---
res:
bibo_abstract:
- 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.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Omar
foaf_name: Anza Hafsa, Omar
foaf_surname: Anza Hafsa
- foaf_Person:
foaf_givenName: Nicolas
foaf_name: Clozeau, Nicolas
foaf_surname: Clozeau
foaf_workInfoHomepage: http://www.librecat.org/personId=fea1b376-906f-11eb-847d-b2c0cf46455b
- foaf_Person:
foaf_givenName: Jean-Philippe
foaf_name: Mandallena, Jean-Philippe
foaf_surname: Mandallena
bibo_doi: 10.5802/ambp.367
bibo_issue: '2'
bibo_volume: 24
dct_date: 2017^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/1259-1734
- http://id.crossref.org/issn/2118-7436
dct_language: eng
dct_publisher: Université Clermont Auvergne@
dct_title: Homogenization of nonconvex unbounded singular integrals@
...