A boundary perturbation analysis for elastic inclusions and interfaces
The Muskhelishvili's complex variable representations of the two- dimensional elasticity theory are applied to perfectly circular or slightly perturbed non-circular inclusions embedded in an infinite plane. For inclusions with smooth polygon shapes are given explicit solutions by means of cosine wavy perturbations along a circular boundary. The results can be extended for other perturbations of boundaries in stressed medium. Meanwhile such boundaries become instable for perturbations bounded by two critical wavelengths. The stress concentrations may also occur, fact which may involve plastic deformation or brittle fracture before the bulk stress reaches a critical value. The results present interest for different mechanical phenomena (as for instance the stability of geologic layers under pressure and gravity effects, etc.).
scientific article; zbMATH DE number 91089