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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) |Du|2
dx ,
and let F be another functional. If the sequence (Fh) is -
(L2
)-converging to F, then for every g H-1
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-
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