---
_id: '10175'
abstract:
- lang: eng
  text: We study periodic homogenization by Γ-convergence of integral functionals
    with integrands W(x,ξ) having no polynomial growth and which are both not necessarily
    continuous with respect to the space variable and not necessarily convex with
    respect to the matrix variable. This allows to deal with homogenization of composite
    hyperelastic materials consisting of two or more periodic components whose the
    energy densities tend to infinity as the volume of matter tends to zero, i.e.,
    W(x,ξ)=∑j∈J1Vj(x)Hj(ξ) where {Vj}j∈J is a finite family of open disjoint subsets
    of RN, with |∂Vj|=0 for all j∈J and ∣∣RN∖⋃j∈JVj|=0, and, for each j∈J, Hj(ξ)→∞
    as detξ→0. In fact, our results apply to integrands of type W(x,ξ)=a(x)H(ξ) when
    H(ξ)→∞ as detξ→0 and a∈L∞(RN;[0,∞[) is 1-periodic and is either continuous almost
    everywhere or not continuous. When a is not continuous, we obtain a density homogenization
    formula which is a priori different from the classical one by Braides–Müller.
    Although applications to hyperelasticity are limited due to the fact that our
    framework is not consistent with the constraint of noninterpenetration of the
    matter, our results can be of technical interest to analysis of homogenization
    of integral functionals.
article_processing_charge: No
article_type: original
author:
- first_name: Omar
  full_name: Anza Hafsa, Omar
  last_name: Anza Hafsa
- first_name: Nicolas
  full_name: Clozeau, Nicolas
  id: fea1b376-906f-11eb-847d-b2c0cf46455b
  last_name: Clozeau
- first_name: Jean-Philippe
  full_name: Mandallena, Jean-Philippe
  last_name: Mandallena
citation:
  ama: Anza Hafsa O, Clozeau N, Mandallena J-P. Homogenization of nonconvex unbounded
    singular integrals. <i>Annales mathématiques Blaise Pascal</i>. 2017;24(2):135-193.
    doi:<a href="https://doi.org/10.5802/ambp.367">10.5802/ambp.367</a>
  apa: Anza Hafsa, O., Clozeau, N., &#38; Mandallena, J.-P. (2017). Homogenization
    of nonconvex unbounded singular integrals. <i>Annales Mathématiques Blaise Pascal</i>.
    Université Clermont Auvergne. <a href="https://doi.org/10.5802/ambp.367">https://doi.org/10.5802/ambp.367</a>
  chicago: Anza Hafsa, Omar, Nicolas Clozeau, and Jean-Philippe Mandallena. “Homogenization
    of Nonconvex Unbounded Singular Integrals.” <i>Annales Mathématiques Blaise Pascal</i>.
    Université Clermont Auvergne, 2017. <a href="https://doi.org/10.5802/ambp.367">https://doi.org/10.5802/ambp.367</a>.
  ieee: O. Anza Hafsa, N. Clozeau, and J.-P. Mandallena, “Homogenization of nonconvex
    unbounded singular integrals,” <i>Annales mathématiques Blaise Pascal</i>, vol.
    24, no. 2. Université Clermont Auvergne, pp. 135–193, 2017.
  ista: Anza Hafsa O, Clozeau N, Mandallena J-P. 2017. Homogenization of nonconvex
    unbounded singular integrals. Annales mathématiques Blaise Pascal. 24(2), 135–193.
  mla: Anza Hafsa, Omar, et al. “Homogenization of Nonconvex Unbounded Singular Integrals.”
    <i>Annales Mathématiques Blaise Pascal</i>, vol. 24, no. 2, Université Clermont
    Auvergne, 2017, pp. 135–93, doi:<a href="https://doi.org/10.5802/ambp.367">10.5802/ambp.367</a>.
  short: O. Anza Hafsa, N. Clozeau, J.-P. Mandallena, Annales Mathématiques Blaise
    Pascal 24 (2017) 135–193.
date_created: 2021-10-23T10:54:23Z
date_published: 2017-11-20T00:00:00Z
date_updated: 2021-10-28T15:16:25Z
day: '20'
ddc:
- '510'
doi: 10.5802/ambp.367
extern: '1'
file:
- access_level: open_access
  checksum: 18f40d13dc5d1e24438260b1875b886f
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  creator: cziletti
  date_created: 2021-10-28T15:02:56Z
  date_updated: 2021-10-28T15:02:56Z
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has_accepted_license: '1'
intvolume: '        24'
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nd/3.0/
month: '11'
oa: 1
oa_version: Published Version
page: 135-193
publication: Annales mathématiques Blaise Pascal
publication_identifier:
  eissn:
  - 2118-7436
  issn:
  - 1259-1734
publication_status: published
publisher: Université Clermont Auvergne
quality_controlled: '1'
status: public
title: Homogenization of nonconvex unbounded singular integrals
tmp:
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  legal_code_url: https://creativecommons.org/licenses/by-nd/3.0/legalcode
  name: Creative Commons Attribution-NoDerivs 3.0 Unported (CC BY-ND 3.0)
  short: CC BY-ND (3.0)
type: journal_article
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volume: 24
year: '2017'
...