2015/01/29 by Hyeonbae Kang, Kang, Hyeonbae, Hyundae Lee +3
Computer Science · Engineering · #35N25 #35Q60 #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.1501.07465
openalex publication_date 2015/01/29 · openalex created_date 2022/03/02 · openalex updated_date 2026/07/28
We consider the neutral inclusion problem in three dimensions which is to\nprove if a coated structure consisting of a core and a shell is neutral to all\nuniform fields, then the core and the shell must be concentric balls if the\nmatrix is isotropic and confocal ellipsoids if the matrix is anisotropic. We\nfirst derive an over-determined boundary value problem in the shell of the\nneutral inclusion, and then prove in the isotropic case that if the over-\ndetermined problem admits a solution, then the core and the shell must be\nconcentric balls. As a consequence it is proved that the structure is neutral\nto all uniform fields if and only if it consists of concentric balls provided\nthat the coefficient of the core is larger than that of the shell.\n