Stress concentration factors for the Lamé system arising from composites

For two neighboring stiff inclusions, the stress, which is the gradient of a solution to the Lamé system of linear elasticity, may exhibit singular behavior as the distance between these two inclusions becomes arbitrarily small. The main contribution of this paper lies in accurately constructing a family of unified stress concentration factors, which determine whether the stress will blow up or not, in the presence of generalized $m$-convex inclusions in all dimensions. As a consequence, we establish the optimal upper and lower bounds on stress blow-up rates in any dimension.