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Discrete Models of Woven Structures Considering Yarn Interactions

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A discrete model of a woven fabric structure has been established at a macroscopic scale, whereby nodes endowed with a mass and a rotational rigidity are connected by rigid bars to form a two-dimensional truss. The set of four bars that delineate a quadrilateral element – the unit cell of the micromechanical analysis - is further endowed with a torsion deformation mode. The equilibrium shape of the structure is obtained as the minimum of its total potential energy versus the whole set of kinematic translational and rotational variables, accounting for eventual kinematic constraints due to contact with a rigid surface by the Lagrange multipliers method. The critical buckling load resulting from a stability analysis has been evaluated, based on Dirichlet-Lagrange criterion. The effect of structure size and orthotropy, and of the nature of boundary conditions on the stability behavior is further assessed. The potentiality of the model is illustrated by fabric draping simulations. The interaction between yarns is further analyzed at a mesoscopic scale of description. Both the macroscopic and mesoscopic models are formulated in a geometrically nonlinear framework, focusing on large rotations, but with small extensions of the individual beam elements. The initial shape of the yarn, represented by a planar undulated beam supposed to be periodic, is described by a Fourier series. The contact force is expressed vs. the mechanical properties of the transverse yarn and vs. the vertical displacement of the contact point. The potential energy of the interaction is then established. The simulated traction curve reproduces in a satisfactorily manner the observed behavior. The consideration of the coupling enhances the rigidity of the response of the yarn; the effect of the mechanical moduli of the transverse yarn is lastly evidenced.


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