An integral equation method for elastostatics of periodic composites

An interface integral equation is presented for the elastostatic problem in a two-dimensional isotropic composite. The displacement is represented by a single layer force density on the component interfaces. In a simple numerical example involving hexagonal arrays of disks the force density is expanded in a Fourier series. This leads to an algorithm with superalgebraic convergence. The integral equation is solved to double precision accuracy with a modest computational eeort. EEective moduli are extracted both for dilute arrays where previously three digit accurate results were available, and for dense arrays where previously no results were available.