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Multiscale modelling and material design of woven textiles using Gaussian processes

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Abstract

A method for multiscale simulation and material design of thin membranes using Gaussian processes is proposed to assist in the mechanical analysis and design of woven textiles. Most of the existing concurrent multiscale simulation schemes have a limited capability in the combined mechanical analysis and design of woven textiles. In addition, the inherent higher computational cost of these existing schemes demands the development of efficient analysis techniques using advanced data-driven statistical methods. The contribution of this paper is aimed at utilising the Gaussian process based data-driven concepts in multiscale analysis and designing of woven textiles in a parametric environment. The proposed data-driven nonlinear multiscale modelling technique is proven to efficiently integrate the two scales using Gaussian process regression (GPR) statistical learning technique. In the microscale, representative volume elements (RVEs), parameterised by geometric, and material properties, are modelled using finite deformable isogeometric rods, and their deformation is homogenised using periodic boundary conditions. An offline GPR statistical model is trained for various strain states, geometric, and material properties of woven textile RVEs. In the macroscale, woven textiles are modelled as nonlinear orthotropic membranes for which the stresses and material responses are predicted by the trained GPR model. This offline trained GPR model acts as the constitutive model predictor for a given combination of analysis and design parameters. The efficient integration of statistical learning in multiscale modelling and material design is proven not only to result in efficient mechanical analysis but also to furnish a framework for material design of woven textiles.

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Notes

  1. Quantities in the reference and deformed configurations are denoted using uppercase and lowercase letters, respectively.

  2. Macroscale and microscale quantities are denoted by subscripts M and m, respectively.

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Acknowledgements

Constructive discussion with Prof. Mark Girolami, Dr. Fehmi Cirak and Dr. Ge Yin at the University of Cambridge is highly appreciated.

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  1. Department of Civil Engineering, University of Moratuwa, Moratuwa, Sri Lanka

    Sumudu Herath

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Herath, S. Multiscale modelling and material design of woven textiles using Gaussian processes. Acta Mech 233, 317–341 (2022). https://doi.org/10.1007/s00707-021-03125-y

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