The limit behavior of the solutions of Signorini's type-like
problems in periodically perforated domains with period
ε is studied. The main feature of this limit behaviour is
the existence of a critical size of the perforations that
separates different emerging phenomena as ε → 0. In the critical case, it is shown that Signorini's problem
converges to a problem associated to a new operator which
is the sum of a standard homogenized operator and an extra zero
order term (“strange term”) coming from the geometry; its
appearance is due to the special size of the holes. The limit
problem captures the two sources of oscillations involved in this
kind of free boundary-value problems, namely, those arising from
the size of the holes and those due to the periodic inhomogeneity
of the medium. The main ingredient of the method used in the proof
is an explicit construction of suitable test functions which
provide a good understanding of the interactions between the above
mentioned sources of oscillations.