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A new 3D beam formulation using full 3D constitutive laws

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Title: A new 3D beam formulation using full 3D constitutive laws
Author: Gao, Sasa; Liang, Biao; Vidal-Sallé, Emmanuelle
Abstract: The present paper aims to present a new tool for modelling textile materials using the yarn as constitutive element. Modeling fabric process at the mesoscopic (i.e. the yarn) scale can be able to give realistic and physically fabric shape predictions. For that, the use of beam elements seems to be a good idea because fibre tows length is much higher than their transverse dimensions. Unfortunately, classical beam theories assume that the cross section acts as a rigid which can’t describe the 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. Inspired by previous works on the shell elements, we start from 2D beam element with thickness change by adding a normal strain component. Then, we extend the formulation to 3D beam elements by adding two coupling normal strain components so that full 3D constitutive strain-stress behaviour can be used directly. Finally, a FEM code is developed in Matlab and some numerical examples are presented using the new 3D beam elements which show that the results are exactly the same as those given by solid element in 3D element in ABAQUS/Standard.
Subject: full 3D constitutive laws; normal strain; beam element; section deformation
Publisher: AFM, Association Française de Mécanique
Date: 2015

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