Historical development of geometrical modelling of textiles reinforcements for polymer composites: A review

Mechanical behaviour of fibre reinforced polymer composites is geared by the geometrical structure of the textile reinforcements. Consistent permeability, predictable impregnation and even distribution of resin are key factors in reaching targeted mechanical performance, whereas these parameters and others are functions of the geometrical composition. Hence numerous analytical geometrical models have been described in literature covering most of the conventional commonly used weave reinforcements. However, no current model can be broadly generalized to address, for instance, manufacturing deformation of fibres cross-section, periodic variability caused by stitching in 2.5D non-crimp stitched fabrics or arbitrary fibre orientation featuring some recently developed three-dimensional textiles reinforcements. Given that the latter structures can potentially provide more favourable mechanical behaviour in terms of bending stiffness, impact resistance and through-thickness properties, it is worthwhile attempting to adapt the available geometrical modelling concepts so as to address versatile structures. This review aims to trace the physical concepts used for modelling the geometrical structures of textile reinforcements at the mesoscale and compare applicability of various analytical and numerical models to types and geometrical dimensionality of woven textile structures.