Inelastic media under uncertainty: Stochastic models and computational approaches

Hermann G. Matthies*, Bojana V. Rosíc

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

9 Citations (Scopus)

Abstract

We discuss inelastic media under uncertainty modelled by probabilistic methods. As a prototype inelastic material we consider perfect plasticity.We propose a mathematical formulation as a stochastic variational inequality. The new element vis à vis a stochastic elastic medium is the so-called return map at each Gauss-point. We concentrate on a stochastic version of this, showing how it may be solved via (generalised) polynomial expansion. Explicit formulas are provided for plane strain, together with results from example computations, giving a stochastic inelastic or irreversible time-step procedure. This may serve as a prototype example for any other irreversible behaviour, especially of the rate-independent kind.

Original languageEnglish
Title of host publicationIUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media - Proceedings of the IUTAM Symposium
Subtitle of host publicationProceedings of the IUTAM Symposium held at Cape Town, South Africa, January 14–18, 2008
EditorsB. Daya Reddy
Place of PublicationDordrecht
PublisherSpringer
Pages185-194
Number of pages10
ISBN (Electronic)978-1-4020-9090-5
ISBN (Print)978-1-4020-9089-9
DOIs
Publication statusPublished - 1 Jan 2008
Externally publishedYes
EventIUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media 2008 - Cape Town, South Africa
Duration: 14 Jan 200818 Jan 2008

Publication series

NameIUTAM Bookseries
PublisherSpringer
Volume11
ISSN (Print)1875-3507

Conference

ConferenceIUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media 2008
CountrySouth Africa
CityCape Town
Period14/01/0818/01/08

Keywords

  • Chaos expansion
  • Inelastic irreversible behaviour
  • Stochastic generalised return map
  • Stochastic model
  • Stochastic variational inequality
  • Uncertainty

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  • Cite this

    Matthies, H. G., & Rosíc, B. V. (2008). Inelastic media under uncertainty: Stochastic models and computational approaches. In B. D. Reddy (Ed.), IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media - Proceedings of the IUTAM Symposium: Proceedings of the IUTAM Symposium held at Cape Town, South Africa, January 14–18, 2008 (pp. 185-194). (IUTAM Bookseries; Vol. 11). Dordrecht: Springer. https://doi.org/10.1007/978-1-4020-9090-5_17