Modeling of hyperelastic bending of fibrous media using second-gradient isogeometric analysis: Weaving and braiding applications

For many applications, numerical modeling of composite reinforcements may require a detailed knowledge of the structure at the scale of the yarn, here called the mesoscopic scale. A numerical description of the yarn can be obtained using beam finite elements, shells, and most often three-dimensional (3D) solid elements. For a reliable description of the geometry, it is necessary to mesh with a large number of elements. With Non Uniform Rational B-Splines (NURBS) interpolation functions, on the other hand, not only is it possible to approximate the yarn geometry with a reduced number of degrees of freedom, but the high-order continuity allows a description of higher deformation gradient mechanics. These two points are exploited here, for a detailed presentation of the hyperelastic formalism considering fiber bending, and its implementation in an iso-geometric framework. Practical examples of weaving and braiding demonstrate the relevance of the formulation.