Numerical Modelling of Multi-ply Polymeric Cords
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Textile reinforcements in the form of polymeric cords are currently employed in rubber composites used in tyres as a lighter alternative to metallic wires. The cords are typically composed of two or three twisted yarns, each one made of several hundreds of filaments. Their numerical modelling is challenging due to the different scales involved, to the geometric nonlinear effects and to the constitutive non-linearity of the filament material. The overall behaviour of cords depends on the trajectory of filaments, that can be reconstructed accurately only with complex experimental techniques, e.g. combining X-ray microtomography and image processing, see [1]. In [2], we developed a model for the simulation of the mechanical behaviour of rayon mono-ply twisted yarns, at macroscopic level. A yarn was represented by an equivalent three-dimensional solid of cylindrical shape with helicoidal anisotropy. The constitutive law accounts for visco-elastic and visco-plastic dissipation mechanisms and includes the direction of the fibers in the free energy definition. In the present work, we consider multi-ply cords and we develop a methodology that, starting from the analytical description of the filaments trajectory proposed in [3] and on the experimental measure of the cross section, allows to define the inclination of the material directions at each point of an equivalent anisotropic cylinder to be used in numerical simulation. The numerical predictions are compared with experimental data on rayon cords under uniaxial tests conducted at different strain rates and humidity conditions. References [1] A. Sibellas, J. Adrien, D. Durville, E. Maire, Experimental study of the fiber orientations in single and multi-ply continuous filament yarns. J. Textile Institute, Vol. 111(5), pp. 646–659, 2020. [2] M. Moscatelli, L. Pires da Costa, P. Caracino, S. Agresti, G. Novati, C. Comi, Elastoviscoplastic model for rayon yarns. to appear, 2023. [3] L. R.G. Treloar, The geometry of multi-ply yarns. J. Textile Institute Transactions, Vol. 47(6), pp. T348–T368, 1956.