{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T22:59:14Z","timestamp":1774047554289,"version":"3.50.1"},"reference-count":77,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,4,10]],"date-time":"2020-04-10T00:00:00Z","timestamp":1586476800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"\u0420\u043e\u0441\u0441\u0438\u0439\u0441\u043a\u0438\u0439 \u0424\u043e\u043d\u0434 \u0424\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0445 \u0418\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u0439 (\u0420\u0424\u0424\u0418)","award":["18-32-20158"],"award-info":[{"award-number":["18-32-20158"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Structure evolution and mechanical response of the carbon nanotube (CNT) bundle under lateral biaxial compression is investigated in plane strain conditions using the chain model. In this model, tensile and bending rigidity of CTN walls, and the van der Waals interactions between them are taken into account. Initially the bundle in cross section is a triangular lattice of circular zigzag CNTs. Under increasing strain control compression, several structure transformations are observed. Firstly, the second-order phase transition leads to the crystalline structure with doubled translational cell. Then the first-order phase transition takes place with the appearance of collapsed CNTs. Further compression results in increase of the fraction of collapsed CNTs at nearly constant compressive stress and eventually all CNTs collapse. It is found that the potential energy of the CNT bundle during deformation changes mainly due to bending of CNT walls, while the contribution from the walls tension-compression and from the van der Waals energies is considerably smaller.<\/jats:p>","DOI":"10.3390\/computation8020027","type":"journal-article","created":{"date-parts":[[2020,4,13]],"date-time":"2020-04-13T04:45:31Z","timestamp":1586753131000},"page":"27","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Mechanical Response of Carbon Nanotube Bundle to Lateral Compression"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6196-6093","authenticated-orcid":false,"given":"Dina U.","family":"Abdullina","sequence":"first","affiliation":[{"name":"Department of Physics and Technology of Nanomaterials, Bashkir State University, Zaki Validi St. 32, 450076 Ufa, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5975-4849","authenticated-orcid":false,"given":"Elena A.","family":"Korznikova","sequence":"additional","affiliation":[{"name":"Institute for Metals Superplasticity Problems, Russian Academy of Sciences, Khalturin St., 39, 450001 Ufa, Russia"},{"name":"Institute for Molecule and Crystal Physics, UFRC, RAS, Oktyabrya Av., 151, 450075 Ufa, Russia"}]},{"given":"Volodymyr I.","family":"Dubinko","sequence":"additional","affiliation":[{"name":"NSC Kharkov Institute of Physics and Technology, 61108 Kharkov, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3374-6020","authenticated-orcid":false,"given":"Denis V.","family":"Laptev","sequence":"additional","affiliation":[{"name":"B. Verkin Institute for Low Temperature Physics and Engineering, 61103 Kharkiv, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7211-0741","authenticated-orcid":false,"given":"Alexey A.","family":"Kudreyko","sequence":"additional","affiliation":[{"name":"Department of Medical Physics and Informatics, Bashkir State Medical University, Lenina St. 3, 450008 Ufa, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3063-9759","authenticated-orcid":false,"given":"Elvira G.","family":"Soboleva","sequence":"additional","affiliation":[{"name":"Yurga Institute of Technology (Branch), National Research Tomsk Polytechnic University, 652050 Yurga, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6744-4445","authenticated-orcid":false,"given":"Sergey V.","family":"Dmitriev","sequence":"additional","affiliation":[{"name":"Institute for Metals Superplasticity Problems, Russian Academy of Sciences, Khalturin St., 39, 450001 Ufa, Russia"},{"name":"Institute for Molecule and Crystal Physics, UFRC, RAS, Oktyabrya Av., 151, 450075 Ufa, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7660-2911","authenticated-orcid":false,"given":"Kun","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1512","DOI":"10.1039\/b802589b","article-title":"Curves ahead: Molecular receptors for fullerenes based on concave-convex complementarity","volume":"37","year":"2008","journal-title":"Chem. Soc. Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1002\/(SICI)1521-3951(199901)211:1<401::AID-PSSB401>3.0.CO;2-N","article-title":"Non-traditional carbon semiconductors prepared from fullerite C60 and carbyne under high pressure","volume":"211","author":"Lyapin","year":"1999","journal-title":"Phys. Status Solidi B"},{"key":"ref_3","first-page":"229","article-title":"Carbon nanocluster-based superhard materials","volume":"12","author":"Popov","year":"2002","journal-title":"New Diam. Front. C. Tech."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.ssc.2007.03.052","article-title":"Raman spectroscopy of graphene and graphite: Disorder, electron-phonon coupling, doping and nonadiabatic effects","volume":"143","author":"Ferrari","year":"2007","journal-title":"Solid State Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"095012","DOI":"10.1088\/1367-2630\/11\/9\/095012","article-title":"Heat conduction in graphene: Experimental study and theoretical interpretation","volume":"11","author":"Ghosh","year":"2009","journal-title":"New J. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1103\/PhysRevLett.73.676","article-title":"Structural properties of a carbon-nanotube crystal","volume":"73","author":"Tersoff","year":"1994","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1126\/science.273.5274.483","article-title":"Crystalline ropes of metallic carbon nanotubes","volume":"273","author":"Thess","year":"1996","journal-title":"Science"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1543","DOI":"10.1016\/S0266-3538(03)00056-3","article-title":"Transverse mechanical properties of single-walled carbon nanotube crystals. Part I: Determination of elastic moduli","volume":"63","author":"Saether","year":"2003","journal-title":"Compos. Sci. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"065501","DOI":"10.1103\/PhysRevLett.88.065501","article-title":"Kinetic theory of symmetry-dependent strength in carbon nanotubes","volume":"88","author":"Samsonidze","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1080\/10408430208500497","article-title":"Carbon nanostructures","volume":"27","author":"Shenderova","year":"2002","journal-title":"Crit. Rev. Solid State"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1115\/1.1755245","article-title":"Fundamental mechanical properties of carbon nanotubes: Current understanding and the related experimental studies","volume":"126","author":"Yu","year":"2004","journal-title":"J. Eng. Mater. T. ASME"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1126\/science.287.5453.637","article-title":"Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load","volume":"287","author":"Yu","year":"2000","journal-title":"Science"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1250","DOI":"10.1016\/j.cap.2016.04.023","article-title":"Multifunctional characterization of carbon nanotube sheets, yarns, and their composites","volume":"16","author":"Truong","year":"2016","journal-title":"Curr. Appl. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1016\/j.carbon.2017.02.043","article-title":"Carbon nanotube forest based electrostatic capacitor with excellent dielectric performances","volume":"116","author":"Yao","year":"2017","journal-title":"Carbon"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.carbon.2018.04.039","article-title":"An advanced anti-icing\/de-icing system utilizing highly aligned carbon nanotube webs","volume":"136","author":"Yao","year":"2018","journal-title":"Carbon"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1016\/j.carbon.2017.12.045","article-title":"Aligned carbon nanotube webs embedded in a composite laminate: A route towards a highly tunable electro-thermal system","volume":"129","author":"Yao","year":"2018","journal-title":"Carbon"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1070\/RC2013v082n06ABEH004340","article-title":"Materials made of carbon nanotubes. The carbon nanotube forest","volume":"82","author":"Rakov","year":"2013","journal-title":"Russ. Chem. Rev."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.mser.2010.06.003","article-title":"Controlled growth and modification of vertically-aligned carbon nanotubes for multifunctional applications","volume":"70","author":"Chen","year":"2010","journal-title":"Mater. Sci. Eng. R Rep."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"20576","DOI":"10.1021\/jp904152v","article-title":"Collective mechanism for the evolution and self-termination of vertically aligned carbon nanotube growth","volume":"113","author":"Bedewy","year":"2009","journal-title":"J. Phys. Chem. C"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1080\/00018732.2011.599963","article-title":"Physics and applications of aligned carbon nanotubes","volume":"60","author":"Lan","year":"2011","journal-title":"Adv. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"365304","DOI":"10.1088\/1361-6528\/aacc5d","article-title":"A bottom-up approach for controlled deformation of carbon nanotubes through blistering of supporting substrate surface","volume":"29","author":"Prudkovskiy","year":"2018","journal-title":"Nanotechnology"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5552","DOI":"10.1103\/PhysRevLett.84.5552","article-title":"Tensile loading of ropes of single wall carbon nanotubes and their mechanical properties","volume":"84","author":"Yu","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3046","DOI":"10.1039\/C8NR07554A","article-title":"Hybrid carbon nanostructured fibers: Stepping stone for intelligent textile-based electronics","volume":"11","author":"Dhanabalan","year":"2019","journal-title":"Nanoscale"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1038\/s41565-018-0141-z","article-title":"Carbon nanotube bundles with tensile strength over 80 GPa","volume":"13","author":"Bai","year":"2018","journal-title":"Nat. Nanotechnol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1016\/j.carbon.2016.04.043","article-title":"Functionalization and densification of inter-bundle interfaces for improvement in electrical and thermal transport of carbon nanotube fibers","volume":"105","author":"Qiu","year":"2016","journal-title":"Carbon"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1016\/j.carbon.2018.04.071","article-title":"Hierarchical structure of carbon nanotube fibers, and the change of structure during densification by wet stretching","volume":"136","author":"Cho","year":"2018","journal-title":"Carbon"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.carbon.2018.03.006","article-title":"Tensile properties of carbon nanotube fibres described by the fibrillar crystallite model","volume":"133","author":"Ridruejo","year":"2018","journal-title":"Carbon"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1016\/j.pmatsci.2011.08.001","article-title":"Fundamentals, processes and applications of high-permittivity polymer-matrix composites","volume":"57","author":"Dang","year":"2012","journal-title":"Prog. Mater. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1179\/095066009X12572530170543","article-title":"Carbon nanotube reinforced metal matrix composites\u2014A review","volume":"55","author":"Bakshi","year":"2010","journal-title":"Int. Mater. Rev."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1016\/j.compositesb.2015.03.014","article-title":"Mechanical and tribological properties of self-lubricating metal matrix nanocomposites reinforced by carbon nanotubes (CNTs) and graphene\u2014A review","volume":"77","author":"Omrani","year":"2015","journal-title":"Compos. Part B: Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"42873","DOI":"10.1038\/srep42873","article-title":"Long-lasting solid lubrication by CNT-coated patterned surfaces","volume":"7","author":"Reinert","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_32","first-page":"39","article-title":"Generalized archard law of wear based on Rabinowicz criterion of wear particle formation","volume":"17","author":"Popov","year":"2019","journal-title":"Facta Univ. Ser. Mech. Eng."},{"key":"ref_33","first-page":"65","article-title":"Synergistic tribological properties of synthetic magnesium silicate hydroxide combined with amphiphilic moleculaes","volume":"17","author":"Wang","year":"2019","journal-title":"Facta Univ. Ser. Mech. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.1126\/science.1118957","article-title":"Super-compressible foamlike carbon nanotube films","volume":"310","author":"Cao","year":"2005","journal-title":"Science"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.mser.2015.02.001","article-title":"Spherical nanoindentation stress\u2013strain curves","volume":"91","author":"Pathak","year":"2015","journal-title":"Mater. Sci. Eng. R Rep."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1969","DOI":"10.1016\/j.carbon.2009.03.042","article-title":"Viscoelasticity and high buckling stress of dense carbon nanotube brushes","volume":"47","author":"Pathak","year":"2009","journal-title":"Carbon"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1016\/j.carbon.2010.09.034","article-title":"Length dependent foam-like mechanical response of axially indented vertically oriented carbon nanotube arrays","volume":"49","author":"Maschmann","year":"2011","journal-title":"Carbon"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"3190","DOI":"10.1016\/j.carbon.2011.03.043","article-title":"Buckling initiation and displacement dependence in compression of vertically aligned carbon nanotube arrays","volume":"49","author":"Cao","year":"2011","journal-title":"Carbon"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.ijsolstr.2017.06.025","article-title":"Compression and recovery of carbon nanotube forests described as a phase transition","volume":"122\u2013123","author":"Liang","year":"2017","journal-title":"Int. J. Solids Struct."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1016\/j.apsusc.2016.11.008","article-title":"Surface analysis and mechanical behaviour mapping of vertically aligned CNT forest array through nanoindentation","volume":"396","author":"Koumoulos","year":"2017","journal-title":"Appl. Surf. Sci."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"223103","DOI":"10.1063\/1.4802080","article-title":"Buckling-driven delamination of carbon nanotube forests","volume":"102","author":"Hutchens","year":"2013","journal-title":"Appl. Phys. Lett."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"568","DOI":"10.1016\/j.carbon.2018.09.076","article-title":"From high pressure radial collapse to graphene ribbon formation in triple-wall carbon nanotubes","volume":"141","author":"Alencar","year":"2019","journal-title":"Carbon"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2268","DOI":"10.1021\/nl051637p","article-title":"Structural transformations of carbon nanotubes under hydrostatic pressure","volume":"5","author":"Tangney","year":"2005","journal-title":"Nano Lett."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"075423","DOI":"10.1103\/PhysRevB.73.075423","article-title":"Transition states and minimum energy pathways for the collapse of carbon nanotubes","volume":"73","author":"Zhang","year":"2006","journal-title":"Phys. Rev. B"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"495705","DOI":"10.1088\/0957-4484\/19\/49\/495705","article-title":"Multiple radial corrugations in multiwalled carbon nanotubes under pressure","volume":"19","author":"Shima","year":"2008","journal-title":"Nanotechnology"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"371","DOI":"10.3103\/S1063457612060111","article-title":"High-pressure behaviors of carbon nanotubes","volume":"34","author":"Zhao","year":"2012","journal-title":"J. Superhard Mater."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"025019","DOI":"10.1088\/2053-1591\/aaecc1","article-title":"An ex-situ method to convert vertically aligned carbon nanotubes array to horizontally aligned carbon nanotubes mat","volume":"6","author":"Islam","year":"2019","journal-title":"Mater. Res. Express"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"3661","DOI":"10.1039\/C7CS00104E","article-title":"Horizontally aligned carbon nanotube arrays: Growth mechanism, controlled synthesis, characterization, properties and applications","volume":"46","author":"Zhang","year":"2017","journal-title":"Chem. Soc. Rev."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/j.compositesa.2015.06.009","article-title":"Effects of CNT diameter on mechanical properties of aligned CNT sheets and composites","volume":"76","author":"Nam","year":"2015","journal-title":"Compos. Part A Appl. Sci. Manuf."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"21014","DOI":"10.1038\/srep21014","article-title":"Remarkably enhanced thermal transport based on a flexible horizontally-aligned carbon nanotube array film","volume":"6","author":"Qiu","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1887","DOI":"10.1103\/PhysRevLett.85.1887","article-title":"Compressibility and polygonization of single-walled carbon nanotubes under hydrostatic pressure","volume":"85","author":"Tang","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"143.1","DOI":"10.1088\/1367-2630\/5\/1\/143","article-title":"Structural changes in single-walled carbon nanotubes under non-hydrostatic pressures: X-ray and Raman studies","volume":"5","author":"Karmakar","year":"2003","journal-title":"New J. Phys."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1115\/1.1490129","article-title":"Mechanics of carbon nanotubes","volume":"55","author":"Qian","year":"2002","journal-title":"Appl. Mech. Rev."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1016\/j.carbon.2018.11.066","article-title":"Phase transformation as the mechanism of mechanical deformation of vertically aligned carbon nanotube arrays: Insights from mesoscopic modeling","volume":"143","author":"Wittmaack","year":"2019","journal-title":"Carbon"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.compscitech.2018.03.014","article-title":"Mesoscopic modeling of the uniaxial compression and recovery of vertically aligned carbon","volume":"166","author":"Wittmaack","year":"2018","journal-title":"Compos. Sci. Technol."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"2511","DOI":"10.1103\/PhysRevLett.76.2511","article-title":"Nanomechanics of carbon tubes: Instabilities beyond linear response","volume":"76","author":"Yakobson","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2016.05.003","article-title":"Nonlocal continuum-based modeling of mechanical characteristics of nanoscopic structures","volume":"638","author":"Ghavanloo","year":"2016","journal-title":"Phys. Rep."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/S0038-1098(01)00383-0","article-title":"Ranges of applicability for the continuum beam model in the mechanics of carbon nanotubes and nanorods","volume":"120","author":"Harik","year":"2001","journal-title":"Solid State Commun."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.jmps.2019.03.023","article-title":"Novel nonlinear coarse-grained potentials of carbon nanotubes","volume":"128","author":"Ji","year":"2019","journal-title":"J. Mech. Phys. Solids"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"115410","DOI":"10.1103\/PhysRevB.100.115410","article-title":"Stacking- and chirality-dependent collapse of single-walled carbon nanotubes: A large-scale density-functional study","volume":"100","author":"Impellizzeri","year":"2019","journal-title":"Phys. Rev. B"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1038\/377135a0","article-title":"Fully collapsed carbon nanotubes","volume":"377","author":"Chopra","year":"1995","journal-title":"Nature"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"175501","DOI":"10.1103\/PhysRevLett.101.175501","article-title":"Dominoes in carbon nanotubes","volume":"101","author":"Chang","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1080\/1536383X.2019.1680974","article-title":"Carbon vs silicon polyprismanes: A comparative study of metallic sp3-hybridized allotropes","volume":"28","author":"Maslov","year":"2020","journal-title":"Fuller. Nanotub. Car. Nanostructures"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.eml.2015.06.002","article-title":"Crack tip fields in soft elastic solids subjected to large quasi-static deformation\u2014A review","volume":"4","author":"Long","year":"2015","journal-title":"Extrem. Mech. Lett."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.eml.2016.10.002","article-title":"Flaw sensitivity of highly stretchable materials","volume":"10","author":"Chen","year":"2017","journal-title":"Extreme Mech. Lett."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"2049","DOI":"10.1002\/adma.201405788","article-title":"Broadband and tunable high-performance microwave absorption of an ultralight and highly compressible graphene foam","volume":"27","author":"Zhang","year":"2015","journal-title":"Adv. Mater."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"215704","DOI":"10.1088\/1361-6528\/aab2f4","article-title":"Graphene nanoribbon as an elastic damper","volume":"29","author":"Evazzade","year":"2018","journal-title":"Nanotechnology"},{"key":"ref_68","first-page":"1","article-title":"Elastic damper based on carbon nanotube bundle","volume":"18","author":"Rysaeva","year":"2020","journal-title":"Facta Univ. Ser. Mech. Eng."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"035412","DOI":"10.1103\/PhysRevB.92.035412","article-title":"Scroll configurations of carbon nanoribbons","volume":"92","author":"Savin","year":"2015","journal-title":"Phys. Rev. B"},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Korznikova, E.A., Rysaeva, L.K., Savin, A.V., Soboleva, E.G., Ekomasov, E.G., Ilgamov, M.A., and Dmitriev, S.V. (2019). Chain model for carbon nanotube bundle under plane strain conditions. Materials, 12.","DOI":"10.3390\/ma12233951"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"2348","DOI":"10.1134\/S1063783415110293","article-title":"Simulation of folded and scrolled packings of carbon nanoribbons","volume":"57","author":"Savin","year":"2015","journal-title":"Phys. Solid State"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"1278","DOI":"10.1134\/S1063783416060317","article-title":"Symmetric scrolled packings of multilayered carbon nanoribbons","volume":"58","author":"Savin","year":"2016","journal-title":"Phys. Solid State"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.commatsci.2017.03.047","article-title":"Graphene nanoribbon winding around carbon nanotube","volume":"135","author":"Savin","year":"2017","journal-title":"Comp. Mater. Sci."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/978-3-319-92234-8_14","article-title":"2D chain models of nanoribbon scrolls","volume":"94","author":"Savin","year":"2019","journal-title":"Adv. Struct. Mater."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"235411","DOI":"10.1103\/PhysRevB.99.235411","article-title":"Dynamics of surface graphene ripplocations on a flat graphite substrate","volume":"99","author":"Savin","year":"2019","journal-title":"Phys. Rev. B"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.pmatsci.2018.09.004","article-title":"Recent progress on graphene-analogous 2D nanomaterials: Properties, modeling and applications","volume":"100","author":"Liu","year":"2019","journal-title":"Progr. Mater. Sci."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"1630001","DOI":"10.1142\/S2424913016300012","article-title":"Discrete breathers in crystals: Energy localization and transport","volume":"1","author":"Dmitriev","year":"2016","journal-title":"J. Micromech. Mol. Phys."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/8\/2\/27\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:17:22Z","timestamp":1760174242000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/8\/2\/27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,10]]},"references-count":77,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["computation8020027"],"URL":"https:\/\/doi.org\/10.3390\/computation8020027","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,10]]}}}