A Fast Boundary Element Method for the Analysis of Fiber-Reinforced Composites Based on a Rigid-Inclusion Model

Abstract

A new boundary element method (BEM) is developed for three-dimensional analysis of fiber-reinforced composites based on a rigid-inclusion model. Elasticity equations are solved in an elastic domain containing inclusions which can be assumed much stiffer than the host elastic medium. Therefore the inclusions can be treated as rigid ones with only six rigid-body displacements. It is shown that the boundary integral equation (BIE) in this case can be simplified and only the integral with the weakly-singular displacement kernel is present. The BEM accelerated with the fast multipole method is used to solve the established BIE. The developed BEM code is validated with the analytical solution for a rigid sphere in an infinite elastic domain and excellent agreement is achieved. Numerical examples of fiber-reinforced composites, with the number of fibers considered reaching above 5800 and total degrees of freedom above 10 millions, are solved successfully by the developed BEM. Effective Young’s moduli of fiber-reinforced composites are evaluated for uniformly and “randomly” distributed fibers with two different aspect ratios and volume fractions. The developed fast multipole BEM is demonstrated to be very promising for large-scale analysis of fiber-reinforced composites, when the fibers can be assumed rigid relative to the matrix materials.