{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T05:03:54Z","timestamp":1787029434434,"version":"build-2736575974"},"reference-count":38,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2022,12,8]],"date-time":"2022-12-08T00:00:00Z","timestamp":1670457600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["21-73-20205"],"award-info":[{"award-number":["21-73-20205"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Polymers"],"abstract":"<jats:p>The reported study was devoted to the investigation of viscoelastic behavior for solid and porous ultra-high molecular weight polyethylene (UHMWPE) under compression. The obtained experimental stress curves were interpreted using a two-term Prony series to represent the superposition of two coexisting activation processes corresponding to long molecular (~160 s) and short structural (~20 s) time scales, respectively, leading to good statistical correlation with the observations. In the case of porous polymer, the internal strain redistribution during relaxation was quantified using digital image correlation (DIC) analysis. The strongly inhomogeneous deformation of the porous polymer was found not to affect the relaxation times. To illustrate the possibility of generalizing the results to three dimensions, X-ray tomography was used to examine the porous structure relaxation at the macro- and micro-scale levels. DIC analysis revealed positive correlation between the applied force and relative density. The apparent stiffness variation for UHMWPE foams with mixed open and closed cells was described using a newly proposed three-term expression. Furthermore, in situ tensile loading and X-ray scattering study was applied for isotropic solid UHMWPE specimens to investigate the evolution of internal structure and orientation during drawing and stress relaxation in another loading mode.<\/jats:p>","DOI":"10.3390\/polym14245374","type":"journal-article","created":{"date-parts":[[2022,12,9]],"date-time":"2022-12-09T03:23:49Z","timestamp":1670556229000},"page":"5374","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Analysis of Stress Relaxation in Bulk and Porous Ultra-High Molecular Weight Polyethylene (UHMWPE)"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1105-9206","authenticated-orcid":false,"given":"Eugene S.","family":"Statnik","sequence":"first","affiliation":[{"name":"HSM Laboratory, Center for Digital Engineering, Skoltech, 121205 Moscow, Russia"},{"name":"\u201cLuch\u201d Laboratory, National University of Science and Technology MISiS, 119049 Moscow, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9048-8083","authenticated-orcid":false,"given":"Alexey I.","family":"Salimon","sequence":"additional","affiliation":[{"name":"HSM Laboratory, Center for Digital Engineering, Skoltech, 121205 Moscow, Russia"},{"name":"\u201cLuch\u201d Laboratory, National University of Science and Technology MISiS, 119049 Moscow, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5016-1553","authenticated-orcid":false,"given":"Yulia E.","family":"Gorshkova","sequence":"additional","affiliation":[{"name":"\u201cLuch\u201d Laboratory, National University of Science and Technology MISiS, 119049 Moscow, Russia"},{"name":"Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia"},{"name":"Institute of Physics, Kazan Federal University, 420008 Kazan, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Natallia S.","family":"Kaladzinskaya","sequence":"additional","affiliation":[{"name":"Laboratory of Electron Probe Analysis, Department of Materials Research and Testing, SSI O.V. Roman Powder Metallurgy Institute, 220005 Minsk, Belarus"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ludmila V.","family":"Markova","sequence":"additional","affiliation":[{"name":"Laboratory of Electron Probe Analysis, Department of Materials Research and Testing, SSI O.V. Roman Powder Metallurgy Institute, 220005 Minsk, Belarus"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3558-5198","authenticated-orcid":false,"given":"Alexander M.","family":"Korsunsky","sequence":"additional","affiliation":[{"name":"MBLEM, Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hussain, M., Naqvi, R.A., Abbas, N., Khan, S.M., Nawaz, S., Hussain, A., Zahra, N., and Khalid, M.W. (2020). Ultra-High-Molecular-Weight-Polyethylene (UHMWPE) as a Promising Polymer Material for Biomedical Applications: A Concise Review. Polymers, 12.","DOI":"10.3390\/polym12020323"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/S0142-9612(00)00195-2","article-title":"Properties of Crosslinked Ultra-High-Molecular-Weight Polyethylene","volume":"22","author":"Gladius","year":"2001","journal-title":"Biomaterials"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2100536","DOI":"10.1002\/mame.202100536","article-title":"Control of Polymer Properties by Entanglement: A Review","volume":"306","author":"Kong","year":"2021","journal-title":"Macromol. Mater. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1080\/1023666X.2011.539006","article-title":"Crystalline Phase in Gelled UHMWPE Reactor Powder","volume":"16","author":"Pakhomov","year":"2011","journal-title":"Int. J. Polym. Anal. Charact."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1016\/j.jmbbm.2008.12.006","article-title":"Ultra High Molecular Weight Polyethylene: Mechanics, Morphology, and Clinical Behavior","volume":"2","author":"Sobieraj","year":"2009","journal-title":"J. Mech. Behav. Biomed. Mater."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1016\/S0142-9612(96)00194-9","article-title":"Properties of Self-reinforced Ultra-high-molecular-weight Polyethylene Composites","volume":"18","author":"Deng","year":"1997","journal-title":"Biomaterials"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Zherebtsov, D., Chukov, D., Royaud, I., Pon\u00e7ot, M., Larin, I., Statnik, E.S., Drozdova, T., Kirichenko, A., Salimon, A., and Sherif, G. (2021). On the Structural Peculiarities of Self-Reinforced Composite Materials Based on UHMWPE Fibers. Polymers, 13.","DOI":"10.20944\/preprints202104.0090.v1"},{"key":"ref_8","unstructured":"Rutledge, G.C., and Park, J.H. (2017). Gel-electrospinning Process for Preparing High Performance Polymer Nanofibers. (WO2017123293A2), Patent."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1002\/polb.21122","article-title":"Electrospinning of Ultra-high-molecular-weight Polyethylene Nanofibers","volume":"45","author":"Rein","year":"2007","journal-title":"J. Polym. Sci. Part B"},{"key":"ref_10","unstructured":"Li, J., Li, R., Gu, Q., Zhang, Q., Yu, T.X., and Gao, P. (2019). Flexible Ultrastrong 100-nm Polyethylene Membranes with Polygonal Pore Structures. arXiv."},{"key":"ref_11","unstructured":"Pluyter, P.B., Lambert, P.S., Unen, L.H.T., and Rutten, H.J.J. (2010). Process of Making Microporous Films of UHMWPE. (Patent US5248461A)."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1016\/j.msec.2016.12.104","article-title":"Multilayer Porous UHMWPE Scaffolds for Bone Defects Replacement","volume":"73","author":"Maksimkin","year":"2017","journal-title":"Mater. Sci. Eng. C"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"121824","DOI":"10.1016\/j.polymer.2019.121824","article-title":"Properties of Highly Porous Aerogels Prepared from Ultra-high Molecular Weight Polyethylene","volume":"182","author":"Lermontov","year":"2019","journal-title":"Polymer"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1181","DOI":"10.1016\/S0266-3538(00)00024-5","article-title":"Relaxation Processes in Polyethylene Fibre-reinforced Polyethylene Composites","volume":"60","author":"Pegoretti","year":"2000","journal-title":"Compos. Sci. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Salimon, A.I., Statnik, E.S., Zadorozhnyy, M.Y., Senatov, F.S., Zherebtsov, D.D., Safonov, A.A., and Korsunsky, A.M. (2019). Porous Open-Cell UHMWPE: Experimental Study of Structure and Mechanical Properties. Materials, 12.","DOI":"10.3390\/ma12132195"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Statnik, E.S., Dragu, C., Besnard, C., Lunt, A.J.G., Salimon, A.I., Maksimkin, A., and Korsunsky, A.M. (2020). Multi-Scale Digital Image Correlation Analysis of In situ Deformation of Open-Cell Porous Ultra-High Molecular Weight Polyethylene Foam. Polymers, 12.","DOI":"10.20944\/preprints202010.0254.v1"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"101052","DOI":"10.1016\/j.mtcomm.2020.101052","article-title":"The Fabrication and Characterization of Bioengineered Ultra-high Molecular Weight Polyethylene-collagen-hap Hybrid Bone-cartilage Patch","volume":"24","author":"Kan","year":"2020","journal-title":"Mater. Today Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"325","DOI":"10.4028\/www.scientific.net\/MSF.660-661.325","article-title":"High-Energy Mechanical Milling of Ultra-High Molecular Weight Polyethylene (UHMWPE)","volume":"660\u2013661","author":"Gabriel","year":"2010","journal-title":"Mater. Sci. Forum"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.mtcomm.2018.01.001","article-title":"Architected UHMWPE Simulating Trabecular Bone Tissue","volume":"14","author":"Senatov","year":"2018","journal-title":"Mater. Today Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"122744","DOI":"10.1016\/j.polymer.2020.122744","article-title":"Ultra-high Molecular Weight Polyethylene with Hybrid Porous Structure","volume":"202","author":"Lermontov","year":"2020","journal-title":"Polymer"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1111\/jmi.12879","article-title":"Innovations in Laboratory-based Dynamic Micro-CT to Accelerate in situ Research","volume":"277","author":"Dewanckele","year":"2020","journal-title":"J. Microsc."},{"key":"ref_22","unstructured":"(2020). Dragonfly 2020.2 [Computer Software], Object Research Systems (ORS) Inc.. Available online: http:\/\/www.theobjects.com\/dragonfly."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1038\/nmeth.2019","article-title":"Fiji: An open-source platform for biological-image analysis","volume":"9","author":"Schindelin","year":"2012","journal-title":"Nat. Methods"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1007\/s11340-015-0009-1","article-title":"Ncorr: Open-Source 2D Digital Image Correlation Matlab Software","volume":"55","author":"Blaber","year":"2015","journal-title":"Exp. Mech."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1590\/1679-78251412","article-title":"Viscoelastic Relaxation Modulus Characterization Using Prony Series","volume":"12","author":"Pacheco","year":"2015","journal-title":"Lat. Am. J. Solids Struct."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1007\/BF00398438","article-title":"Volume changes during stress relaxation in polyethylene","volume":"34","author":"Delin","year":"1995","journal-title":"Rheol. Acta"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1021\/ma501633f","article-title":"In situ SAXS Studies of Structural Relaxation of an Ordered Block Copolymer Melt Following Cessation of Uniaxial Extensional Flow","volume":"48","author":"McCready","year":"2015","journal-title":"Macromolecules"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"6796","DOI":"10.1021\/acs.macromol.0c01077","article-title":"Polymerization of Low-Entangled Ultrahigh Molecular Weight Polyethylene: Analytical Model and Computer Simulations","volume":"53","author":"Petrov","year":"2020","journal-title":"Macromolecules"},{"key":"ref_29","unstructured":"McDaniel, P., Deitzel, J.M., and Gillespie, J.W. (2022, October 07). Structural Hierarchy of Ultra High Molecular Weight Polyethylene (UHMWPE) Fibers Studied by Atomic Force Microscopy. Available online: https:\/\/www.ccm.udel.edu\/research_summaries\/structural-hierarchy-of-ultra-high-molecular-weight-polyethylene-uhmwpe-fibers-studied-by-atomic-force-microscopy\/."},{"key":"ref_30","first-page":"e10060","article-title":"Formation and evolution of shish-kebab structure during hot stretching in gel-spun ultra-high molecular weight polyethylene fibers with high concentration gel solution","volume":"2","author":"An","year":"2019","journal-title":"Polym. Cryst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"107524","DOI":"10.1016\/j.polymertesting.2022.107524","article-title":"Classifying condition of ultra-high-molecular-weight polyethylene ropes with wide-angle X-ray scattering","volume":"109","author":"Obdrup","year":"2022","journal-title":"Polym. Test."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"6583","DOI":"10.1038\/ncomms7583","article-title":"Multiple-length-scale deformation analysis in a thermoplastic polyurethane","volume":"6","author":"Sui","year":"2015","journal-title":"Nat. Commun."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"916","DOI":"10.1038\/s41598-017-00904-3","article-title":"Strain softening of nano-scale fuzzy interfaces causes Mullins effect in thermoplastic polyurethane","volume":"7","author":"Sui","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.polymer.2015.03.002","article-title":"Structure-morphology correlation in electrospun fibers of semicrystalline polymers by simultaneous synchrotron SAXS-WAXD","volume":"63","author":"Gazzano","year":"2015","journal-title":"Polymer"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1177\/0021955X6500100107","article-title":"Deformations of Foamed Elastomers","volume":"1","author":"Ko","year":"1965","journal-title":"J. Cell. Plast."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Gibson, L., and Ashby, M. (1997). Cellular Solids: Structure and Properties, Cambridge University Press.","DOI":"10.1017\/CBO9781139878326"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1590\/S1679-78252014000200004","article-title":"Mechanical properties and impact behavior of a microcellular structural foam","volume":"11","author":"Avalle","year":"2014","journal-title":"Lat. Am. J. Solids Struct."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1016\/j.mechmat.2011.05.005","article-title":"Tensile Static, Fatigue and Relaxation Behaviour of Closed Cell Electret PVDF Foams","volume":"43","author":"Bezazi","year":"2011","journal-title":"Mech. Mater."}],"container-title":["Polymers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4360\/14\/24\/5374\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:36:36Z","timestamp":1760146596000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4360\/14\/24\/5374"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,8]]},"references-count":38,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["polym14245374"],"URL":"https:\/\/doi.org\/10.3390\/polym14245374","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints202211.0191.v1","asserted-by":"object"}]},"ISSN":["2073-4360"],"issn-type":[{"value":"2073-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,8]]}}}