Modelling the mechanical properties of textiles

These examples explain the continuous practical and theoretical interest in modelling all aspects of properties of textiles. In this section, approaches to modelling mechanical and physical properties of textiles are outlined. 

It has been mentioned in Section 1.4 that models of textile geometry and mechanics are closely interlinked, where the level of structural detail and complexity is an additional factor the same is true for modelling physical properties such as heat transfer or air/liquid flow in porous media. 

In modelling the physical and the mechanical properties of textiles, there are usually two choices, i.e. whether to consider a discrete or a continuum model. A continuum model assumes that the property of any small part of the material can be considered equal to that of the whole volume. In order to model a textile structure as a continuum, its volume is divided into small parts termed unit cells or representative volume elements (RVE). RVEs model the material structure at a miaoscopic level, i.e. at the level of individual fibre arrangements. The mechanical properties of RVEs are modelled and then used at a macroscopic level, which is the level of yarn or fabric, under the assumption that the whole volume of the material can be re-constructed from a number of RVEs. 

Textile materials can often be characterized by preferential orientation and symmetry in fibre arrangement, so that they can be considered not as general anisotropic, but orthotropic or even transversely isotropic materials (Fig. 1.12). This simplifies the models development and experimental verification where there would be a smaller number of parameters to be measured. For example, the linear elastic behaviour of anisotropic material can be described in a matrix form as follows  

Out of 36 elements in matrices S and C above, there are only 21 independent elements due to symmetry in stresses and strains. For orthotropic materials, which have different properties in orthogonal directions, there are nine independent constants in matrix C 

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