2018/09/27 by Mikyoung Lim, Graeme W. Milton, Lim, Mikyoung +1
Computer Science · Engineering · #35B30 #35Q74 #Advanced Mathematical Modeling in Engineering #Classical Physics (physics.class-ph) #Composite Material Mechanics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1809.10373
openalex publication_date 2018/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For certain shapes of inclusions embedded in a body, the field inside the\ninclusion is uniform for some boundary condition. We provide a construction\nscheme for inclusions of general shapes having such a uniformity property in\ntwo dimensions based on the conformal mapping technique for the potential\nproblem. Using this complex analysis method, we also design non-elliptical\nneutral coated inclusions with anisotropic conductivity. Neutral coated\ninclusions do not perturb a background uniform field when they are inserted\ninto a homogeneous matrix. Although coated inclusions of various shapes are\nneutral to a single field, only concentric ellipses or confocal ellipsoids can\nbe neutral to all uniform fields. This paper presents our work relating to the\nconstruction of non-elliptical coated inclusions with anisotropic conductivity\nin two dimensions that are neutral to all uniform fields, where the assignment\nof the flux condition on the boundary of the core depends on the applied\nbackground field. Using these neutral inclusions, we obtain cylindrical neutral\ninclusions in three dimensions, with no flux applied to the boundary of the\ncore and with the anisotropic conductivity function of the shell given in\naccordance with the background uniform field.\n