Efficient computational homogenisation of 2D beams of heterogeneous elasticity using the patch scheme
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(Published version)
Date
2024
Authors
Tran-Duc, T.
Bunder, J.E.
Roberts, A.J.
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Journal article
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International Journal of Solids and Structures, 2024; 292:112719-1-112719-15
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Thien Tran-Duc, J.E. Bunder, A.J. Roberts
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Abstract
Modern ‘smart’ materials have complex heterogeneous microscale structure, often with unknown macroscale closure but one we need to realise for large scale engineering and science. The multiscale Equation-Free Patch Scheme empowers us to non-intrusively, efficiently, and accurately predict large scale, system level, solutions through computations on only small sparse patches of the given detailed microscale system. Here the microscale system is that of a 2D beam of heterogeneous elasticity, with either fixed–fixed, fixed–free, or periodic boundary conditions. We demonstrate that the described multiscale Patch Scheme simply, efficiently, and stably predicts the beam’s macroscale, with a controllable accuracy, at finite scale separation. Dynamical systems theory supports the scheme. This article points the way for others to use this innovative systematic non-intrusive approach, via a developing toolbox of functions, to model and compute accurately macroscale system-levels of general complex physical and engineering systems.
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Dissertation Note
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Available online 15 February 2024
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© 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).