  Since the seminal contribution of Geymonat, M{\"u}ller, and Triantafyllidis,
it is known that strong ellipticity is not necessarily conserved by
homogenization in linear elasticity. This phenomenon is typically related to
microscopic buckling of the composite material. The present contribution is
concerned with the interplay between isotropy and strong ellipticity in the
framework of periodic homogenization in linear elasticity. Mixtures of two
isotropic phases may indeed lead to loss of strong ellipticity when arranged in
a laminate manner. We show that if a matrix/inclusion type mixture of isotropic
phases produces macroscopic isotropy, then strong ellipticity cannot be lost.
R{\'e}sum{\'e}. Nous savons depuis l'article fondateur de Geymonat, M{\"u}ller
et Triantafyl-lidis qu'en{\'e}lasticit{\'e}en{\'e}lasticit{\'e} lin{\'e}aire
l'homog{\'e}n{\'e}isation p{\'e}riodique ne conserve pas n{\'e}cessairement
l'ellipticit{\'e} forte. Ce ph{\'e}nom{\`e}ne est li{\'e} au flambage
microscopique des composites. Notre contribution consiste examiner le r{\^o}le
de l'isotropie dans ce type de pathologie. Le m{\'e}lange de deux phases
isotropes peut en effet conduir{\`e} a cette perte si l'arrangement est celui
d'un lamin{\'e}. Nous montrons qu'en revanche, si un arrangement de type
ma-trice/inclusion produit un tenseur homog{\'e}n{\'e}is{\'e} isotrope, alors
la forte ellipticit{\'e} est con-serv{\'e}e.
