Modelling of woven fabrics with the Discrete Element Method

The mechanical behaviour of woven fabrics is dominated by the kinematics of the constituents on the microscopic scale. Their macroscopic response usually shows non-linearities which are due to the mobility of the interlaced yarns. The major deformation mechanisms of fabrics, i.e. the crimp interchange in case of biaxial tension and the trellising motion of the yarns in case of shear, reflect the dependency of the macroscopic material behaviour on the microstructural deformation mechanisms. The adaption of crimp and yarn directions according to the loading state leads to a significantly different material behaviour than observed for common homogeneous materials.

We present a novel modelling approach for woven fabrics which is capable to represent directly and locally the microstructure and its kinematics. With only a small set of assumptions on the micro-scale the complex macroscopic material behaviour can be directly obtained. The proposed model uses the Discrete Element Method (DEM) [

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] for the representation of the fabric s microstructure. It is modelled by discrete point masses and force interactions between them. These interactions can be rheological elements like springs and dashpots or any arbitrary function relating a reaction force to the kinematic state variables of the nodes. The model is intrinsically dynamic since the equations of motion are solved numerically for every mass point using a predictor-corrector algorithm taking into account the changing interaction forces. It thus can cover the full mobility of the fabric s microstructure while being efficiently enough to model macroscopic patches of the material.

With this model we can study the influence of the different material features of the microscale on the macroscopic material behaviour. With some further extensions accounting for coatings or embeddings, the range from pure fabrics to fabric reinforced membranes and composites can be covered. Problems related to large deformations and localization as well as damage can be addressed with this modelling approach. Numerical results for the constitutive material behaviour of fabrics are presented in order to demonstrate the capabilities of this kind of approach.