Elastic study on singularities interacting with interfaces using alternating technique

Abstract

Singularity problems in an isotropic trimaterial are analyzed by the same procedure as in an anisotropic trimaterial of Part I [Int. J. Solids Struct. 39, 943–957]. `Trimaterial' denotes an infinite body composed of three dissimilar materials bonded along two parallel interfaces. Linear elastic isotropic materials under plane deformations are assumed, in which the plane of deformation is perpendicular to the two parallel interface planes, and thus Muskhelishvili's complex potentials are used. The method of analytic continuation is alternatively applied across the two parallel interfaces in order to derive the trimaterial solution in a series form from the corresponding homogeneous solution. A variety of problems, e.g. a bimaterial (including a half-plane problem), a finite thin film on semi-infinite substrate, and a finite strip of thin film, etc, can be analyzed as special cases of the present study. A film/substrate structure with a dislocation is exemplified to verify the usefulness of the solutions obtained.