Localized modeling of uncertainty in the Arlequin framework

  • R. Cottereau
  • D. Clouteau
  • H. Ben Dhia
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 27)


This paper discusses the coupling and interaction of a classical continuum model with another continuum model with random parameters. The former model, deterministic, aims at representing a part of the domain where the local fluctuations of the parameters, such as Young’s modulus, do not influence the output of interest in a significant manner, and where a homogenized model is sufficient to predict this output. The latter model, stochastic, stands for the part of the domain where the local behavior is of interest and the fluctuations of the parameters cannot be considered only in a homogenized way. The coupling of these models is performed in the Arlequin framework. This paper focuses on the technical definitions of the spaces and operators introduced in the Arlequin framework for that particular problem, and on the definition of the corresponding discretized formulations. A simple example is shown, emphasizing the gain in computational power to compute the mean and confidence intervals in the region of interest.


Representative Volume Element Homogeneous Dirichlet Boundary Condition Representative Volume Element Size Coupling Zone Indented Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Laboratoire MSSMatÉcole Centrale Paris, CNRS UMR 8579Châtenay-Malabry cedexFrance

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