An analytical closed-form solution for the in-plane elastic modulus of plain-woven textile composites

Abstract

Engineering application of textile composites needs simple relations for the estimation of their mechanical properties. Many homogenization and simplified models have been already proposed for the analytical characterization of the elastic moduli of this class of materials. Along this route, the current study introduces an analytical solution for the longitudinal elastic modulus of plain-woven textile composites. A hybrid beam-spring model of the representative unit cell (RUC) is postulated consisting of a horizontal beam connected to an inclined beam, two supporting springs beneath the free end of the horizontal beam and the common end of the horizontal and inclined beams, and a torsion spring at the free end of the inclined beam. The mechanical and geometrical properties of the beams and springs are calculated from the weave structure and the symmetry conditions. A reduction technique from the matrix analysis of structures is borrowed to consider the effect of internal degrees of freedom on the in-plane stiffness coefficient and a closed-form formula is extracted for the elastic modulus. The proposed analytical formula is finally verified against available experimental data and a wide range of FE predictions for the GFRP and CFRP plain-woven composites.