Revisiting the problem of a 2D infinite elastic isotropic medium with a rigid inclusion or a cavity

The problem of analytically finding the elastic fields inside a 2D infinite elastic isotropic medium containing a rigid inclusion or a cavity and subjected to uniform remote loading is a classical elasticity problem of theoretical and practical interest. In the present work, we revisit the Kolosov-Muskhelishvili potential theory which is a powerful tool for solving the problem in question. In particular, a novel strategy is proposed to deal with the rigid-body displacements that the rigid inclusion or cavity may undergo. When the shape of the rigid inclusion or cavity is described by a Laurent polynomial, a general method is elaborated to solve the problem. The results obtained by using our method include as special cases all the relevant results reported in the literature. In light of our results, some errors in the literature are corrected. Finally, the cases of a rhombus rigid inclusion and a pentagonal cavity saturated with a fluid are studied in detail and some general properties are discussed.