---
_id: '30644'
abstract:
- lang: eng
  text: Computational homogenization is a powerful tool allowing to obtain homogenized
    properties of materials on the macroscale from simulations of the underlying microstructure.
    The response of the microstructure is, however, strongly affected by variations
    in the microstructure geometry. In particular, we consider heterogeneous materials
    with randomly distributed non-overlapping inclusions, which radii are also random.
    In this work we extend the earlier proposed non-deterministic computational homogenization
    framework to plastic materials, thereby increasing the model versatility and overall
    realism. We apply novel soft periodic boundary conditions and estimate their effect
    in case of non-periodic material microstructures. We study macroscopic plasticity
    signatures like the macroscopic von-Mises stress and make useful conclusions for
    further constitutive modeling. Simulations demonstrate the effect of the novel
    boundary conditions, which significantly differ from the standard periodic boundary
    conditions, and the large influence of parameter variations and hence the importance
    of the stochastic modeling.
author:
- first_name: D.
  full_name: Pivovarov, D.
  last_name: Pivovarov
- first_name: J.
  full_name: Mergheim, J.
  last_name: Mergheim
- first_name: K.
  full_name: Willner, K.
  last_name: Willner
- first_name: P.
  full_name: Steinmann, P.
  last_name: Steinmann
citation:
  ama: Pivovarov D, Mergheim J, Willner K, Steinmann P. Stochastic local FEM for computational
    homogenization of heterogeneous materials exhibiting large plastic deformations.
    <i>Computational Mechanics</i>. Published online 2021. doi:<a href="https://doi.org/10.1007/s00466-021-02099-x">10.1007/s00466-021-02099-x</a>
  apa: Pivovarov, D., Mergheim, J., Willner, K., &#38; Steinmann, P. (2021). Stochastic
    local FEM for computational homogenization of heterogeneous materials exhibiting
    large plastic deformations. <i>Computational Mechanics</i>. <a href="https://doi.org/10.1007/s00466-021-02099-x">https://doi.org/10.1007/s00466-021-02099-x</a>
  bibtex: '@article{Pivovarov_Mergheim_Willner_Steinmann_2021, title={Stochastic local
    FEM for computational homogenization of heterogeneous materials exhibiting large
    plastic deformations}, DOI={<a href="https://doi.org/10.1007/s00466-021-02099-x">10.1007/s00466-021-02099-x</a>},
    journal={Computational Mechanics}, author={Pivovarov, D. and Mergheim, J. and
    Willner, K. and Steinmann, P.}, year={2021} }'
  chicago: Pivovarov, D., J. Mergheim, K. Willner, and P. Steinmann. “Stochastic Local
    FEM for Computational Homogenization of Heterogeneous Materials Exhibiting Large
    Plastic Deformations.” <i>Computational Mechanics</i>, 2021. <a href="https://doi.org/10.1007/s00466-021-02099-x">https://doi.org/10.1007/s00466-021-02099-x</a>.
  ieee: 'D. Pivovarov, J. Mergheim, K. Willner, and P. Steinmann, “Stochastic local
    FEM for computational homogenization of heterogeneous materials exhibiting large
    plastic deformations,” <i>Computational Mechanics</i>, 2021, doi: <a href="https://doi.org/10.1007/s00466-021-02099-x">10.1007/s00466-021-02099-x</a>.'
  mla: Pivovarov, D., et al. “Stochastic Local FEM for Computational Homogenization
    of Heterogeneous Materials Exhibiting Large Plastic Deformations.” <i>Computational
    Mechanics</i>, 2021, doi:<a href="https://doi.org/10.1007/s00466-021-02099-x">10.1007/s00466-021-02099-x</a>.
  short: D. Pivovarov, J. Mergheim, K. Willner, P. Steinmann, Computational Mechanics
    (2021).
date_created: 2022-03-28T12:24:19Z
date_updated: 2022-03-29T12:42:38Z
doi: 10.1007/s00466-021-02099-x
language:
- iso: eng
project:
- _id: '130'
  grant_number: '418701707'
  name: 'TRR 285: TRR 285'
- _id: '131'
  name: 'TRR 285 - A: TRR 285 - Project Area A'
- _id: '139'
  name: 'TRR 285 – A05: TRR 285 - Subproject A05'
publication: Computational Mechanics
status: public
title: Stochastic local FEM for computational homogenization of heterogeneous materials
  exhibiting large plastic deformations
type: journal_article
user_id: '68518'
year: '2021'
...