Development of a new 3D beam element with section changes: The first step for large scale textile modelling

The need of efficient modelling of textile materials at meso-scale increased considerably in the last decade. Several approaches have been proposed which present different kinds of drawbacks, the most important being their high computation time. The present paper aims to present a new tool for modelling textile materials using the yarn as constitutive element. Because fibre tows length is much higher than their transverse dimensions, beam elements seem to be the most convenient structural finite element tool. Unfortunately, classical beam theories assume that the cross section acts as a rigid which cannot describe the transverse compression and shape change of the yarn. In this paper, we present a new 3D beam element with the aim to achieve the results with section changes while breaking from classical beam hypothesis. Firstly, we start from 2D beam element with thickness change by adding a transverse strain component, which is inspired by previous works on the shell elements. Secondly, the formulation is extended to 3D beam elements, two transverse normal strain components are added with coupling so that full 3D constitutive law can be used. Finally, some numerical examples are presented using the new 3D beam elements which show that the results are exactly the same as those given by 3D elements in ABAQUS/Standard.