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A general analytical framework for the mechanics of heterogeneous hexagonal lattices

Shuvajit Mukherjee, Sondipon Adhikari

Thin-Walled Structures, Volume: 167, Start page: 108188

Swansea University Authors: Shuvajit Mukherjee, Sondipon Adhikari

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DOI (Published version): 10.1016/j.tws.2021.108188

Abstract

The in-plane mechanics of two-dimensional heterogeneous hexagonal lattices are investigated. The heterogeneity originates from two physically realistic considerations: different constituent materials and different wall thicknesses. Through the combination of multi-material and multi-thickness elemen...

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Published in: Thin-Walled Structures
ISSN: 0263-8231
Published: Elsevier BV 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa57492
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spelling 2021-09-10T17:21:10.0510992 v2 57492 2021-08-02 A general analytical framework for the mechanics of heterogeneous hexagonal lattices 0d6adf4c1873dddc78ba26dba8b1c04f Shuvajit Mukherjee Shuvajit Mukherjee true false 4ea84d67c4e414f5ccbd7593a40f04d3 Sondipon Adhikari Sondipon Adhikari true false 2021-08-02 AERO The in-plane mechanics of two-dimensional heterogeneous hexagonal lattices are investigated. The heterogeneity originates from two physically realistic considerations: different constituent materials and different wall thicknesses. Through the combination of multi-material and multi-thickness elements, the most general form of 2D heterogeneous hexagonal lattices is proposed in this paper. By exploiting the mechanics of a unit cell with multi-material and multi-thickness characteristics, exact closed-form analytical expressions of equivalent elastic properties of the general heterogeneous lattice have been derived. The equivalent elastic properties of the 2D heterogeneous lattice are Young’s modulli and Poisson’s ratios in both directions and the shear modulus. Two distinct cases, namely lattices with thin and thick constituent members, are considered. Euler–Bernoulli beam theory is employed for the thin-wall case, and Timoshenko beam theory is employed for the thick-wall case. The closed-form expressions are validated by independent finite element simulation results. The generalized expressions can be considered as benchmark solutions for validating future numerical and experimental investigations. The conventional single-material and single-thickness homogeneous lattice appears as a special case of the heterogeneous considered here. By introducing the Material Disparity Ratio (MDR) and Geometric Disparity Ratio (GDR), variability in the equivalent elastic properties has been graphically demonstrated. As opposed to classical homogeneous lattices, heterogeneous lattices significantly expand the design space for 2D lattices. Orders-of-magnitude of variability in the equivalent elastic properties is possible by suitably selecting material and geometric disparities within the lattices. The general closed-form expressions proposed in this paper open up the opportunity to design next-generation heterogeneous lattices with highly tailored effective elastic properties. Journal Article Thin-Walled Structures 167 108188 Elsevier BV 0263-8231 Hexagonal lattices, Stiffness matrix, Homogen properties, Elastic constants, 2D materials 1 10 2021 2021-10-01 10.1016/j.tws.2021.108188 COLLEGE NANME Aerospace Engineering COLLEGE CODE AERO Swansea University 2021-09-10T17:21:10.0510992 2021-08-02T10:55:25.4708379 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Shuvajit Mukherjee 1 Sondipon Adhikari 2 57492__20506__4043844b2f6d49fb85bf24b063237c6d.pdf 57492.pdf 2021-08-02T12:07:28.6234316 Output 4829385 application/pdf Accepted Manuscript true 2022-07-29T00:00:00.0000000 ©2021 All rights reserved. All article content, except where otherwise noted, is licensed under a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND) true eng https://creativecommons.org/licenses/by-nc-nd/4.0/
title A general analytical framework for the mechanics of heterogeneous hexagonal lattices
spellingShingle A general analytical framework for the mechanics of heterogeneous hexagonal lattices
Shuvajit Mukherjee
Sondipon Adhikari
title_short A general analytical framework for the mechanics of heterogeneous hexagonal lattices
title_full A general analytical framework for the mechanics of heterogeneous hexagonal lattices
title_fullStr A general analytical framework for the mechanics of heterogeneous hexagonal lattices
title_full_unstemmed A general analytical framework for the mechanics of heterogeneous hexagonal lattices
title_sort A general analytical framework for the mechanics of heterogeneous hexagonal lattices
author_id_str_mv 0d6adf4c1873dddc78ba26dba8b1c04f
4ea84d67c4e414f5ccbd7593a40f04d3
author_id_fullname_str_mv 0d6adf4c1873dddc78ba26dba8b1c04f_***_Shuvajit Mukherjee
4ea84d67c4e414f5ccbd7593a40f04d3_***_Sondipon Adhikari
author Shuvajit Mukherjee
Sondipon Adhikari
author2 Shuvajit Mukherjee
Sondipon Adhikari
format Journal article
container_title Thin-Walled Structures
container_volume 167
container_start_page 108188
publishDate 2021
institution Swansea University
issn 0263-8231
doi_str_mv 10.1016/j.tws.2021.108188
publisher Elsevier BV
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 1
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description The in-plane mechanics of two-dimensional heterogeneous hexagonal lattices are investigated. The heterogeneity originates from two physically realistic considerations: different constituent materials and different wall thicknesses. Through the combination of multi-material and multi-thickness elements, the most general form of 2D heterogeneous hexagonal lattices is proposed in this paper. By exploiting the mechanics of a unit cell with multi-material and multi-thickness characteristics, exact closed-form analytical expressions of equivalent elastic properties of the general heterogeneous lattice have been derived. The equivalent elastic properties of the 2D heterogeneous lattice are Young’s modulli and Poisson’s ratios in both directions and the shear modulus. Two distinct cases, namely lattices with thin and thick constituent members, are considered. Euler–Bernoulli beam theory is employed for the thin-wall case, and Timoshenko beam theory is employed for the thick-wall case. The closed-form expressions are validated by independent finite element simulation results. The generalized expressions can be considered as benchmark solutions for validating future numerical and experimental investigations. The conventional single-material and single-thickness homogeneous lattice appears as a special case of the heterogeneous considered here. By introducing the Material Disparity Ratio (MDR) and Geometric Disparity Ratio (GDR), variability in the equivalent elastic properties has been graphically demonstrated. As opposed to classical homogeneous lattices, heterogeneous lattices significantly expand the design space for 2D lattices. Orders-of-magnitude of variability in the equivalent elastic properties is possible by suitably selecting material and geometric disparities within the lattices. The general closed-form expressions proposed in this paper open up the opportunity to design next-generation heterogeneous lattices with highly tailored effective elastic properties.
published_date 2021-10-01T04:13:16Z
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