A series solution of the volume integral equation for multiple-inclusion interaction problems

Abstract A modification of the volume integral equation (VIE) method is proposed for the solution of elastostatic 2-D problems in unbounded solids containing interacting multiple fibers. The efficiency of the VIE method developed by Lee and Mal (Lee, J., Mal, A. A volume integral equation technique for multiple inclusion and crack interaction problems. Journal of Applied Mechanics – Transactions of ASME 1997;64:23–31) where a weakly singular integral equation is involved has been improved by the use of a modification in the spirit of a subtraction technique for a single inclusion. The accuracy and efficiency of the method are examined through comparison with results obtained from finite element analysis.