Uniform hydrostatic thermal stress fields inside two interacting inclusions of irregular shape and related problem

By using the technique of conformal mapping, we construct the irregular shapes of two interacting elastic inclusions with internal uniform hydrostatic thermal stresses due to a uniform change in temperature. It is found that the hoop stresses along the two inclusion/matrix interfaces on the matrix side are constant. The internal uniform hydrostatic thermal stresses within the two inclusions and the hoop stresses along the two interfaces are independent of the specific inclusion shapes. Numerical results are presented to validate and demonstrate the findings. Furthermore, we design the optimum shapes of the two inclusions that permit internal uniform stresses when uniform anti-plane eigenstrains are imposed on the two inclusions of irregular shape.