An irregular-shaped inclusion with imperfect interface in antiplane elasticity

Despite extensive studies of inclusions with simple shape, little effort has been devoted to inclusions of irregular shape. In this study, we consider an inclusion of irregular shape embedded within an infinite isotropic elastic matrix subject to antiplane shear deformations. The inclusion–matrix interface is assumed to be imperfect characterized by a single, non-negative, and constant interface parameter. Using complex variable techniques, the analytic function that is defined within the irregular-shaped inclusion is expanded into a Faber series, and in conjunction with the Fourier series, a set of linear algebraic equations for a finite number of unknown coefficients is determined. With this approach and without imposing any constraints on the stress distribution, a semi-analytical solution is derived for the elastic fields within the irregular-shaped inclusion and the surrounding matrix. The method is illustrated using three examples and verified, when possible, with existing solutions. The results from the calculations reveal that the stress distribution within the inclusion is highly non-uniform and depends on the inclusion shape and the weak mechanical contact at the inclusion/matrix boundary. In fact, the results illustrate that the imperfect interface parameter significantly influences the stress distribution.