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It is interesting to study the stress concentration between two adjacentstiff inclusions in composite materials, which can be modeled by the Lam\'esystem with partially infinite coefficients. To overcome the difficulty fromthe lack of maximum principle for elliptic systems, we use the energy methodand an iteration technique to study the gradient estimates of the solution. Wefirst find a novel phenomenon that the gradient will not blow up any more oncethese two adjacent inclusions fail to be locally relatively strictly convex,namely, the top and bottom boundaries of the narrow region are partially"flat". This is contrary to our expectation. In order to further explore theblow-up mechanism of the gradient, we next investigate two adjacent inclusionswith relative convexity of order m and finally reveal an underlyingrelationship between the blow-up rate of the stress and the order of therelative convexity of the subdomains in all dimensions.

The convexity of inclusions and gradient's concentration for Lam\'e systems with partially infinite coefficients