Singularities of the stress concentration in the presence of $C^{1,α}$-inclusions with core-shell geometry

Abstract

In high-contrast composites, if an inclusion is in close proximity to the matrix boundary, then the stress, which is represented by the gradient of a solution to the Lamé systems of linear elasticity, may exhibits the singularities with respect to the distance ε between them. In this paper, we establish the asymptotic formulas of the stress concentration for core-shell geometry with C 1,α boundaries in all dimensions by precisely capturing all the blow-up factor matrices, as the distance ε between interfacial boundaries of a core and a surrounding shell goes to zero. Further, a direct application of these blow-up factor matrices gives the optimal gradient estimates.