---
_id: '49866'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>The use of heterogeneous materials,
    such as composites with Prandtl‐Reuss‐type material laws, has increased in industrial
    praxis, making finite element modeling with homogenization techniques a well‐accepted
    tool. These methods are particularly advantageous to account for microstructural
    mechanisms which can be related to nonlinearities and time‐dependency due to elasto‐plasticity
    behavior. However, their advantages are diminished by increasing computational
    demand. The present contribution deals with the balance of accuracy and numerical
    efficiency of nonlinear homogenization associated with a framework of goal‐oriented
    adaptivity, which takes into account error accumulation over time. To this end,
    model adaptivity of homogenization methods is coupled to mesh adaptivity on the
    macro scale. Our new proposed adaptive procedure is driven by a goal‐oriented
    a posteriori error estimator based on duality techniques using downwind and upwind
    approximations. Due to nonlinearities and time‐dependency of the plasticity, the
    estimation of error transport and error generation is obtained with a backward‐in‐time
    dual method despite a high demand on memory capacity. In this contribution, the
    dual problem is solved with a forward‐in‐time dual method that allows estimating
    the full error during the resolution of the primal problem without the need for
    extra memory capacity. Finally, a numerical example illustrates the effectiveness
    of the proposed adaptive approach.</jats:p>
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. Downwind and upwind approximations for mesh and
    model adaptivity of elasto‐plastic composites. <i>PAMM</i>. Published online 2023.
    doi:<a href="https://doi.org/10.1002/pamm.202300136">10.1002/pamm.202300136</a>
  apa: Tchomgue Simeu, A., &#38; Mahnken, R. (2023). Downwind and upwind approximations
    for mesh and model adaptivity of elasto‐plastic composites. <i>PAMM</i>. <a href="https://doi.org/10.1002/pamm.202300136">https://doi.org/10.1002/pamm.202300136</a>
  bibtex: '@article{Tchomgue Simeu_Mahnken_2023, title={Downwind and upwind approximations
    for mesh and model adaptivity of elasto‐plastic composites}, DOI={<a href="https://doi.org/10.1002/pamm.202300136">10.1002/pamm.202300136</a>},
    journal={PAMM}, publisher={Wiley}, author={Tchomgue Simeu, Arnold and Mahnken,
    Rolf}, year={2023} }'
  chicago: Tchomgue Simeu, Arnold, and Rolf Mahnken. “Downwind and Upwind Approximations
    for Mesh and Model Adaptivity of Elasto‐plastic Composites.” <i>PAMM</i>, 2023.
    <a href="https://doi.org/10.1002/pamm.202300136">https://doi.org/10.1002/pamm.202300136</a>.
  ieee: 'A. Tchomgue Simeu and R. Mahnken, “Downwind and upwind approximations for
    mesh and model adaptivity of elasto‐plastic composites,” <i>PAMM</i>, 2023, doi:
    <a href="https://doi.org/10.1002/pamm.202300136">10.1002/pamm.202300136</a>.'
  mla: Tchomgue Simeu, Arnold, and Rolf Mahnken. “Downwind and Upwind Approximations
    for Mesh and Model Adaptivity of Elasto‐plastic Composites.” <i>PAMM</i>, Wiley,
    2023, doi:<a href="https://doi.org/10.1002/pamm.202300136">10.1002/pamm.202300136</a>.
  short: A. Tchomgue Simeu, R. Mahnken, PAMM (2023).
date_created: 2023-12-19T12:20:05Z
date_updated: 2023-12-19T12:20:51Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.1002/pamm.202300136
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: Downwind and upwind approximations for mesh and model adaptivity of elasto‐plastic
  composites
type: journal_article
user_id: '335'
year: '2023'
...