Discrete models of woven structures. Macroscopic approach
B. Ben Boubaker
, B. Haussy
, J.F. Ganghoﬀer
ESEO, 4, rue Merlet de la Boulaye, B.P. 926, 49009 Angers Cedex 01, France
ENSEM, LEMTA, 2, Avenue de la Fore
t de Haye, B.P. 160, 54504 Vandoeuvre Cedex, France
Received 15 June 2005; accepted 29 January 2006
Available online 4 October 2006
A discrete model of a woven fabric structure has been established, whereby nodes endowed with a mass and a rotational rigidity are
connected by extensible bars to form a two-dimensional truss. The set of four bars that delineate a quadrilateral element—the unit cell of
the micromechanical analysis—is further endowed with a torsion deformation mode. The equilibrium shape of the structure is obtained
as the minimum of its total potential energy versus the set of kinematic translational and rotational variables, accounting for eventual
kinematic constraints due to contact with a rigid surface. A linearized stability analysis is performed, and the potentiality of the model is
illustrated by fabric draping simulations.
Ó 2006 Published by Elsevier Ltd.
Keywords: A. Fabrics/textiles; B. Mechanical properties; C. Computational modeling; Discrete models
The analysis of the deformations and shape forming of
woven structures such as textiles is nowadays an important
scientiﬁc and technological topic, due to the wide range of
applications of these structures: mention, e.g. mechanical
parts made of dry fabric used in car and aerospace industry
for their gain of weight; apparel industry, or geotextiles.
Since mechanical parts having complex shapes are pro-
duced on a large-scale, it becomes important to have at
hand models and simulation tools for predicting the shape
formability of fabric sheets. Relatively little work has been
spent on dry fabrics [1–3], despite their wide range of appli-
cations. The dry fabric behavior is quite peculiar, due to
the ease of relative motions between yarns, which becomes
prohibited when the initially dry fabric is impregnated with
a resin: the lack of a matrix has thereby an important inﬂu-
ence on the fabric behavior, due to the microweaving struc-
ture and the ease of shearing and sliding of the ﬁbers, see
the recent works in [4,5].
Research in computational mechanics of fabric
appeared for the ﬁrst time in the late 1960s , following
two diﬀerent routes, either the continuum models (labeled
CM in the sequel), or discontinuum models (labeled DM
in the sequel). In the ﬁrst approach, the fabric is treated
as a continuum without an explicit account of its discrete
microstructure. The cloth is divided into a set of small
patches—the ﬁnite elements—and the bending/stretching
deformation modes are modeled using ﬂat or curved spe-
cial shell elements. In contrast to this, the discontinuum
method, usually referred to as structural mechanics of fab-
ric, considers fabric as an assembly of their constitutive
yarns, accounting for yarn properties, yarn undulations
(use of curved rod models) and inter-yarn interactions.
The organization of the yarns within the unit cell (such
as satin, serge) plays indeed an important role in the shape
forming capacity of the initially ﬂat structure (the pattern).
It is therefore important to develop reliable and accurate
micromechanical models, in order to predict the 3D defor-
mation of woven structures during real forming processes.
1359-8368/$ - see front matter Ó 2006 Published by Elsevier Ltd.
Corresponding author. Tel.: +33 383595724; fax: +33 383595551.
E-mail addresses: email@example.com (B. Ben Boubaker),
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Composites: Part B 38 (2007) 498–505