NONLINEAR MODEL OF A FABRIC WARP AND WEFT

Abstract

This study aims to develop a realistic mathematical model of fabric. In contrast to other studies on fabric modeling as a deformable surface, the model described in this article takes into account the geometry of the object. Moreover, it integrates the nonlinear phenomena of the dynamic behavior of material. As input parameters, the weaving data that define the 3D structure of the object and the mechanical properties of the yarn that express its dynamics are used. Thus, the fabric model is composed of a geometrical model of fabric (structure) on which a model of yarn (material characterization) is added. This hypothesis may be reasonable since a fabric shows the result of a three-dimensional assembly of yarns judiciously disposed. Since these yarns interact dynamically: the main difficulty consists of defining the yarn model. In our case, it is composed of various nonlinear functions representing the dynamic behavior of yarn. In order to characterize the flexibility of material, the weight, the elasticity and any other mechanical characteristics defining the relation between the strain and the stretching out of the shape should be taken into account. Firstly, several works dealing with realistic mathematical models of fabric are described. A taxonomic classification is achieved in order to position our study (in comparison to the scientific community). Secondly, the model of the fabric is described. A geometrical model of the object is presented. It allows one to dimension the object in a 3D space and then to position it at its initial state. Subsequently, a nodal model of yarns is described, step by step, in order to demonstrate the separability of the various dynamic behaviors. These nodal links make it simple to integrate the proposed model in the global geometrical model. Thus, the methods of numerical resolution used to simulate the complete model of the fabric are exposed. One method is selected and used in order to improve the performances of the fabric simulator and to obtain better stability. Several simulations illustrate the quality of the results obtained.