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Discrete Model of Fabric Yarn – Deflection and Stability Analysis

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The paper addresses the issue of the modelling of the mechanical behaviour of yarns using a mass-spring system of discrete elements. For this purpose, the yarn is discretized into straight, elastic bars modelled by stretching springs which are connected at frictionless hinges by rotational springs. Shear springs are used, in order to model the shearing stiffness of the yarn. An energy study is conducted, taking into account the various strain energy contributions of the yarn and the work of the external forces. From the energy expression, a stability analysis is performed, relying on the Dirichlet-Lagrange stability criterion. The effects of boundary conditions as well as the heterogeneity of the nodes' rigidity are analysed. The equilibrium shapes of the structure, submitted to its own weight, are obtained as shapes associated to the minimum of the total potential energy versus the whole set of kinematic translational and rotational variables. The obtained results show that the effects of boundary conditions and heterogeneity of the yarn's rigidity on the stability of the structure are important.

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