---
_id: '9862'
abstract:
- lang: eng
  text: 'In order to improve the credibility of modern simulation tools, uncertainties
    of different kinds have to be considered. This work is focused on epistemic uncertainties
    in the framework of continuum mechanics, which are taken into account by fuzzy
    analysis. The underlying min-max optimization problem of the extension principle
    is approximated by α-discretization, resulting in a separation of minimum and
    maximum problems. To become more universal, so-called quantities of interest are
    employed, which allow a general formulation for the target problem of interest.
    In this way, the relation to parameter identification problems based on least-squares
    functions is highlighted. The solutions of the related optimization problems with
    simple constraints are obtained with a gradient-based scheme, which is derived
    from a sensitvity analysis for the target problem by means of a variational formulation.
    Two numerical examples for the fuzzy analysis of material parameters are concerned
    with a necking problem at large strain elastoplasticity and a perforated strip
    at large strain hyperelasticity to demonstrate the versatility of the proposed
    variational formulation. '
author:
- first_name: Rolf
  full_name: Mahnken, Rolf
  last_name: Mahnken
citation:
  ama: Mahnken R. “A variational formulation for fuzzy analysis in continuum mechanics.”
    <i>Mathematics and Mechanics of complex systems</i>. 2017;5(3-4).
  apa: Mahnken, R. (2017). “A variational formulation for fuzzy analysis in continuum
    mechanics.” <i>Mathematics and Mechanics of Complex Systems</i>, <i>5</i>(3–4).
  bibtex: '@article{Mahnken_2017, title={“A variational formulation for fuzzy analysis
    in continuum mechanics”}, volume={5}, number={3–4}, journal={Mathematics and Mechanics
    of complex systems}, author={Mahnken, Rolf}, year={2017} }'
  chicago: Mahnken, Rolf. “‘A Variational Formulation for Fuzzy Analysis in Continuum
    Mechanics.’” <i>Mathematics and Mechanics of Complex Systems</i> 5, no. 3–4 (2017).
  ieee: R. Mahnken, “‘A variational formulation for fuzzy analysis in continuum mechanics,’”
    <i>Mathematics and Mechanics of complex systems</i>, vol. 5, no. 3–4, 2017.
  mla: Mahnken, Rolf. “‘A Variational Formulation for Fuzzy Analysis in Continuum
    Mechanics.’” <i>Mathematics and Mechanics of Complex Systems</i>, vol. 5, no.
    3–4, 2017.
  short: R. Mahnken, Mathematics and Mechanics of Complex Systems 5 (2017).
date_created: 2019-05-20T11:36:47Z
date_updated: 2019-05-27T12:54:35Z
department:
- _id: '154'
intvolume: '         5'
issue: 3-4
keyword:
- fuzzy analysis
- α-level optimization
- quantities of interest
- optimization with simple constraints
- large strain elasticity
- large strain elastoplasticity
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://msp.org/memocs/2017/5-3/memocs-v5-n3-p03-s.pdf
oa: '1'
publication: Mathematics and Mechanics of complex systems
publication_identifier:
  issn:
  - ' 2325-3444'
publication_status: published
status: public
title: '"A variational formulation for fuzzy analysis in continuum mechanics"'
type: journal_article
user_id: '78813'
volume: 5
year: '2017'
...