Micromechanical response of fibre-reinforced materials using the boundary element technique

The boundary element method (BEM) and the embedded cell approach (ECA) have been used to analyse the effects of constituent material properties and fibre spatial distribution on the localised behaviour of a transversely loaded, unidirectional fibre-reinforced composite. The geometrical structures examined were perfectly periodic, uniformly spaced fibre arrangements in square and hexagonal embedded cells and 10 cells in which 60 fibres were randomly placed within the matrix. The models involve both elastic fibres and matrix, with the interfaces between the different phases being fully bonded. The results indicate that both the fibre packing and the material properties of the constituent phases have a significant effect on the overall stress distribution and the magnitude of localised stress concentrations within a composite. Non-periodic arrangements give rise to higher local stresses, and the magnitudes of these stress concentrations have a strong dependence on the ligament length (distance between the two neighbouring fibres that have a common high-stress region), and to a lesser extent on the angle relative to the applied load (angle between a plane containing the two fibre centres and the applied load). Furthermore, analysis of a three-phase composite, comprised of a mixture of both stiff and compliant fibres, had higher stress concentrations than the equivalent two-phase composites.