{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,30]],"date-time":"2026-08-30T02:10:54Z","timestamp":1788055854803,"version":"build-2784847793"},"reference-count":56,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2021,7,10]],"date-time":"2021-07-10T00:00:00Z","timestamp":1625875200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100002427","name":"Ford Motor Company","doi-asserted-by":"publisher","award":["000654-2015-2214R-H"],"award-info":[{"award-number":["000654-2015-2214R-H"]}],"id":[{"id":"10.13039\/100002427","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>The solution to an elastic-plastic rough surface contact problem can be applied to phenomena such as friction and contact resistance. Many different types of models have therefore been developed to solve rough surface contact. A deterministic approach may accurately describe the entire surface, but the computing time is too long for practical use. Thus, mathematically abbreviated models have been developed to describe rough surface contact. Many popular models employ a statistical methodology to solve the contact problem, and they borrow the solution for spherical or parabolic contact to represent individual asperities. However, it is believed that a sinusoidal geometry may be a more realistic asperity representation. This has been applied to a newer version of the stacked multiscale model and statistical models. While no single model can accurately describe every contact problem better than any other, this work aims to help establish guidelines that determine the best model to solve a rough surface contact problem by applying mathematical and deterministic models to two reference surfaces in contact with a rigid flat. The discrepancies and similarities form the basis of those guidelines.<\/jats:p>","DOI":"10.3390\/ma14143864","type":"journal-article","created":{"date-parts":[[2021,7,12]],"date-time":"2021-07-12T00:23:36Z","timestamp":1626049416000},"page":"3864","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Evaluating Elastic-Plastic Wavy and Spherical Asperity-Based Statistical and Multi-Scale Rough Surface Contact Models with Deterministic Results"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9115-8206","authenticated-orcid":false,"given":"Nolan Ryan","family":"Chu","sequence":"first","affiliation":[{"name":"Mechanical Engineering Department, Auburn University, Auburn, AL 36849, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3316-9510","authenticated-orcid":false,"given":"Robert L.","family":"Jackson","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Department, Auburn University, Auburn, AL 36849, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xianzhang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical and Power Engineeing, Guangdong Ocean University, Zhanjiang 524088, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arup","family":"Gangopadhyay","sequence":"additional","affiliation":[{"name":"Ford Motor Company, Dearborn, MI 48124, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hamed","family":"Ghaednia","sequence":"additional","affiliation":[{"name":"Gehring L. P., Farmington Hills, MI 48335, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,10]]},"reference":[{"key":"ref_1","first-page":"300","article-title":"Contact of nominally flat surfaces","volume":"295","author":"Greenwood","year":"1966","journal-title":"Proc. R. Soc. London. Ser. A Math. Phys. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1115\/1.3261348","article-title":"An Elastic-Plastic Model for the Contact of Rough Surfaces","volume":"109","author":"Chang","year":"1987","journal-title":"J. Tribol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1016\/j.triboint.2005.09.001","article-title":"A Statistical model of Elastic-Plastic Asperity Contact between Rough Surfaces","volume":"39","author":"Jackson","year":"2006","journal-title":"Trib. 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