Singular Behavior of Electric Field of High-Contrast Concentrated Composites

A heterogeneous medium of constituents with vastly different mechanical properties, whose inhomogeneities are in close proximity to each other, is considered. The gradient of the solution to the corresponding problem exhibits singular behavior (blow up) with respect to the distance between inhomogeneities. This paper introduces a concise procedure for capturing the leading term of the gradient’s asymptotics precisely, which is based on thorough study of the system’s energy. The methodology developed in the paper allows for a straightforward generalization to heterogeneous media with a nonlinear constitutive description.