  When two stiff inclusions are closely located, the gradient of the solution
to the Lam\'{e} system, in other words the stress, may become arbitrarily large
as the distance between two inclusions tends to zero. To compute the gradient
of the solution in the narrow region, extremely fine meshes are required. It is
a challenging problem to numerically compute the stress near the narrow region
between two inclusions of general shapes as their distance goes to zero. A
recent study [15] has shown that the major singularity of the gradient can be
extracted in an explicit way for two general shaped inclusions. Thus the
complexity of the computation can be greatly reduced by removing the singular
term 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 a
fast and efficient way. In this paper, we compute the value of the stress
concentration factor, which is the normalized magnitude of the stress
concentration, for general shaped domain as the distance between two inclusions
tends to zero. We also compute the solution for two closely located inclusions
of general shapes and show the convergence of the solution. Only regular meshes
are used in our numerical computation and the results clearly show that the
characterization of the singular term method can be efficiently used for
computation of the stress concentration between two closely located inclusions
of general shapes.
