University of Cambridge > Talks.cam > Engineering Department Bio- and Micromechanics Seminars > Effective constitutive relations for waves in composites and metamaterials

Effective constitutive relations for waves in composites and metamaterials

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The description of waves propagating through strongly-heterogeneous material requires some kind of averaging to be performed. Here, the material is taken to be random and ensemble averaging is considered; it is noted in this context that, although the ensemble average is not seen in any one realisation, it nevertheless provides a scaffold upon which the solution in any particular realisation can in principle be built. In practice, resort must be made to approximations. This work establishes exact variational principles which the ensemble averaged solutions must satisfy, and from which “effective constitutive relations” follow. It is demonstrated also that a similar variational structure follows if weighted ensemble averages are employed. Such weighted averages are relevant to so-called metamaterials which contain micro-resonators, whose displacements are best excluded from the averaging process.

This talk is part of the Engineering Department Bio- and Micromechanics Seminars series.

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