{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T14:50:46Z","timestamp":1772290246243,"version":"3.50.1"},"reference-count":24,"publisher":"Elsevier BV","issue":"10","license":[{"start":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T00:00:00Z","timestamp":1556668800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T00:00:00Z","timestamp":1556668800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2023,5,15]],"date-time":"2023-05-15T00:00:00Z","timestamp":1684108800000},"content-version":"vor","delay-in-days":1475,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"},{"start":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T00:00:00Z","timestamp":1556668800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T00:00:00Z","timestamp":1556668800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T00:00:00Z","timestamp":1556668800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T00:00:00Z","timestamp":1556668800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T00:00:00Z","timestamp":1556668800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"name":"cooperative project of Tongji Zhejiang College and Haiyan County Environmental Protection Bureau","award":["Yanwupu(2018)-001-2"],"award-info":[{"award-number":["Yanwupu(2018)-001-2"]}]},{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["DMS-1521684"],"award-info":[{"award-number":["DMS-1521684"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"publisher","award":["11671098"],"award-info":[{"award-number":["11671098"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"publisher","award":["91630309"],"award-info":[{"award-number":["91630309"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013314","name":"111 Project","doi-asserted-by":"crossref","award":["B08018"],"award-info":[{"award-number":["B08018"]}],"id":[{"id":"10.13039\/501100013314","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100007931","name":"Shanghai University of Finance and Economics","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100007931","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computers & Mathematics with Applications"],"published-print":{"date-parts":[[2019,5]]},"DOI":"10.1016\/j.camwa.2018.12.038","type":"journal-article","created":{"date-parts":[[2019,1,28]],"date-time":"2019-01-28T22:12:02Z","timestamp":1548713522000},"page":"2596-2607","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":20,"title":["Numerical analysis of history-dependent hemivariational inequalities and applications to viscoelastic contact problems with normal penetration"],"prefix":"10.1016","volume":"77","author":[{"given":"Wei","family":"Xu","sequence":"first","affiliation":[]},{"given":"Ziping","family":"Huang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0960-2281","authenticated-orcid":false,"given":"Weimin","family":"Han","sequence":"additional","affiliation":[]},{"given":"Wenbin","family":"Chen","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3440-1596","authenticated-orcid":false,"given":"Cheng","family":"Wang","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.camwa.2018.12.038_b1","series-title":"Optimization and Nonsmooth Analysis","author":"Clarke","year":"1983"},{"key":"10.1016\/j.camwa.2018.12.038_b2","series-title":"An Introduction to Nonlinear Analysis: Applications","author":"Denkowski","year":"2003"},{"key":"10.1016\/j.camwa.2018.12.038_b3","series-title":"Nonlinear Inclusions and Hemivariational Inequalities. Models and Analysis of Contact Problems","volume":"vol. 26","author":"Mig\u00f3rski","year":"2013"},{"key":"10.1016\/j.camwa.2018.12.038_b4","series-title":"Finite Element Method for Hemivariational Inequalities. Theory, Methods and Applications","author":"Haslinger","year":"1999"},{"key":"10.1016\/j.camwa.2018.12.038_b5","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1023\/A:1008234502169","article-title":"Finite element approximation of vector-valued hemivariational problems","volume":"10","author":"Miettinen","year":"1997","journal-title":"J. Global Optim."},{"key":"10.1016\/j.camwa.2018.12.038_b6","doi-asserted-by":"crossref","first-page":"3891","DOI":"10.1137\/140963248","article-title":"A class of variational-hemivariational inequalities with applications to frictional contact problems","volume":"46","author":"Han","year":"2014","journal-title":"SIAM J. Math. Anal."},{"key":"10.1016\/j.camwa.2018.12.038_b7","first-page":"640","article-title":"Numerical analysis of elliptic hemivariational inequalities","volume":"55","author":"Han","year":"2017","journal-title":"SIAM J. Math. Anal."},{"key":"10.1016\/j.camwa.2018.12.038_b8","unstructured":"W. Han, Error analysis for internal and external approximations of elliptic hemivariational inequalities, preprint."},{"key":"10.1016\/j.camwa.2018.12.038_b9","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1177\/1081286517713342","article-title":"Numerical analysis of stationary variational-hemivariational inequalities with applications in contact mechanics","volume":"23","author":"Han","year":"2018","journal-title":"Math. Mech. Solids"},{"key":"10.1016\/j.camwa.2018.12.038_b10","first-page":"364","article-title":"Numerical analysis for elliptic hemivariational inequalities for semipermeable media","volume":"351","author":"Han","year":"2019","journal-title":"J. Comput. Math."},{"key":"10.1016\/j.camwa.2018.12.038_b11","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.jmaa.2016.05.012","article-title":"A quasistatic viscoelastic frictional contact problem with multivalued normal compliance, unilateral constraint and material damage","volume":"443","author":"Han","year":"2016","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/j.camwa.2018.12.038_b12","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1051\/m2an\/2013127","article-title":"Numerical analysis of history-dependent quasivariational inequalities with applications in contact mechanics","volume":"48","author":"Kamran","year":"2014","journal-title":"Math. Model. Numer. Anal."},{"key":"10.1016\/j.camwa.2018.12.038_b13","doi-asserted-by":"crossref","first-page":"3384","DOI":"10.1016\/j.nonrwa.2011.06.002","article-title":"History-dependent subdifferential inclusions and hemivariational inequalities in contact mechanics","volume":"12","author":"Mig\u00f3rski","year":"2011","journal-title":"Nonlinear Anal. RWA"},{"key":"10.1016\/j.camwa.2018.12.038_b14","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1016\/j.nonrwa.2014.09.021","article-title":"History-dependent variational-hemivariational inequalities in contact mechanics","volume":"22","author":"Mig\u00f3rski","year":"2015","journal-title":"Nonlinear Anal. RWA"},{"key":"10.1016\/j.camwa.2018.12.038_b15","unstructured":"J. Ogorzaly, Quasistatic contact problem with unilateral constraint for elastic-viscoplastic materials, 2016, arXiv:1608.04660v1."},{"key":"10.1016\/j.camwa.2018.12.038_b16","doi-asserted-by":"crossref","first-page":"645","DOI":"10.3934\/cpaa.2008.7.645","article-title":"A fixed point result with applications in the study of viscoplastic frictionless contact problems","volume":"7","author":"Sofonea","year":"2008","journal-title":"Commun. Pure Appl. Anal."},{"key":"10.1016\/j.camwa.2018.12.038_b17","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1017\/S095679251500011X","article-title":"Numerical analysis of history-dependent variational-hemivariational inequalities with applications to contact problems","volume":"26","author":"Sofonea","year":"2015","journal-title":"European J. Appl. Math."},{"issue":"3","key":"10.1016\/j.camwa.2018.12.038_b18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00030-016-0391-0","article-title":"A class of history-dependent variational-hemivariational inequalities","volume":"23","author":"Sofonea","year":"2016","journal-title":"Nonlinear Differential Equations Appl."},{"key":"10.1016\/j.camwa.2018.12.038_b19","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1016\/j.cam.2018.08.046","article-title":"Numerical analysis of history-dependent variational-hemivariational inequalities with applications in Contact Mechanics","volume":"351","author":"Xu","year":"2019","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.camwa.2018.12.038_b20","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1017\/S0956792511000192","article-title":"History-dependent quasivariational inequalities arising in Contact Mechanics","volume":"22","author":"Sofonea","year":"2011","journal-title":"European J. Appl. Math."},{"key":"10.1016\/j.camwa.2018.12.038_b21","series-title":"Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity","volume":"vol. 30","author":"Han","year":"2002"},{"key":"10.1016\/j.camwa.2018.12.038_b22","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1177\/1081286512448185","article-title":"Weak solvability of two quasistatic viscoelastic contact problems","volume":"18","author":"Mig\u00f3rski","year":"2012","journal-title":"Math. Mech. Solids"},{"key":"10.1016\/j.camwa.2018.12.038_b23","series-title":"Theoretical Numerical Analysis: A Functional Analysis Framework","author":"Atkinson","year":"2009"},{"key":"10.1016\/j.camwa.2018.12.038_b24","series-title":"The Finite Element Method for Elliptic Problems","author":"Ciarlet","year":"1978"}],"container-title":["Computers & Mathematics with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0898122118307363?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0898122118307363?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T10:07:44Z","timestamp":1760263664000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0898122118307363"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5]]},"references-count":24,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2019,5]]}},"alternative-id":["S0898122118307363"],"URL":"https:\/\/doi.org\/10.1016\/j.camwa.2018.12.038","relation":{},"ISSN":["0898-1221"],"issn-type":[{"value":"0898-1221","type":"print"}],"subject":[],"published":{"date-parts":[[2019,5]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Numerical analysis of history-dependent hemivariational inequalities and applications to viscoelastic contact problems with normal penetration","name":"articletitle","label":"Article Title"},{"value":"Computers & Mathematics with Applications","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.camwa.2018.12.038","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2019 Elsevier Ltd.","name":"copyright","label":"Copyright"}]}}