{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T14:20:44Z","timestamp":1762352444745,"version":"3.37.3"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","funder":[{"DOI":"10.13039\/501100001659","name":"German Research Foundation","doi-asserted-by":"crossref","award":["priority program 1180"],"award-info":[{"award-number":["priority program 1180"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>A variational inequality formulation is derived for some frictional contact problems from linear elasticity. The formulation exhibits a two-fold saddle point structure\nand is of dual-dual type, involving the stress tensor as primary unknown as well as the friction force on the contact surface by means of a Lagrange multiplier.\nThe approach starts with the minimization of the conjugate elastic potential. Applying Fenchel's duality theory to this dual minimization problem, the connection to the primal minimization problem and a dual saddle point problem is achieved. The saddle point problem possesses the displacement field and the rotation tensor as\nfurther unknowns. Introducing the friction force yields the dual-dual saddle point problem. The equivalence and unique solvability of both problems is shown with the\nhelp of the variational inequality formulations corresponding to the saddle point formulations, respectively.<\/jats:p>","DOI":"10.1515\/cmam-2015-0021","type":"journal-article","created":{"date-parts":[[2015,10,14]],"date-time":"2015-10-14T00:04:54Z","timestamp":1444781094000},"page":"1-16","source":"Crossref","is-referenced-by-count":1,"title":["Dual-Dual Formulation for a Contact Problem with Friction"],"prefix":"10.1515","volume":"16","author":[{"given":"Michael","family":"Andres","sequence":"first","affiliation":[{"name":"Institute for Applied Mathematics, Leibniz University Hannover, Welfengarten 1, 30167 Hannover, Germany"}]},{"given":"Matthias","family":"Maischak","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Brunel University Uxbridge, London, UK"}]},{"given":"Ernst P.","family":"Stephan","sequence":"additional","affiliation":[{"name":"Institute for Applied Mathematics, Leibniz University Hannover, Welfengarten 1, 30167 Hannover, Germany"}]}],"member":"374","published-online":{"date-parts":[[2015,10,13]]},"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/16\/1\/article-p1.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0021\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0021\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T21:33:32Z","timestamp":1680298412000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0021\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,1]]},"published-print":{"date-parts":[[2016,1,1]]}},"alternative-id":["10.1515\/cmam-2015-0021"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2015-0021","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"type":"electronic","value":"1609-9389"},{"type":"print","value":"1609-4840"}],"subject":[],"published":{"date-parts":[[2015,10,13]]}}}