 
Summary: To appear on the Proceedings of the Symposium Year on
Material Instabilities and Continuum Mechanics
Homogenization of Periodic Structures With Holes
by EMILIO ACERBI
In the last decade, the concept of convergence of functionals has been widely investigated; to clarify its
link with mechanics, consider the following simple consequence of convergence.
Assume (Fh) is a sequence of functionals defined, say, on H1
0 , and all satisfying
(1) Fh(u) Du2
dx ,
and let F be another functional. If the sequence (Fh) is 
(L2
)converging to F, then for every g H1
and every minimizing sequence (uh) of
Fh(u) + g, u
we may select a subsequence (uhk
) converging in L2
to a minimum point of
F(u) + g, u .
If the functionals Fh are the free energies of some materials, then we may well say that the material repre
