Evaluation of Poisson’s ratio of textiles from mesoscopic models

Abstract

The magnitudes of Poisson’s ratios can attain some peculiar values for woven fabrics, in contrast to conventional engineering materials, leading to unusual stress–strain relationships. A mesoscopic discrete model of dry fabric has been presently developed at the scale of the armor, accounting for the yarn–yarn interactions at the yarns crossing points. From a mechanical viewpoint, yarns are modeled as elastic straight bar elements representing stretching springs connected at frictionless hinges by rotational springs. The motion of each node along the yarn is described by a lateral displacement and a local rotation. The reaction force exerted by the transverse yarns at the contact points is calculated from Timoshenko theory, and the work of the reaction forces is incorporated into the structure potential energy. The equilibrium shape of textile structures submitted to external loading is identified as configurations achieving the minimum of the potential energy; a genetic search algorithm has been implemented for the determination of the global minimum of the total potential energy. The transverse behavior of plain weave fabric is evaluated in terms of the Poisson’s ratio, based on virtual simulations at the mesoscopic scale of analysis. Poisson’s ratio first increases towards a maximum due to the rapid shrinkage of the sample in the transverse direction, and decreases thereafter when the crimp changes are exhausted, with yarn extension as the main deformation mechanism. The influence of the mechanical properties of both warp and weft on Poisson’s coefficient is assessed. Scaling laws of the equivalent elastic properties of plain weave versus characteristic geometrical parameters (as the pick spacing) of the plain weave armor are determined. The predictions of the mesoscopic models provide a guideline for the design of woven fabrics.