Estimation of stress in the presence of closely located elastic inclusions: A numerical study

When there are adjacent inclusions with extreme bulk modulus inside an elastic body, it is expected that the stress (the gradient of solutions to the Lame system) becomes arbitrarily large as the distance 5 between two inclusions tends to 0. In this paper we find the order of blow-up of the stress by numerical computations. Our findings show that the stress becomes arbitrarily large at the rate of delta(-0.5) as delta -> 0. This result is in agreement with rigorous estimations of the gradient of solutions for the conductivity equation. For computations we use the boundary integral method.