Mathematical Modelling of Internal Geometry and Deformability of Woven Preforms

摘要

The paper presents an approach to model the behaviour of a representative volume element (unit cell) of textile reinforcement in in-plane deformation (bi-axial tension and shear) and in compression. The model is a further development of a virtual textile concept implemented in the WiseTex software, and is based on the concept of hierarchical description of textile properties and systematic application of the principle of minimum energy to calculate the textile geometry in the relaxed and deformed state. With the internal geometry of the unit cell built, the model computes overall parameters of the deformed textile, such as fibre volume fraction, porosity etc. The internal geometry is visualised and such properties as pore structure in typical cross-sections are analysed. The load-deformation curves for compression, tension and shear are computed via the balance between change of the internal energy of the unit cell and mechanical work of the applied loads. The internal geometry description is further fed into flow modelling software, which allows computing local permeability of the deformed reinforcement, and micro-mechanical modelling to calculate homogenised local stiffness of the composite.