Mesoscopic fabric models using a discrete mass-spring approach: Yarn-yarn interactions analysis

A meso/macro discrete model of fabric has been developed, accounting for yarn-yarn interactions occurring at the crossing points. The fabric yarns, described initially by a Fourier series development, are discretized into elastic straight bars represented by stretching springs and connected at frictionless hinges by rotational springs. The motion of each node is described by a lateral displacement and a rotation. The compressibility of both yarns is expressed as a kinematic relationship, considering frictionless motions of the yarns. The expression of the reaction force exerted by the transverse yarns at the contact points is then assessed, from which the work of the reaction forces is established. The equilibrium shape of the yarn is obtained as the minimum of its total potential energy, accounting for the work of the reaction forces due to the transverse yarns. Simulations of a traction curve of a single yarn are performed, that evidence the effect of the yarn interactions and the main deformation mechanisms.

[1]  Jun Wang,et al.  Prediction of shear force using 3D non-linear FEM analyses for a plain weave carbon fabric in a bias extension state , 2002 .

[2]  Stephen P. Timoshenko,et al.  Theorie de la stabilite elastique , 1966 .

[3]  Richard L. Grimsdale,et al.  Computer graphics techniques for modeling cloth , 1996, IEEE Computer Graphics and Applications.

[4]  Philippe Boisse,et al.  Finite element simulations of textile composite forming including the biaxial fabric behaviour , 1997 .

[5]  S. Kawabata,et al.  3—THE FINITE-DEFORMATION THEORY OF PLAIN-WEAVE FABRICS PART I: THE BIAXIAL-DEFORMATION THEORY , 1973 .

[6]  Gilles Hivet,et al.  Analyses of fabric tensile behaviour: determination of the biaxial tension–strain surfaces and their use in forming simulations , 2001 .

[7]  Bilel Ben Boubaker,et al.  Modèles discrets de structures tissées : Analyse de stabilité et de drapé , 2002 .

[8]  Philippe Boisse,et al.  Meso/macro-mechanical behaviour of textile reinforcements for thin composites , 2001 .

[9]  D. Mckenzie,et al.  Density functional theory modelling of amorphous silicon , 2000 .

[10]  Edward H. Glaessgen,et al.  Geometrical and finite element modelling of textile composites , 1996 .

[11]  T. Chou,et al.  In-Plane Thermal Expansion and Thermal Bending Coefficients of Fabric Composites , 1983 .

[12]  Forward modelling in cross-hole seismic tomography using reciprocity , 1997 .

[13]  Philippe Boisse,et al.  Mechanical behaviour of dry fabric reinforcements. 3D simulations versus biaxial tests , 2000 .