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Apparent negative values of Young’s moduli of lattice materials under dynamic conditions

Sondipon Adhikari Orcid Logo, T. Mukhopadhyay, Alexander Shaw Orcid Logo, Nicholas Lavery Orcid Logo

International Journal of Engineering Science, Volume: 150, Start page: 103231

Swansea University Authors: Sondipon Adhikari Orcid Logo, Alexander Shaw Orcid Logo, Nicholas Lavery Orcid Logo

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DOI (Published version): 10.1016/j.ijengsci.2020.103231

Abstract

Lattice materials are characterised by their equivalent elastic moduli for analysing mechanical properties of the microstructures. The values of the elastic moduli under static forcing condition are primarily dependent on the geometric properties of the constituent unit cell and the mechanical prope...

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Published in: International Journal of Engineering Science
ISSN: 0020-7225 1879-2197
Published: Elsevier BV 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa53739
first_indexed 2020-03-05T13:32:00Z
last_indexed 2025-03-05T05:03:49Z
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The values of the elastic moduli under static forcing condition are primarily dependent on the geometric properties of the constituent unit cell and the mechanical properties of the intrinsic material. Under a static forcing condition, the equivalent elastic moduli (such as Young&#x2019;s modulus) are always positive. When dynamic forcing is considered, the equivalent elastic moduli become functions of the applied frequency and they can be negative at certain frequency values. This paper, for the first time, explicitly demonstrates the occurrence of negative equivalent Young&#x2019;s modulus in lattice materials experimentally. Using additively manufactured titanium-alloy lattice metastructures, it is shown that the real part of experimentally measured in-plane Young&#x2019;s modulus becomes negative under a dynamic environment. In fact, we show that the onset of such negative Young&#x2019;s modulus in lattice materials can be precisely determined by capturing the sub-wavelength scale dynamics of the system. Experimental confirmation of the negative Young&#x2019;s moduli and the onset of the same as a function of frequency provide the necessary physical insights and confidence for its potential exploitation in various multi-functional structural systems and devices across different length scales.</abstract><type>Journal Article</type><journal>International Journal of Engineering Science</journal><volume>150</volume><journalNumber/><paginationStart>103231</paginationStart><paginationEnd/><publisher>Elsevier BV</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>0020-7225</issnPrint><issnElectronic>1879-2197</issnElectronic><keywords>Negative Young&#x2019;s modulus; Lattice material; Dynamic analysis of honeycomb; Frequency-dependent elastic property; Onset of negative elastic moduli; Dynamics of additively manufactured lattice</keywords><publishedDay>1</publishedDay><publishedMonth>5</publishedMonth><publishedYear>2020</publishedYear><publishedDate>2020-05-01</publishedDate><doi>10.1016/j.ijengsci.2020.103231</doi><url/><notes>Short communication</notes><college>COLLEGE NANME</college><department>Aerospace, Civil, Electrical, and Mechanical Engineering</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>ACEM</DepartmentCode><institution>Swansea University</institution><apcterm>Not Required</apcterm><funders>SA acknowledges the financial support from MSCA-IF-2017-799201. 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spelling 2025-03-04T13:41:02.1627901 v2 53739 2020-03-05 Apparent negative values of Young’s moduli of lattice materials under dynamic conditions 4ea84d67c4e414f5ccbd7593a40f04d3 0000-0003-4181-3457 Sondipon Adhikari Sondipon Adhikari true false 10cb5f545bc146fba9a542a1d85f2dea 0000-0002-7521-827X Alexander Shaw Alexander Shaw true false 9f102ff59824fd4f7ce3d40144304395 0000-0003-0953-5936 Nicholas Lavery Nicholas Lavery true false 2020-03-05 ACEM Lattice materials are characterised by their equivalent elastic moduli for analysing mechanical properties of the microstructures. The values of the elastic moduli under static forcing condition are primarily dependent on the geometric properties of the constituent unit cell and the mechanical properties of the intrinsic material. Under a static forcing condition, the equivalent elastic moduli (such as Young’s modulus) are always positive. When dynamic forcing is considered, the equivalent elastic moduli become functions of the applied frequency and they can be negative at certain frequency values. This paper, for the first time, explicitly demonstrates the occurrence of negative equivalent Young’s modulus in lattice materials experimentally. Using additively manufactured titanium-alloy lattice metastructures, it is shown that the real part of experimentally measured in-plane Young’s modulus becomes negative under a dynamic environment. In fact, we show that the onset of such negative Young’s modulus in lattice materials can be precisely determined by capturing the sub-wavelength scale dynamics of the system. Experimental confirmation of the negative Young’s moduli and the onset of the same as a function of frequency provide the necessary physical insights and confidence for its potential exploitation in various multi-functional structural systems and devices across different length scales. Journal Article International Journal of Engineering Science 150 103231 Elsevier BV 0020-7225 1879-2197 Negative Young’s modulus; Lattice material; Dynamic analysis of honeycomb; Frequency-dependent elastic property; Onset of negative elastic moduli; Dynamics of additively manufactured lattice 1 5 2020 2020-05-01 10.1016/j.ijengsci.2020.103231 Short communication COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University Not Required SA acknowledges the financial support from MSCA-IF-2017-799201. TM acknowledges the 'initiation grant form IIT Kanpur during this research work. NPL would like to thank the Welsh European Funding Office (WEFO) for the ASTUTE, ASTUTE 2020 and M2A funding which have enabled Swansea University to invest in an ALM machine. Further thanks go to the Welsh Assembly Government for the funds to set up the Materials Advanced Characterisation Centre (MACH1). The authors would also like to thank Dan Butcher for printing the builds. 2025-03-04T13:41:02.1627901 2020-03-05T09:11:04.7830119 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering Sondipon Adhikari 0000-0003-4181-3457 1 T. Mukhopadhyay 2 Alexander Shaw 0000-0002-7521-827X 3 Nicholas Lavery 0000-0003-0953-5936 4 53739__16781__36b382e7d6fb45b2a827f322ad7cf991.pdf adhikari2020.pdf 2020-03-06T09:57:07.9266663 Output 744206 application/pdf Accepted Manuscript true 2021-02-20T00:00:00.0000000 true eng © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
title Apparent negative values of Young’s moduli of lattice materials under dynamic conditions
spellingShingle Apparent negative values of Young’s moduli of lattice materials under dynamic conditions
Sondipon Adhikari
Alexander Shaw
Nicholas Lavery
title_short Apparent negative values of Young’s moduli of lattice materials under dynamic conditions
title_full Apparent negative values of Young’s moduli of lattice materials under dynamic conditions
title_fullStr Apparent negative values of Young’s moduli of lattice materials under dynamic conditions
title_full_unstemmed Apparent negative values of Young’s moduli of lattice materials under dynamic conditions
title_sort Apparent negative values of Young’s moduli of lattice materials under dynamic conditions
author_id_str_mv 4ea84d67c4e414f5ccbd7593a40f04d3
10cb5f545bc146fba9a542a1d85f2dea
9f102ff59824fd4f7ce3d40144304395
author_id_fullname_str_mv 4ea84d67c4e414f5ccbd7593a40f04d3_***_Sondipon Adhikari
10cb5f545bc146fba9a542a1d85f2dea_***_Alexander Shaw
9f102ff59824fd4f7ce3d40144304395_***_Nicholas Lavery
author Sondipon Adhikari
Alexander Shaw
Nicholas Lavery
author2 Sondipon Adhikari
T. Mukhopadhyay
Alexander Shaw
Nicholas Lavery
format Journal article
container_title International Journal of Engineering Science
container_volume 150
container_start_page 103231
publishDate 2020
institution Swansea University
issn 0020-7225
1879-2197
doi_str_mv 10.1016/j.ijengsci.2020.103231
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 Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering
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description Lattice materials are characterised by their equivalent elastic moduli for analysing mechanical properties of the microstructures. The values of the elastic moduli under static forcing condition are primarily dependent on the geometric properties of the constituent unit cell and the mechanical properties of the intrinsic material. Under a static forcing condition, the equivalent elastic moduli (such as Young’s modulus) are always positive. When dynamic forcing is considered, the equivalent elastic moduli become functions of the applied frequency and they can be negative at certain frequency values. This paper, for the first time, explicitly demonstrates the occurrence of negative equivalent Young’s modulus in lattice materials experimentally. Using additively manufactured titanium-alloy lattice metastructures, it is shown that the real part of experimentally measured in-plane Young’s modulus becomes negative under a dynamic environment. In fact, we show that the onset of such negative Young’s modulus in lattice materials can be precisely determined by capturing the sub-wavelength scale dynamics of the system. Experimental confirmation of the negative Young’s moduli and the onset of the same as a function of frequency provide the necessary physical insights and confidence for its potential exploitation in various multi-functional structural systems and devices across different length scales.
published_date 2020-05-01T16:14:36Z
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score 11.08899

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