Characterisation of the mechanical behaviour of networks and woven fabrics with a discrete homogenization model

Abstract

In the past decades there has been an impressive progress in the development of new materials for mechanical related applications. New generations of composites have been developed, that can offer advantages over the unidirectional fibre-reinforced mats commonly used then materials take the name of woven fabrics. The behaviour of this material is strongly influenced by the micro-structure of the material. In the thesis mechanical models and a numerical scheme able to model the mechanical behaviour of woven fabrics and general network materials have been developed. The model takes in to account the micro-structure by means of a homogenization technique. The fibres in the network have been treated like microbeams, having both extensional and bending stiffness, with different types of connection, according to the pattern and detail of the network. The developed procedure was applied for obtaining the homogenized mechanical models for some types of biaxial and quadriaxial networks of fibres, simulating either fibre nets (in this case rigid connection were assumed among the fibres) or tissues with negligible interaction between the fibre bundles, and with relative sliding prevented (in this case the connections were simulated by means of pivots). Different geometries were analysed, including the cases in which the fibres are not orthogonal. A first gradient medium is usually obtained but, in some cases, the homogenization procedure itself indicates that a higher order continuum is better fit to represent the deformation of the micro-structure. Special results were obtained for the case of fibres connected by pivots. In this cases an orthotropic material with zero shear modulus was obtained. Such a material has a not elliptic constitutive tensor, thus it can lead to strain concentrations. However, it was shown that some considerations about the physical behaviour of such networks indicated that higher order terms had to be included in the expansion of the internal forces and deformations, so that a strain gradient material was obtained. The results obtained can be used for the design of specific materials requiring ad-hoc properties. Although the reference model is a network material, the results obtained can be applied to other similar kinds of microstructures, like pantographic materials, micro devices composed by microbeams etc. They have been limited at the range of linear elasticity, that is small deformation and linear elastic behaviour. Then, numerical simulations were focused on extension tests and bias tests. The obtained deformed configurations are consistent with the literature experimental tests, both for balanced and unbalanced tissues. Moreover, a comparison between first and second gradient numerical predictions was performed. It was observed that second gradient predictions better simulate the experimental evidences.