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Stochastic Multiscale Coupling of Inelastic Processes in Solid Mechanics

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Multiscale Modeling and Uncertainty Quantification of Materials and Structures

Abstract

Here we consider the inelastic nonlinear response of heterogeneous materials, possibly undergoing localised failure. We regard the material to be heterogeneous on many scales, but for simplicity we only look at one scale transition. The micro-scale is regarded as incompletely known and hence uncertain, therefore modelled probabilistically. Two alternative approaches are discussed: one for localised regions where a rather detailed micro-description is necessary to capture relevant effects, and the other in domains where it is accurate enough to define phenomenological models of ‘generalised standard materials’ on the macro-scale, which have to be identified via micro-scale computations. Apart from a proper transfer of mechanical quantities across scales, the same has to be achieved for the stochastic part of the model. Several main ingredients of the proposed approaches are discussed in detail, including micro-structure approximation with a structured mesh, random field representation, and Bayesian updating.

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Acknowledgements

This work was partially supported by the French Ministry of Research, the Franco-German University (DFH-UFA), and the German research foundation “Deutsche Forschungsgemeinschaft” (DFG).

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Authors and Affiliations

  1. TU Braunschweig, Brunswick, Germany

    Hermann G. Matthies

  2. ENS Cachan, Paris, France

    Adnan Ibrahimbegović

Authors
  1. Hermann G. Matthies
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  2. Adnan Ibrahimbegović
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Correspondence to Hermann G. Matthies .

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Editors and Affiliations

  1. Institute of Structural Analysis & Antiseismic Research, National Technical University of Athens, Athens, Greece

    Manolis Papadrakakis

  2. Institute of Structural Analysis & Antiseismic Research, National Technical University of Athens, Athens, Greece

    George Stefanou

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Matthies, H.G., Ibrahimbegović, A. (2014). Stochastic Multiscale Coupling of Inelastic Processes in Solid Mechanics. In: Papadrakakis, M., Stefanou, G. (eds) Multiscale Modeling and Uncertainty Quantification of Materials and Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-06331-7_9

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  • DOI: https://doi.org/10.1007/978-3-319-06331-7_9

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