Model reduction for the forming process of fibrous composites structures via second gradient enriched continuum models

Abstract

This paper describes phenomena associated to the microstructure, such as the local bending stiffness of the yarns, with a second gradient parameter associated to terms in the energy with higher order derivatives. The results obtained with this enriched continuous model are presented and it is shown how the main deformation mode can be controlled to reproduce experimental evidence. In particular, increasing the second gradient parameter, the deformation mode switches from shear to one with a constant curvature along the specimen. Two fibrous composite reinforcements with two different geometries are modeled: composite airframe for aeronautic industry and an automotive leaf-spring for automotive industry. The two application cases are described as homogeneous second gradient continua with an energy depending on the in-plane and out-of-plane curvature of the yarns. This addition allows to take into account the effects of the local bending stiffness of the yarns at the mesoscale in a homogenized way.