publication_status: published
publisher: Wiley
quality_controlled: '1'
status: public
title: Improvements for finite-element implementation of the Gurson Model
type: journal_article
user_id: '335'
volume: 80
year: '2011'
...
---
_id: '45431'
author:
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
citation:
  ama: Mahnken R. A Newton-Multigrid algrithm for elasto-plastic/viscoplastic problems.
    <i>Computational Mechanics</i>. 2008;15(5):408-425. doi:<a href="https://doi.org/10.1007/bf00350355">10.1007/bf00350355</a>
  apa: Mahnken, R. (2008). A Newton-Multigrid algrithm for elasto-plastic/viscoplastic
    problems. <i>Computational Mechanics</i>, <i>15</i>(5), 408–425. <a href="https://doi.org/10.1007/bf00350355">https://doi.org/10.1007/bf00350355</a>
  bibtex: '@article{Mahnken_2008, title={A Newton-Multigrid algrithm for elasto-plastic/viscoplastic
    problems}, volume={15}, DOI={<a href="https://doi.org/10.1007/bf00350355">10.1007/bf00350355</a>},
    number={5}, journal={Computational Mechanics}, publisher={Springer Science and
    Business Media LLC}, author={Mahnken, Rolf}, year={2008}, pages={408–425} }'
  chicago: 'Mahnken, Rolf. “A Newton-Multigrid Algrithm for Elasto-Plastic/Viscoplastic
    Problems.” <i>Computational Mechanics</i> 15, no. 5 (2008): 408–25. <a href="https://doi.org/10.1007/bf00350355">https://doi.org/10.1007/bf00350355</a>.'
  ieee: 'R. Mahnken, “A Newton-Multigrid algrithm for elasto-plastic/viscoplastic
    problems,” <i>Computational Mechanics</i>, vol. 15, no. 5, pp. 408–425, 2008,
    doi: <a href="https://doi.org/10.1007/bf00350355">10.1007/bf00350355</a>.'
  mla: Mahnken, Rolf. “A Newton-Multigrid Algrithm for Elasto-Plastic/Viscoplastic
    Problems.” <i>Computational Mechanics</i>, vol. 15, no. 5, Springer Science and
    Business Media LLC, 2008, pp. 408–25, doi:<a href="https://doi.org/10.1007/bf00350355">10.1007/bf00350355</a>.
  short: R. Mahnken, Computational Mechanics 15 (2008) 408–425.
date_created: 2023-05-31T12:26:42Z
date_updated: 2023-05-31T12:27:11Z
department:
- _id: '9'
- _id: '154'
doi: 10.1007/bf00350355
intvolume: '        15'
issue: '5'
keyword:
- Applied Mathematics
- Computational Mathematics
- Computational Theory and Mathematics
- Mechanical Engineering
- Ocean Engineering
- Computational Mechanics
language:
- iso: eng
page: 408-425
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: A Newton-Multigrid algrithm for elasto-plastic/viscoplastic problems
type: journal_article
user_id: '335'
volume: 15
year: '2008'
...
---
_id: '45307'
author:
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
citation:
  ama: Mahnken R. Strength difference in compression and tension and pressure dependence
    of yielding in elasto-plasticity. <i>Computer Methods in Applied Mechanics and
    Engineering</i>. 2002;190(39):5057-5080. doi:<a href="https://doi.org/10.1016/s0045-7825(00)00364-9">10.1016/s0045-7825(00)00364-9</a>
  apa: Mahnken, R. (2002). Strength difference in compression and tension and pressure
    dependence of yielding in elasto-plasticity. <i>Computer Methods in Applied Mechanics
    and Engineering</i>, <i>190</i>(39), 5057–5080. <a href="https://doi.org/10.1016/s0045-7825(00)00364-9">https://doi.org/10.1016/s0045-7825(00)00364-9</a>
  bibtex: '@article{Mahnken_2002, title={Strength difference in compression and tension
    and pressure dependence of yielding in elasto-plasticity}, volume={190}, DOI={<a
    href="https://doi.org/10.1016/s0045-7825(00)00364-9">10.1016/s0045-7825(00)00364-9</a>},
    number={39}, journal={Computer Methods in Applied Mechanics and Engineering},
    publisher={Elsevier BV}, author={Mahnken, Rolf}, year={2002}, pages={5057–5080}
    }'
  chicago: 'Mahnken, Rolf. “Strength Difference in Compression and Tension and Pressure
    Dependence of Yielding in Elasto-Plasticity.” <i>Computer Methods in Applied Mechanics
    and Engineering</i> 190, no. 39 (2002): 5057–80. <a href="https://doi.org/10.1016/s0045-7825(00)00364-9">https://doi.org/10.1016/s0045-7825(00)00364-9</a>.'
  ieee: 'R. Mahnken, “Strength difference in compression and tension and pressure
    dependence of yielding in elasto-plasticity,” <i>Computer Methods in Applied Mechanics
    and Engineering</i>, vol. 190, no. 39, pp. 5057–5080, 2002, doi: <a href="https://doi.org/10.1016/s0045-7825(00)00364-9">10.1016/s0045-7825(00)00364-9</a>.'
  mla: Mahnken, Rolf. “Strength Difference in Compression and Tension and Pressure
    Dependence of Yielding in Elasto-Plasticity.” <i>Computer Methods in Applied Mechanics
    and Engineering</i>, vol. 190, no. 39, Elsevier BV, 2002, pp. 5057–80, doi:<a
    href="https://doi.org/10.1016/s0045-7825(00)00364-9">10.1016/s0045-7825(00)00364-9</a>.
  short: R. Mahnken, Computer Methods in Applied Mechanics and Engineering 190 (2002)
    5057–5080.
date_created: 2023-05-26T12:21:04Z
date_updated: 2023-05-26T12:22:12Z
department:
- _id: '9'
- _id: '154'
doi: 10.1016/s0045-7825(00)00364-9
intvolume: '       190'
issue: '39'
keyword:
- Computer Science Applications
- General Physics and Astronomy
- Mechanical Engineering
- Mechanics of Materials
- Computational Mechanics
language:
- iso: eng
page: 5057-5080
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: Strength difference in compression and tension and pressure dependence of yielding
  in elasto-plasticity
type: journal_article
user_id: '335'
volume: 190
year: '2002'
...
---
_id: '45413'
author:
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
- first_name: P.
  full_name: Steinmann, P.
  last_name: Steinmann
citation:
  ama: Mahnken R, Steinmann P. A finite element algorithm for parameter identification
    of material models for fluid saturated porous media. <i>International Journal
    for Numerical and Analytical Methods in Geomechanics</i>. 2002;25(5):415-434.
    doi:<a href="https://doi.org/10.1002/nag.136">10.1002/nag.136</a>
  apa: Mahnken, R., &#38; Steinmann, P. (2002). A finite element algorithm for parameter
    identification of material models for fluid saturated porous media. <i>International
    Journal for Numerical and Analytical Methods in Geomechanics</i>, <i>25</i>(5),
    415–434. <a href="https://doi.org/10.1002/nag.136">https://doi.org/10.1002/nag.136</a>
  bibtex: '@article{Mahnken_Steinmann_2002, title={A finite element algorithm for
    parameter identification of material models for fluid saturated porous media},
    volume={25}, DOI={<a href="https://doi.org/10.1002/nag.136">10.1002/nag.136</a>},
    number={5}, journal={International Journal for Numerical and Analytical Methods
    in Geomechanics}, publisher={Wiley}, author={Mahnken, Rolf and Steinmann, P.},
    year={2002}, pages={415–434} }'
  chicago: 'Mahnken, Rolf, and P. Steinmann. “A Finite Element Algorithm for Parameter
    Identification of Material Models for Fluid Saturated Porous Media.” <i>International
    Journal for Numerical and Analytical Methods in Geomechanics</i> 25, no. 5 (2002):
    415–34. <a href="https://doi.org/10.1002/nag.136">https://doi.org/10.1002/nag.136</a>.'
  ieee: 'R. Mahnken and P. Steinmann, “A finite element algorithm for parameter identification
    of material models for fluid saturated porous media,” <i>International Journal
    for Numerical and Analytical Methods in Geomechanics</i>, vol. 25, no. 5, pp.
    415–434, 2002, doi: <a href="https://doi.org/10.1002/nag.136">10.1002/nag.136</a>.'
  mla: Mahnken, Rolf, and P. Steinmann. “A Finite Element Algorithm for Parameter
    Identification of Material Models for Fluid Saturated Porous Media.” <i>International
    Journal for Numerical and Analytical Methods in Geomechanics</i>, vol. 25, no.
    5, Wiley, 2002, pp. 415–34, doi:<a href="https://doi.org/10.1002/nag.136">10.1002/nag.136</a>.
  short: R. Mahnken, P. Steinmann, International Journal for Numerical and Analytical
    Methods in Geomechanics 25 (2002) 415–434.
date_created: 2023-05-31T11:55:35Z
date_updated: 2023-05-31T11:55:54Z
department:
- _id: '9'
- _id: '154'
doi: 10.1002/nag.136
intvolume: '        25'
issue: '5'
keyword:
- Mechanics of Materials
- Geotechnical Engineering and Engineering Geology
- General Materials Science
- Computational Mechanics
language:
- iso: eng
page: 415-434
publication: International Journal for Numerical and Analytical Methods in Geomechanics
publication_identifier:
  issn:
  - 0363-9061
  - 1096-9853
publication_status: published
publisher: Wiley
quality_controlled: '1'
status: public
title: A finite element algorithm for parameter identification of material models
  for fluid saturated porous media
type: journal_article
user_id: '335'
volume: 25
year: '2002'
...
---
_id: '45412'
author:
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
- first_name: M.
  full_name: Kohlmeier, M.
  last_name: Kohlmeier
citation:
  ama: Mahnken R, Kohlmeier M. Finite element simulation for rock salt with dilatancy
    boundary coupled to fluid permeation. <i>Computer Methods in Applied Mechanics
    and Engineering</i>. 2002;190(32-33):4259-4278. doi:<a href="https://doi.org/10.1016/s0045-7825(00)00317-0">10.1016/s0045-7825(00)00317-0</a>
  apa: Mahnken, R., &#38; Kohlmeier, M. (2002). Finite element simulation for rock
    salt with dilatancy boundary coupled to fluid permeation. <i>Computer Methods
    in Applied Mechanics and Engineering</i>, <i>190</i>(32–33), 4259–4278. <a href="https://doi.org/10.1016/s0045-7825(00)00317-0">https://doi.org/10.1016/s0045-7825(00)00317-0</a>
  bibtex: '@article{Mahnken_Kohlmeier_2002, title={Finite element simulation for rock
    salt with dilatancy boundary coupled to fluid permeation}, volume={190}, DOI={<a
    href="https://doi.org/10.1016/s0045-7825(00)00317-0">10.1016/s0045-7825(00)00317-0</a>},
    number={32–33}, journal={Computer Methods in Applied Mechanics and Engineering},
    publisher={Elsevier BV}, author={Mahnken, Rolf and Kohlmeier, M.}, year={2002},
    pages={4259–4278} }'
  chicago: 'Mahnken, Rolf, and M. Kohlmeier. “Finite Element Simulation for Rock Salt
    with Dilatancy Boundary Coupled to Fluid Permeation.” <i>Computer Methods in Applied
    Mechanics and Engineering</i> 190, no. 32–33 (2002): 4259–78. <a href="https://doi.org/10.1016/s0045-7825(00)00317-0">https://doi.org/10.1016/s0045-7825(00)00317-0</a>.'
  ieee: 'R. Mahnken and M. Kohlmeier, “Finite element simulation for rock salt with
    dilatancy boundary coupled to fluid permeation,” <i>Computer Methods in Applied
    Mechanics and Engineering</i>, vol. 190, no. 32–33, pp. 4259–4278, 2002, doi:
    <a href="https://doi.org/10.1016/s0045-7825(00)00317-0">10.1016/s0045-7825(00)00317-0</a>.'
  mla: Mahnken, Rolf, and M. Kohlmeier. “Finite Element Simulation for Rock Salt with
    Dilatancy Boundary Coupled to Fluid Permeation.” <i>Computer Methods in Applied
    Mechanics and Engineering</i>, vol. 190, no. 32–33, Elsevier BV, 2002, pp. 4259–78,
    doi:<a href="https://doi.org/10.1016/s0045-7825(00)00317-0">10.1016/s0045-7825(00)00317-0</a>.
  short: R. Mahnken, M. Kohlmeier, Computer Methods in Applied Mechanics and Engineering
    190 (2002) 4259–4278.
date_created: 2023-05-31T11:52:51Z
date_updated: 2023-05-31T11:53:38Z
department:
- _id: '9'
- _id: '154'
doi: 10.1016/s0045-7825(00)00317-0
intvolume: '       190'
issue: 32-33
keyword:
- Computer Science Applications
- General Physics and Astronomy
- Mechanical Engineering
- Mechanics of Materials
- Computational Mechanics
language:
- iso: eng
page: 4259-4278
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: Finite element simulation for rock salt with dilatancy boundary coupled to
  fluid permeation
type: journal_article
user_id: '335'
volume: 190
year: '2002'
...
---
_id: '45417'
author:
- first_name: C.
  full_name: Döbert, C.
  last_name: Döbert
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
- first_name: E.
  full_name: Stein, E.
  last_name: Stein
citation:
  ama: Döbert C, Mahnken R, Stein E. Numerical simulation of interface debonding with
    a combined damage/friction constitutive model. <i>Computational Mechanics</i>.
    2002;25(5):456-467. doi:<a href="https://doi.org/10.1007/s004660050493">10.1007/s004660050493</a>
  apa: Döbert, C., Mahnken, R., &#38; Stein, E. (2002). Numerical simulation of interface
    debonding with a combined damage/friction constitutive model. <i>Computational
    Mechanics</i>, <i>25</i>(5), 456–467. <a href="https://doi.org/10.1007/s004660050493">https://doi.org/10.1007/s004660050493</a>
  bibtex: '@article{Döbert_Mahnken_Stein_2002, title={Numerical simulation of interface
    debonding with a combined damage/friction constitutive model}, volume={25}, DOI={<a
    href="https://doi.org/10.1007/s004660050493">10.1007/s004660050493</a>}, number={5},
    journal={Computational Mechanics}, publisher={Springer Science and Business Media
    LLC}, author={Döbert, C. and Mahnken, Rolf and Stein, E.}, year={2002}, pages={456–467}
    }'
  chicago: 'Döbert, C., Rolf Mahnken, and E. Stein. “Numerical Simulation of Interface
    Debonding with a Combined Damage/Friction Constitutive Model.” <i>Computational
    Mechanics</i> 25, no. 5 (2002): 456–67. <a href="https://doi.org/10.1007/s004660050493">https://doi.org/10.1007/s004660050493</a>.'
  ieee: 'C. Döbert, R. Mahnken, and E. Stein, “Numerical simulation of interface debonding
    with a combined damage/friction constitutive model,” <i>Computational Mechanics</i>,
    vol. 25, no. 5, pp. 456–467, 2002, doi: <a href="https://doi.org/10.1007/s004660050493">10.1007/s004660050493</a>.'
  mla: Döbert, C., et al. “Numerical Simulation of Interface Debonding with a Combined
    Damage/Friction Constitutive Model.” <i>Computational Mechanics</i>, vol. 25,
    no. 5, Springer Science and Business Media LLC, 2002, pp. 456–67, doi:<a href="https://doi.org/10.1007/s004660050493">10.1007/s004660050493</a>.
  short: C. Döbert, R. Mahnken, E. Stein, Computational Mechanics 25 (2002) 456–467.
date_created: 2023-05-31T12:04:03Z
date_updated: 2023-05-31T12:04:35Z
department:
- _id: '9'
- _id: '154'
doi: 10.1007/s004660050493
intvolume: '        25'
issue: '5'
keyword:
- Applied Mathematics
- Computational Mathematics
- Computational Theory and Mathematics
- Mechanical Engineering
- Ocean Engineering
- Computational Mechanics
language:
- iso: eng
page: 456-467
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: Numerical simulation of interface debonding with a combined damage/friction
  constitutive model
type: journal_article
user_id: '335'
volume: 25
year: '2002'
...
---
_id: '45429'
author:
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
- first_name: Erwin
  full_name: Stein, Erwin
  last_name: Stein
citation:
  ama: Mahnken R, Stein E. A unified approach for parameter identification of inelastic
    material models in the frame of the finite element method. <i>Computer Methods
    in Applied Mechanics and Engineering</i>. 2002;136(3-4):225-258. doi:<a href="https://doi.org/10.1016/0045-7825(96)00991-7">10.1016/0045-7825(96)00991-7</a>
  apa: Mahnken, R., &#38; Stein, E. (2002). A unified approach for parameter identification
    of inelastic material models in the frame of the finite element method. <i>Computer
    Methods in Applied Mechanics and Engineering</i>, <i>136</i>(3–4), 225–258. <a
    href="https://doi.org/10.1016/0045-7825(96)00991-7">https://doi.org/10.1016/0045-7825(96)00991-7</a>
  bibtex: '@article{Mahnken_Stein_2002, title={A unified approach for parameter identification
    of inelastic material models in the frame of the finite element method}, volume={136},
    DOI={<a href="https://doi.org/10.1016/0045-7825(96)00991-7">10.1016/0045-7825(96)00991-7</a>},
    number={3–4}, journal={Computer Methods in Applied Mechanics and Engineering},
    publisher={Elsevier BV}, author={Mahnken, Rolf and Stein, Erwin}, year={2002},
    pages={225–258} }'
  chicago: 'Mahnken, Rolf, and Erwin Stein. “A Unified Approach for Parameter Identification
    of Inelastic Material Models in the Frame of the Finite Element Method.” <i>Computer
    Methods in Applied Mechanics and Engineering</i> 136, no. 3–4 (2002): 225–58.
    <a href="https://doi.org/10.1016/0045-7825(96)00991-7">https://doi.org/10.1016/0045-7825(96)00991-7</a>.'
  ieee: 'R. Mahnken and E. Stein, “A unified approach for parameter identification
    of inelastic material models in the frame of the finite element method,” <i>Computer
    Methods in Applied Mechanics and Engineering</i>, vol. 136, no. 3–4, pp. 225–258,
    2002, doi: <a href="https://doi.org/10.1016/0045-7825(96)00991-7">10.1016/0045-7825(96)00991-7</a>.'
  mla: Mahnken, Rolf, and Erwin Stein. “A Unified Approach for Parameter Identification
    of Inelastic Material Models in the Frame of the Finite Element Method.” <i>Computer
    Methods in Applied Mechanics and Engineering</i>, vol. 136, no. 3–4, Elsevier
    BV, 2002, pp. 225–58, doi:<a href="https://doi.org/10.1016/0045-7825(96)00991-7">10.1016/0045-7825(96)00991-7</a>.
  short: R. Mahnken, E. Stein, Computer Methods in Applied Mechanics and Engineering
    136 (2002) 225–258.
date_created: 2023-05-31T12:22:58Z
date_updated: 2023-05-31T12:23:36Z
department:
- _id: '9'
- _id: '154'
doi: 10.1016/0045-7825(96)00991-7
intvolume: '       136'
issue: 3-4
keyword:
- Computer Science Applications
- General Physics and Astronomy
- Mechanical Engineering
- Mechanics of Materials
- Computational Mechanics
language:
- iso: eng
page: 225-258
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: A unified approach for parameter identification of inelastic material models
  in the frame of the finite element method
type: journal_article
user_id: '335'
volume: 136
year: '2002'
...
---
_id: '45428'
author:
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
- first_name: Erwin
  full_name: Stein, Erwin
  last_name: Stein
citation:
  ama: Mahnken R, Stein E. Parameter identification for finite deformation elasto-plasticity
    in principal directions. <i>Computer Methods in Applied Mechanics and Engineering</i>.
    2002;147(1-2):17-39. doi:<a href="https://doi.org/10.1016/s0045-7825(97)00008-x">10.1016/s0045-7825(97)00008-x</a>
  apa: Mahnken, R., &#38; Stein, E. (2002). Parameter identification for finite deformation
    elasto-plasticity in principal directions. <i>Computer Methods in Applied Mechanics
    and Engineering</i>, <i>147</i>(1–2), 17–39. <a href="https://doi.org/10.1016/s0045-7825(97)00008-x">https://doi.org/10.1016/s0045-7825(97)00008-x</a>
  bibtex: '@article{Mahnken_Stein_2002, title={Parameter identification for finite
    deformation elasto-plasticity in principal directions}, volume={147}, DOI={<a
    href="https://doi.org/10.1016/s0045-7825(97)00008-x">10.1016/s0045-7825(97)00008-x</a>},
    number={1–2}, journal={Computer Methods in Applied Mechanics and Engineering},
    publisher={Elsevier BV}, author={Mahnken, Rolf and Stein, Erwin}, year={2002},
    pages={17–39} }'
  chicago: 'Mahnken, Rolf, and Erwin Stein. “Parameter Identification for Finite Deformation
    Elasto-Plasticity in Principal Directions.” <i>Computer Methods in Applied Mechanics
    and Engineering</i> 147, no. 1–2 (2002): 17–39. <a href="https://doi.org/10.1016/s0045-7825(97)00008-x">https://doi.org/10.1016/s0045-7825(97)00008-x</a>.'
  ieee: 'R. Mahnken and E. Stein, “Parameter identification for finite deformation
    elasto-plasticity in principal directions,” <i>Computer Methods in Applied Mechanics
    and Engineering</i>, vol. 147, no. 1–2, pp. 17–39, 2002, doi: <a href="https://doi.org/10.1016/s0045-7825(97)00008-x">10.1016/s0045-7825(97)00008-x</a>.'
  mla: Mahnken, Rolf, and Erwin Stein. “Parameter Identification for Finite Deformation
    Elasto-Plasticity in Principal Directions.” <i>Computer Methods in Applied Mechanics
    and Engineering</i>, vol. 147, no. 1–2, Elsevier BV, 2002, pp. 17–39, doi:<a href="https://doi.org/10.1016/s0045-7825(97)00008-x">10.1016/s0045-7825(97)00008-x</a>.
  short: R. Mahnken, E. Stein, Computer Methods in Applied Mechanics and Engineering
    147 (2002) 17–39.
date_created: 2023-05-31T12:21:53Z
date_updated: 2023-05-31T12:22:12Z
department:
- _id: '9'
- _id: '154'
doi: 10.1016/s0045-7825(97)00008-x
intvolume: '       147'
issue: 1-2
keyword:
- Computer Science Applications
- General Physics and Astronomy
- Mechanical Engineering
- Mechanics of Materials
- Computational Mechanics
language:
- iso: eng
page: 17-39
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: Parameter identification for finite deformation elasto-plasticity in principal
  directions
type: journal_article
user_id: '335'
volume: 147
year: '2002'
...