Journal article 445 views 272 downloads
Broadband dynamic elastic moduli of honeycomb lattice materials: A generalized analytical approach
Sondipon Adhikari,
T. Mukhopadhyay,
X. Liu
Mechanics of Materials, Volume: 157, Start page: 103796
Swansea University Author: Sondipon Adhikari
-
PDF | Accepted Manuscript
©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)
Download (6.05MB)
DOI (Published version): 10.1016/j.mechmat.2021.103796
Abstract
A generic analytical framework is proposed to obtain the dynamic elastic moduli of lattice materials under steady-state vibration conditions. The dynamic deformation behaviour of the individual beam elements of a lattice is distinct from the behaviour under a static condition. This leads to a comple...
| Published in: | Mechanics of Materials |
|---|---|
| ISSN: | 0167-6636 |
| Published: |
Elsevier BV
2021
|
| Online Access: |
Check full text
|
| URI: | https://cronfa.swan.ac.uk/Record/cronfa56683 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| first_indexed |
2021-04-19T10:20:40Z |
|---|---|
| last_indexed |
2021-05-22T03:24:04Z |
| id |
cronfa56683 |
| recordtype |
SURis |
| fullrecord |
<?xml version="1.0"?><rfc1807><datestamp>2021-05-21T14:44:47.5449403</datestamp><bib-version>v2</bib-version><id>56683</id><entry>2021-04-19</entry><title>Broadband dynamic elastic moduli of honeycomb lattice materials: A generalized analytical approach</title><swanseaauthors><author><sid>4ea84d67c4e414f5ccbd7593a40f04d3</sid><firstname>Sondipon</firstname><surname>Adhikari</surname><name>Sondipon Adhikari</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2021-04-19</date><deptcode>FGSEN</deptcode><abstract>A generic analytical framework is proposed to obtain the dynamic elastic moduli of lattice materials under steady-state vibration conditions. The dynamic deformation behaviour of the individual beam elements of a lattice is distinct from the behaviour under a static condition. This leads to a completely different global deformation pattern of the lattice material and subsequently opens up a tremendous opportunity to modulate amplitude and phase of the elastic properties of lattices as a function of the ambient vibration. The dynamic stiffness approach proposed in this article precisely captures the sub-wavelength scale dynamics of the periodic network of beams in a lattice material using a single beam-like member. Here the dynamic stiffness matrix of a damped beam element based on the Timoshenko beam theory along with axial stretching is coupled with the unit cell-based approach to derive the most general closed-form analytical formulae for the elastic moduli of lattice materials across the whole frequency range. It is systematically shown how the general expressions of dynamic elastic moduli can be reduced to different special cases by neglecting axial and shear deformations under dynamic as well as classical static conditions. The significance of developing the dynamic stiffness approach compared to conventional dynamic finite element approach is highlighted by presenting detailed analytical derivations and representative numerical results. Further, it is shown how the analytical framework can be readily extended to lattices with non-prismatic beam elements with any spatial variation in geometry and intrinsic material properties. In general, research activities in the field of lattice metamaterials dealing with elastic properties revolve around intuitively designing the microstructural geometry of the lattice structure. Here we propose to couple the physics of deformation as a function of vibrating frequency along with the conventional approach of designing microstructural geometry to expand the effective design space significantly. The stretching-enriched physics of deformation in the lattice materials in addition to the bending and shear deformations under dynamic conditions lead to complex-valued elastic moduli due to the presence of damping in the constituent material. The amplitude, as well as the phase of effective elastic properties of lattice materials, can be quantified using the proposed approach. The dependence of Poisson's ratio on the intrinsic material physics in case of a geometrically regular lattice is found to be in contrary to the common notion that Poisson's ratios of perfectly periodic lattices are only the function of microstructural geometry. The generic analytical approach for analysing the elastic moduli is applicable to any form of two- or three-dimensional lattices, and any profile of the constituent beam-like elements (different cross-sections as well as spatially varying geometry and intrinsic material properties) through a wide range of frequency band. The closed-form expressions of elastic moduli derived in this article can be viewed as the broadband dynamic generalisation of the well-established classical expressions of elastic moduli under static loading, essentially adding a new exploitable dimension in the metamaterials research in terms of dynamics of the intrinsic material.</abstract><type>Journal Article</type><journal>Mechanics of Materials</journal><volume>157</volume><journalNumber/><paginationStart>103796</paginationStart><paginationEnd/><publisher>Elsevier BV</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>0167-6636</issnPrint><issnElectronic/><keywords>Frequency-dependent dynamic elastic moduli, Dynamic stiffness for Timoshenko beams, Elastic moduli of lattice metamaterials, Axial and shear deformation effects in lattices, Non-prismatic beam networks</keywords><publishedDay>1</publishedDay><publishedMonth>6</publishedMonth><publishedYear>2021</publishedYear><publishedDate>2021-06-01</publishedDate><doi>10.1016/j.mechmat.2021.103796</doi><url/><notes/><college>COLLEGE NANME</college><department>Science and Engineering - Faculty</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>FGSEN</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2021-05-21T14:44:47.5449403</lastEdited><Created>2021-04-19T11:17:16.9709085</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Engineering and Applied Sciences - Uncategorised</level></path><authors><author><firstname>Sondipon</firstname><surname>Adhikari</surname><order>1</order></author><author><firstname>T.</firstname><surname>Mukhopadhyay</surname><order>2</order></author><author><firstname>X.</firstname><surname>Liu</surname><order>3</order></author></authors><documents><document><filename>56683__19703__ccc1448749d14f559b979f7b42598bb8.pdf</filename><originalFilename>56683.pdf</originalFilename><uploaded>2021-04-20T09:56:39.8933204</uploaded><type>Output</type><contentLength>6344828</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2022-02-18T00:00:00.0000000</embargoDate><documentNotes>©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)</documentNotes><copyrightCorrect>true</copyrightCorrect><language>eng</language><licence>http://creativecommons.org/licenses/by-nc-nd/4.0/</licence></document></documents><OutputDurs/></rfc1807> |
| spelling |
2021-05-21T14:44:47.5449403 v2 56683 2021-04-19 Broadband dynamic elastic moduli of honeycomb lattice materials: A generalized analytical approach 4ea84d67c4e414f5ccbd7593a40f04d3 Sondipon Adhikari Sondipon Adhikari true false 2021-04-19 FGSEN A generic analytical framework is proposed to obtain the dynamic elastic moduli of lattice materials under steady-state vibration conditions. The dynamic deformation behaviour of the individual beam elements of a lattice is distinct from the behaviour under a static condition. This leads to a completely different global deformation pattern of the lattice material and subsequently opens up a tremendous opportunity to modulate amplitude and phase of the elastic properties of lattices as a function of the ambient vibration. The dynamic stiffness approach proposed in this article precisely captures the sub-wavelength scale dynamics of the periodic network of beams in a lattice material using a single beam-like member. Here the dynamic stiffness matrix of a damped beam element based on the Timoshenko beam theory along with axial stretching is coupled with the unit cell-based approach to derive the most general closed-form analytical formulae for the elastic moduli of lattice materials across the whole frequency range. It is systematically shown how the general expressions of dynamic elastic moduli can be reduced to different special cases by neglecting axial and shear deformations under dynamic as well as classical static conditions. The significance of developing the dynamic stiffness approach compared to conventional dynamic finite element approach is highlighted by presenting detailed analytical derivations and representative numerical results. Further, it is shown how the analytical framework can be readily extended to lattices with non-prismatic beam elements with any spatial variation in geometry and intrinsic material properties. In general, research activities in the field of lattice metamaterials dealing with elastic properties revolve around intuitively designing the microstructural geometry of the lattice structure. Here we propose to couple the physics of deformation as a function of vibrating frequency along with the conventional approach of designing microstructural geometry to expand the effective design space significantly. The stretching-enriched physics of deformation in the lattice materials in addition to the bending and shear deformations under dynamic conditions lead to complex-valued elastic moduli due to the presence of damping in the constituent material. The amplitude, as well as the phase of effective elastic properties of lattice materials, can be quantified using the proposed approach. The dependence of Poisson's ratio on the intrinsic material physics in case of a geometrically regular lattice is found to be in contrary to the common notion that Poisson's ratios of perfectly periodic lattices are only the function of microstructural geometry. The generic analytical approach for analysing the elastic moduli is applicable to any form of two- or three-dimensional lattices, and any profile of the constituent beam-like elements (different cross-sections as well as spatially varying geometry and intrinsic material properties) through a wide range of frequency band. The closed-form expressions of elastic moduli derived in this article can be viewed as the broadband dynamic generalisation of the well-established classical expressions of elastic moduli under static loading, essentially adding a new exploitable dimension in the metamaterials research in terms of dynamics of the intrinsic material. Journal Article Mechanics of Materials 157 103796 Elsevier BV 0167-6636 Frequency-dependent dynamic elastic moduli, Dynamic stiffness for Timoshenko beams, Elastic moduli of lattice metamaterials, Axial and shear deformation effects in lattices, Non-prismatic beam networks 1 6 2021 2021-06-01 10.1016/j.mechmat.2021.103796 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2021-05-21T14:44:47.5449403 2021-04-19T11:17:16.9709085 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Sondipon Adhikari 1 T. Mukhopadhyay 2 X. Liu 3 56683__19703__ccc1448749d14f559b979f7b42598bb8.pdf 56683.pdf 2021-04-20T09:56:39.8933204 Output 6344828 application/pdf Accepted Manuscript true 2022-02-18T00:00:00.0000000 ©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 http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| title |
Broadband dynamic elastic moduli of honeycomb lattice materials: A generalized analytical approach |
| spellingShingle |
Broadband dynamic elastic moduli of honeycomb lattice materials: A generalized analytical approach Sondipon Adhikari |
| title_short |
Broadband dynamic elastic moduli of honeycomb lattice materials: A generalized analytical approach |
| title_full |
Broadband dynamic elastic moduli of honeycomb lattice materials: A generalized analytical approach |
| title_fullStr |
Broadband dynamic elastic moduli of honeycomb lattice materials: A generalized analytical approach |
| title_full_unstemmed |
Broadband dynamic elastic moduli of honeycomb lattice materials: A generalized analytical approach |
| title_sort |
Broadband dynamic elastic moduli of honeycomb lattice materials: A generalized analytical approach |
| author_id_str_mv |
4ea84d67c4e414f5ccbd7593a40f04d3 |
| author_id_fullname_str_mv |
4ea84d67c4e414f5ccbd7593a40f04d3_***_Sondipon Adhikari |
| author |
Sondipon Adhikari |
| author2 |
Sondipon Adhikari T. Mukhopadhyay X. Liu |
| format |
Journal article |
| container_title |
Mechanics of Materials |
| container_volume |
157 |
| container_start_page |
103796 |
| publishDate |
2021 |
| institution |
Swansea University |
| issn |
0167-6636 |
| doi_str_mv |
10.1016/j.mechmat.2021.103796 |
| publisher |
Elsevier BV |
| college_str |
Faculty of Science and Engineering |
| hierarchytype |
|
| 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 |
| active_str |
0 |
| description |
A generic analytical framework is proposed to obtain the dynamic elastic moduli of lattice materials under steady-state vibration conditions. The dynamic deformation behaviour of the individual beam elements of a lattice is distinct from the behaviour under a static condition. This leads to a completely different global deformation pattern of the lattice material and subsequently opens up a tremendous opportunity to modulate amplitude and phase of the elastic properties of lattices as a function of the ambient vibration. The dynamic stiffness approach proposed in this article precisely captures the sub-wavelength scale dynamics of the periodic network of beams in a lattice material using a single beam-like member. Here the dynamic stiffness matrix of a damped beam element based on the Timoshenko beam theory along with axial stretching is coupled with the unit cell-based approach to derive the most general closed-form analytical formulae for the elastic moduli of lattice materials across the whole frequency range. It is systematically shown how the general expressions of dynamic elastic moduli can be reduced to different special cases by neglecting axial and shear deformations under dynamic as well as classical static conditions. The significance of developing the dynamic stiffness approach compared to conventional dynamic finite element approach is highlighted by presenting detailed analytical derivations and representative numerical results. Further, it is shown how the analytical framework can be readily extended to lattices with non-prismatic beam elements with any spatial variation in geometry and intrinsic material properties. In general, research activities in the field of lattice metamaterials dealing with elastic properties revolve around intuitively designing the microstructural geometry of the lattice structure. Here we propose to couple the physics of deformation as a function of vibrating frequency along with the conventional approach of designing microstructural geometry to expand the effective design space significantly. The stretching-enriched physics of deformation in the lattice materials in addition to the bending and shear deformations under dynamic conditions lead to complex-valued elastic moduli due to the presence of damping in the constituent material. The amplitude, as well as the phase of effective elastic properties of lattice materials, can be quantified using the proposed approach. The dependence of Poisson's ratio on the intrinsic material physics in case of a geometrically regular lattice is found to be in contrary to the common notion that Poisson's ratios of perfectly periodic lattices are only the function of microstructural geometry. The generic analytical approach for analysing the elastic moduli is applicable to any form of two- or three-dimensional lattices, and any profile of the constituent beam-like elements (different cross-sections as well as spatially varying geometry and intrinsic material properties) through a wide range of frequency band. The closed-form expressions of elastic moduli derived in this article can be viewed as the broadband dynamic generalisation of the well-established classical expressions of elastic moduli under static loading, essentially adding a new exploitable dimension in the metamaterials research in terms of dynamics of the intrinsic material. |
| published_date |
2021-06-01T04:11:49Z |
| _version_ |
1763753810419777536 |
| score |
11.036531 |