Fast BEM multi-domain approach for the elastostatic analysis of short fibre composites

Composite materials are usually treated as homogeneous when carrying out structural design. However, failure in these materials often originated at their heterogeneous microstructure or constituents; hence, the different materials should be considered in the analysis. The use of composite materials has increased considerably over the years due to their relative superior properties. The accurate determination of their mechanical properties and behaviour is thus of great practical significance. The Boundary Element Method (BEM) has demonstrated to be a powerful computational technique for the analysis of many physical and engineering problems. The present work deals with the use of the multi-domain BEM to obtain a more appropriate characterisation of fibre–matrix composites. The generally anisotropic fundamental solution based on a double-Fourier series is employed together with a fast BEM approach, namely, the Adaptive Cross Approximation (ACA) technique. The ACA technique is aimed at speeding up the process required to generate the BEM matrices. Some numerical examples are presented to demonstrate its applicability. The present work is a precursor to treating problems involving anisotropic inclusions in general composites.