First-order perturbation solutions of embedded strained wires

Abstract

The paper presents the first-order perturbation solutions to the two-dimensional elasticity problems of strained wires embedded in a multilayered film-substrate system with homogeneous elastic properties. The solutions are accurate to the first order of the characteristic slope of the wires; the expressions of the solutions are concise for wires containing multiple facets; and the solutions are valid for single wire, multiple wires with different shapes, and a periodic array of identical wires. The perturbation solutions provide an efficient scheme for studying the effects of embedded wires on the stresses in the multilayered system. © 2006 American Institute of Physics.