MESOSCOPIC MODELS OF WOVENS: A GENERAL STRATEGY BASED ON THE MINIMIZATION OF THE POTENTIAL ENERGY INVOLVING GENETIC ALGORITHMS

ABSTRACT

Mesoscopic discrete models of dry fabric have been developed based on a discretization of the yarn geometry, 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 expression of the reaction force exerted by the transverse yarns at the contact points is assessed from Timoshenko beam theory. In a general situation, the reaction force is obtained by solving a linear system of equations involving all the nodal displacements at the contact points (with the transverse yarns) for each yarn. The equilibrium shape of the woven is obtained as the minimum of its total potential energy, accounting for the work of the reaction forces due to the transverse yarns. The finding of the absolute minimum of the structure’s total potential energy is achieved by a genetic algorithm, based on an initial guess of the solution relying on beam mechanics. Simulations of the fabric response under uniaxial tension evidence the effect of yarn-yarn interactions due to the increase of the reaction forces, as well as the effect of the transverse yarn properties. Plain weave has a nonlinear response due to the crimp change, whereas serge shows a quasi linear response due to yarn extension being the dominant deformation mechanism.