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New Counterexamples to the Cell Formula in Nonconvex Homogenization

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Abstract

In this article we show that for the homogenization of multiple integrals, the quasiconvexification of the cell formula is different from the asymptotic formula in general. To this aim, we construct three examples in three different settings: the homogenization of a discrete model, the homogenization of a composite material and the homogenization of a homogeneous material on a perforated domain.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Marco Barchiesi

  2. Project-team SIMPAF, INRIA Lille-Nord Europe, 40 avenue Halley, 59650, Villeneuve d’Ascq, France

    Antoine Gloria

Authors
  1. Marco Barchiesi
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  2. Antoine Gloria
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Correspondence to Antoine Gloria.

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Communicated by S. Müller

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Barchiesi, M., Gloria, A. New Counterexamples to the Cell Formula in Nonconvex Homogenization. Arch Rational Mech Anal 195, 991–1024 (2010). https://doi.org/10.1007/s00205-009-0226-9

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  • DOI: https://doi.org/10.1007/s00205-009-0226-9

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