A poly-inclusion approach for the elastic modelling of knitted fabric composites

Abstract

Mean field Eshelby based models are proposed for the prediction of the overall properties and the internal stress/strain distribution of knitted fabric composites. The use of a mean field is justified by the partial random character of the textile geometry in multi-layered applications. The position dependent deformation state in the curved yarns is piecewise approximated using the concept of effective ellipsoids replacing each yarn segment, taking into account the local yarn curvature. Conventional averaging methods are applied to the reduced, poly-inclusion composite with non-trivial orientation distribution to predict the internal field variables inside the original yarns. The Mori–Tanaka model and a first order self consistent method are compared and their potential and limitations are briefly discussed. Predicted tensile and shear moduli agree well with experimental data for both mean field methods, although the internal stress distribution for both methods is significantly different.