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When two stiff inclusions are closely located, the gradient of the solutionto the Lam\'{e} system, in other words the stress, may become arbitrarily largeas the distance between two inclusions tends to zero. To compute the gradientof the solution in the narrow region, extremely fine meshes are required. It isa challenging problem to numerically compute the stress near the narrow regionbetween two inclusions of general shapes as their distance goes to zero. Arecent study [15] has shown that the major singularity of the gradient can beextracted in an explicit way for two general shaped inclusions. Thus thecomplexity of the computation can be greatly reduced by removing the singularterm and it suffices to compute the residual term only using regular meshes.The goal of this paper is to numerically compute the stress concentration in afast and efficient way. In this paper, we compute the value of the stressconcentration factor, which is the normalized magnitude of the stressconcentration, for general shaped domain as the distance between two inclusionstends to zero. We also compute the solution for two closely located inclusionsof general shapes and show the convergence of the solution. Only regular meshesare used in our numerical computation and the results clearly show that thecharacterization of the singular term method can be efficiently used forcomputation of the stress concentration between two closely located inclusionsof general shapes.

A fast and efficient numerical method for computing the stress concentration between closely located stiff inclusions of general shapes