Homogenization theory and multiscale numerical approaches for disordered media: some recent contributions***

E-ISSN： 2267-3059|45|issue|18-31

ISSN： 2267-3059

Source： ESAIM: Proceedings and surveys, Vol.45, Iss.issue, 2014-11, pp. : 18-31

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Abstract

We overview a series of recent works related to some multiscale problems motivated by practical problems in Mechanics. The common denominator of all these works is that they address multiscale problems where the geometry of the microstructures is not periodic. Random modelling, as well as other types of nonperiodic modelling, can then be used to account for the imperfections of the medium. The theory at play is that of homogenization, in its many variants (stochastic, general deterministic, periodic). The numerical methods developed and adapted are finite element type methods. A special emphasis is laid on situations where the amount of randomness is small, or, put differently, when the disorder is limited. Then, specific, computationally efficient techniques can be designed and employed.