Robust topological designs for extreme metamaterial micro-structures

Abstract We demonstrate that the consideration of material uncertainty can dramatically impact the optimal topological micro-structural configuration of mechanical metamaterials. The robust optimization problem is formulated in such a way that it facilitates the emergence of extreme mechanical prope...

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Autores principales:	Tanmoy Chatterjee, Souvik Chakraborty, Somdatta Goswami, Sondipon Adhikari, Michael I. Friswell
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/92006aa9bf8f435e8e5852b223323e9a
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spelling	oai:doaj.org-article:92006aa9bf8f435e8e5852b223323e9a2021-12-02T18:46:55ZRobust topological designs for extreme metamaterial micro-structures10.1038/s41598-021-94520-x2045-2322https://doaj.org/article/92006aa9bf8f435e8e5852b223323e9a2021-07-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-94520-xhttps://doaj.org/toc/2045-2322Abstract We demonstrate that the consideration of material uncertainty can dramatically impact the optimal topological micro-structural configuration of mechanical metamaterials. The robust optimization problem is formulated in such a way that it facilitates the emergence of extreme mechanical properties of metamaterials. The algorithm is based on the bi-directional evolutionary topology optimization and energy-based homogenization approach. To simulate additive manufacturing uncertainty, combinations of spatial variation of the elastic modulus and/or, parametric variation of the Poisson’s ratio at the unit cell level are considered. Computationally parallel Monte Carlo simulations are performed to quantify the effect of input material uncertainty to the mechanical properties of interest. Results are shown for four configurations of extreme mechanical properties: (1) maximum bulk modulus (2) maximum shear modulus (3) minimum negative Poisson’s ratio (auxetic metamaterial) and (4) maximum equivalent elastic modulus. The study illustrates the importance of considering uncertainty for topology optimization of metamaterials with extreme mechanical performance. The results reveal that robust design leads to improvement in terms of (1) optimal mean performance (2) least sensitive design, and (3) elastic properties of the metamaterials compared to the corresponding deterministic design. Many interesting topological patterns have been obtained for guiding the extreme material robust design.Tanmoy ChatterjeeSouvik ChakrabortySomdatta GoswamiSondipon AdhikariMichael I. FriswellNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-14 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Tanmoy Chatterjee Souvik Chakraborty Somdatta Goswami Sondipon Adhikari Michael I. Friswell Robust topological designs for extreme metamaterial micro-structures
description	Abstract We demonstrate that the consideration of material uncertainty can dramatically impact the optimal topological micro-structural configuration of mechanical metamaterials. The robust optimization problem is formulated in such a way that it facilitates the emergence of extreme mechanical properties of metamaterials. The algorithm is based on the bi-directional evolutionary topology optimization and energy-based homogenization approach. To simulate additive manufacturing uncertainty, combinations of spatial variation of the elastic modulus and/or, parametric variation of the Poisson’s ratio at the unit cell level are considered. Computationally parallel Monte Carlo simulations are performed to quantify the effect of input material uncertainty to the mechanical properties of interest. Results are shown for four configurations of extreme mechanical properties: (1) maximum bulk modulus (2) maximum shear modulus (3) minimum negative Poisson’s ratio (auxetic metamaterial) and (4) maximum equivalent elastic modulus. The study illustrates the importance of considering uncertainty for topology optimization of metamaterials with extreme mechanical performance. The results reveal that robust design leads to improvement in terms of (1) optimal mean performance (2) least sensitive design, and (3) elastic properties of the metamaterials compared to the corresponding deterministic design. Many interesting topological patterns have been obtained for guiding the extreme material robust design.
format	article
author	Tanmoy Chatterjee Souvik Chakraborty Somdatta Goswami Sondipon Adhikari Michael I. Friswell
author_facet	Tanmoy Chatterjee Souvik Chakraborty Somdatta Goswami Sondipon Adhikari Michael I. Friswell
author_sort	Tanmoy Chatterjee
title	Robust topological designs for extreme metamaterial micro-structures
title_short	Robust topological designs for extreme metamaterial micro-structures
title_full	Robust topological designs for extreme metamaterial micro-structures
title_fullStr	Robust topological designs for extreme metamaterial micro-structures
title_full_unstemmed	Robust topological designs for extreme metamaterial micro-structures
title_sort	robust topological designs for extreme metamaterial micro-structures
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/92006aa9bf8f435e8e5852b223323e9a
work_keys_str_mv	AT tanmoychatterjee robusttopologicaldesignsforextrememetamaterialmicrostructures AT souvikchakraborty robusttopologicaldesignsforextrememetamaterialmicrostructures AT somdattagoswami robusttopologicaldesignsforextrememetamaterialmicrostructures AT sondiponadhikari robusttopologicaldesignsforextrememetamaterialmicrostructures AT michaelifriswell robusttopologicaldesignsforextrememetamaterialmicrostructures
_version_	1718377691775762432

Robust topological designs for extreme metamaterial micro-structures

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