---
res:
  bibo_abstract:
  - <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>@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Arnold
      foaf_name: Tchomgue Simeu, Arnold
      foaf_surname: Tchomgue Simeu
      foaf_workInfoHomepage: http://www.librecat.org/personId=83075
  - foaf_Person:
      foaf_givenName: Rolf
      foaf_name: Mahnken, Rolf
      foaf_surname: Mahnken
      foaf_workInfoHomepage: http://www.librecat.org/personId=335
  bibo_doi: 10.1002/pamm.202300136
  dct_date: 2023^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/1617-7061
  - http://id.crossref.org/issn/1617-7061
  dct_language: eng
  dct_publisher: Wiley@
  dct_subject:
  - Electrical and Electronic Engineering
  - Atomic and Molecular Physics
  - and Optics
  dct_title: Downwind and upwind approximations for mesh and model adaptivity of elasto‐plastic
    composites@
...