2014/01/25 by Yuliya Gorb, Gorb, Yuliya · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Applied mathematics #Artificial intelligence #Composite Material Mechanics #Computer science #Contrast (vision) #Elasticity and Wave Propagation #Electric field #Energy (signal processing) #FOS: Mathematics #Field (mathematics) #Generalization #Geometry #Materials science #Mathematical analysis #Mathematics #Mechanics #Nonlinear system #Physics #Pure mathematics #Statistical physics #Term (time) #Vector field #math.AP
paper · pdf · doi:10.48550/arxiv.1401.6556
arxiv created 2014/01/25 · openalex publication_date 2014/01/25 · arxiv updated 2014/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
A heterogeneous medium of constituents with vastly different mechanical\nproperties, whose inhomogeneities are in close proximity to each other, is\nconsidered. The gradient of the solution to the corresponding problem exhibits\nsingular behavior (blow up) with respect to the distance between\ninhomogeneities. This paper introduces a concise procedure for capturing the\nleading term of gradient's asymptotics precisely. This procedure is based on a\nthorough study of the system's energy. The developed methodology allows for\nstraightforward generalization to heterogeneous media with a nonlinear\nconstitutive description.\n