A Galerkin boundary integral method for multiple circular elastic inclusions with uniform interphase layers

The paper presents a numerical method for solving the problem of an infinite, isotropic elastic plane containing a large number of randomly distributed circular elastic inclusions with uniform interphase layers. The bonds between the inclusions and the interphases as well as between the interphases and the matrix are assumed to be perfect. In general, the inclusions may have different elastic properties and sizes; the thicknesses of the interphases and their elastic properties are arbitrary. The analysis is based on a numerical solution of a complex singular integral equation with the unknown tractions at each circular boundary approximated by a truncated complex Fourier series. The Galerkin technique is used to obtain a system of linear algebraic equations. The resulting numerical method allows one to calculate the elastic fields everywhere in the matrix and inside the inclusions and the interphases. Using the assumption of macro-isotropic behavior in a plane section one can find the effective elastic moduli for an equivalent homogeneous material. The method can be viewed as an extension of our previous work (Int. J. Solids Struct. 39 (2002) 4723) where simpler spring-like interface conditions were modeled. The problem of overlapping of the fibers and matrix inherent to spring type interface is discussed in the context of the present model. Numerical examples are included to demonstrate the effectiveness of the new approach.