Rate constitutive equations for computational analyses of textile composite reinforcement mechanical behaviour during forming

Textile composite reinforcements are made up of fibres. Consequently, their mechanical behaviour is a result of the possible sliding and the interactions between the fibres. When they are formed on double curved shapes, these fabrics are submitted to large strains, in particular large in-plane shear. Among the mechanical behaviour models for these textile reinforcements, continuous models are most commonly used for forming simulations because they can be used with standard finite elements. The objective of the present paper is to propose a continuous approach for textile reinforcement deformation analysis based on a rate constitutive equation specific to materials made of fibres. The objective derivative of this constitutive model is defined by the fibre rotation. This constitutive model is implemented in ABAQUS and can be used in most commercial F.E. software. The approach is extended to materials with two-fibre directions in order to perform simulations of woven fabric forming processes. A set of simulations of large deformations of textile composite reinforcements at the mesoscopic scale (deformation of a woven unit cell) and at the macroscopic scale (deep drawing) is presented to show the efficiency of the proposed approach.