2018/07/26 by Doosung Choi, Choi, Doosung, Kyoungsun Kim +3
Engineering · #30C35 #35J05 #45P05 #Analysis of PDEs (math.AP) #Composite Material Mechanics #Composite Structure Analysis and Optimization #Elasticity and Material Modeling #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1807.09981
openalex publication_date 2018/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
According to the Eshelby conjecture, an ellipse or ellipsoid is the only\nshape that induces an interior uniform strain under a uniform far-field\nloading. We extend the Eshelby conjecture to domains of general shape for\nanti-plane elasticity. Specifically, we show that for each positive integer\nN, an inclusion induces an interior uniform strain under a polynomial loading\nof degree N if and only if the exterior conformal map of the inclusion is a\nLaurent series of degree N. Furthermore, for the isotropic case, we\ncharacterize the shape of an inclusion by only using the first-degree\npolynomial loading and explicitly solve the interior potential of the inclusion\nin terms of the Grunsky coefficients.\n