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Multiscale modelling of woven and knitted fabric membranes
Light-weight fabric membranes have gained increasing popularity over the past years due to their tailorable structural and material performances. These tailorable properties include stretch forming and deep drawing formability that exhibits excellent stretchability and drapeability properties of textiles and textile composites. Since the inception of computerised numerical control for three-dimensional textile-manufacturing machines,
technical textiles paved their way to numerous applications, certainly not limited to; aerospace, biomedical, civil engineering, defence, marine and medical industries. Digital interlooping and digital interlacing technology in additive manufacturing greatly advanced the manufacturing processes of textiles. In this work, we consider two branches of technical fabrics, namely plain-woven and weft-knitted.
Multiscale modelling is the tool of choice for homogenising periodic structures and has been used extensively to model and analyse the mechanical behaviour of woven and knitted fabrics. But there is a plethora of literature discussing the demerits of such conventional multiscale modelling. These demerits include higher computational costs,
rigid numerical models, ineffcient algorithmic computations and inability to incorporate geometric nonlinearities. We propose a data-driven nonlinear multiscale modelling technique to analyse the complex mechanical behaviour of plain-woven and weft-knitted fabrics with a neat extension to fabric material designing. We show how the integration of statistical learning techniques mitigates the weaknesses of conventional multiscale modelling. Moreover, we discuss the avenues that will open in many potential fields with regard to material modelling, structural engineering and textile industries.
In the proposed data-driven nonlinear computational homogenisation technique, we effi ciently integrate the microscale and macroscale using Gaussian Process Regression (GPR) statistical learning technique. In the microscale, representative volume elements (RVEs) are modelled using nite deformable isogeometric spatial rods and deformation is homogenised using periodic boundary conditions. This nite deformable rod is profi cient in handling large deformations, rod-to-rod contacts, arbitrary cross-section de finitions and follower loads. Respecting the principle of separation of scales, we construct response databases by applying different homogenised strain states to the RVEs and recording the respective incremental volume-averaged energy values. We use GPR
to learn a model using a 5-fold cross-validation technique by optimising the log marginal likelihood. In the macroscale, textiles are modelled as nonlinear orthotropic membranes for which the stresses and material constitutive relations are predicted by the trained GPR model. This coupling between GPR and membrane models is achieved through a
systematic and seamless nite element integration using C++ and Python environments. A neat extension to material designing is also discussed with potentials to extend the work into other related fi elds.Cambridge trust and Trinity Hall scholarshi
Study of artificially disordered optical fibers
Light transmission through photo-sensitive multi-mode fibers (MMF) with controlled volume disorder is investigated. Experiment shows that a segment of disordered MMF as short as 10 cm is sufficient to distribute power uniformly over all co-propagating modes and the intensity at the output surface of the fiber follows the Rayleigh negative exponential function. To explain the experimental findings, a comprehensive theoretical model is developed with three main results. First, statistical properties of all components of the dielectric tensor are obtained and analyzed in the framework a microscopical model of photo-sensitivity in a germano-silicate glasses. Secondly, it is shown that induced birefringence is insufficient to explain mode mixing, and that cross-polarization mode coupling is essential. Such a coupling is shown to originate from the spatial correlation in the off-diagonal elements of the dielectric tensor. Third, a hybrid theory to describe propagation in a fiber with a spatially correlated disorder is developed. The proposed theory treats the deterministic part of the light via coupled-amplitude equations, and the randomly-phased component with coupled-power equations. The complete theory developed in this work has a predictive power -- it can guide the design of an artificial disorder based on the desired transmission properties of the fiber. Experiment shows that mixing all co-propagating modes can, indeed, be attained in a short segment of a suitably designed disordered MMF without a prohibitive loss. Such fibers can be useful for e.g. maximizing the information capacity multi-mode fiber links --Abstract, page v