Title: A proof of the Flaherty-Keller formula on the effective property of densely packed elastic composites,
Abstract: We prove in a mathematically rigorous way the asymptotic formula of Flaherty
and Keller on the effective property of densely packed periodic elastic
composites with hard inclusions. The proof is based on the primal-dual
variational principle, where the upper bound is derived by using the
Keller-type test functions and the lower bound by singular functions made of
nuclei of strain. Singular functions are solutions of the Lamé system and
capture precisely singular behavior of the stress in the narrow region between
two adjacent hard inclusions.