A proof of the Flaherty-Keller formula on the effective property of densely packed elastic composites

2017/07/07 by Hyeonbae Kang, Kang, Hyeonbae, Sanghyeon Yu +1
Computer Science · Engineering · #35J47 #74B05 #74Q20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #Contact Mechanics and Variational Inequalities #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1707.02205

openalex publication_date 2017/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Gradient estimates for solutions of the Lamé system with partially infinite coefficients in dimensions greater than two

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