Inelastic media under uncertainty: Stochastic models and computational approaches

Hermann G. Matthies; Bojana V. Rosíc

doi:10.1007/978-1-4020-9090-5_17

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 proceeding › Conference contribution › Academic › peer-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 language	English
Title of host publication	IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media - Proceedings of the IUTAM Symposium
Subtitle of host publication	Proceedings of the IUTAM Symposium held at Cape Town, South Africa, January 14–18, 2008
Editors	B. Daya Reddy
Place of Publication	Dordrecht
Publisher	Springer
Pages	185-194
Number of pages	10
ISBN (Electronic)	978-1-4020-9090-5
ISBN (Print)	978-1-4020-9089-9
DOIs	https://doi.org/10.1007/978-1-4020-9090-5_17
Publication status	Published - 1 Jan 2008
Externally published	Yes
Event	IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media 2008 - Cape Town, South Africa Duration: 14 Jan 2008 → 18 Jan 2008

Publication series

Name	IUTAM Bookseries
Publisher	Springer
Volume	11
ISSN (Print)	1875-3507

Conference

Conference	IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media 2008
Country	South Africa
City	Cape Town
Period	14/01/08 → 18/01/08

Keywords

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

Access to Document

10.1007/978-1-4020-9090-5_17

Link to publication in Scopus

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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

Matthies, Hermann G. ; Rosíc, Bojana V. / Inelastic media under uncertainty : Stochastic models and computational approaches. 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. editor / B. Daya Reddy. Dordrecht : Springer, 2008. pp. 185-194 (IUTAM Bookseries).

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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 {\`a} 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.",

keywords = "Chaos expansion, Inelastic irreversible behaviour, Stochastic generalised return map, Stochastic model, Stochastic variational inequality, Uncertainty",

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Matthies, HG & Rosíc, BV 2008, Inelastic media under uncertainty: Stochastic models and computational approaches. in BD 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. IUTAM Bookseries, vol. 11, Springer, Dordrecht, pp. 185-194, IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media 2008, Cape Town, South Africa, 14/01/08. https://doi.org/10.1007/978-1-4020-9090-5_17

Inelastic media under uncertainty : Stochastic models and computational approaches. / Matthies, Hermann G.; Rosíc, Bojana V.

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. ed. / B. Daya Reddy. Dordrecht : Springer, 2008. p. 185-194 (IUTAM Bookseries; Vol. 11).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AB - 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.

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Matthies HG, Rosíc BV. Inelastic media under uncertainty: Stochastic models and computational approaches. In Reddy BD, editor, 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. Dordrecht: Springer. 2008. p. 185-194. (IUTAM Bookseries). https://doi.org/10.1007/978-1-4020-9090-5_17