Singular analysis of the stress concentration in the narrow regions between the inclusions and the matrix boundary

Abstract

We consider the Lamé system arising from high-contrast composite materials whose inclusions (fibers) are nearly touching the matrix boundary. The stress, which is the gradient of the solution, always concentrates highly in the narrow regions between the inclusions and the external boundary. This paper aims to provide a complete characterization in terms of the singularities of the stress concentration by accurately capturing all the blow-up factor matrices and making clear the dependence on the Lamé constants and the curvature parameters of geometry. Moreover, the precise asymptotic expansions of the stress concentration are also presented in the presence of a strictly convex inclusion close to touching the external boundary for the convenience of application.

Minor revision

References in corpus (1)

• Boundary blow-up analysis of gradient estimates for Lamé systems in the presence of $M$-convex hard inclusions

Cited by in corpus (1)

• Asymptotic analysis of the stress concentration between two adjacent stiff inclusions in all dimensions