Open Access

Murat Topçu, Gopal S.P. Madabhushi, Manfred Staat

• A generalized shear-lag theory for fibres with variable radius is developed to analyse elastic fibre/matrix stress transfer. The theory accounts for the reinforcement of biological composites, such as soft tissue and bone tissue, as well as for the reinforcement of technical composite materials, such as fibre-reinforced polymers (FRP). The original shear-lag theory proposed by Cox in 1952 is generalized for fibres with variable radius and with symmetric and asymmetric ends. Analytical solutions are derived for the distribution of axial and interfacial shear stress in cylindrical and elliptical fibres, as well as conical and paraboloidal fibres with asymmetric ends. Additionally, the distribution of axial and interfacial shear stress for conical and paraboloidal fibres with symmetric ends are numerically predicted. The results are compared with solutions from axisymmetric finite element models. A parameter study is performed, to investigate the suitability of alternative fibre geometries for use in FRP.