{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:27:22Z","timestamp":1787318842429,"version":"build-2736575974"},"reference-count":69,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["F 65"],"award-info":[{"award-number":["F 65"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["I 2375"],"award-info":[{"award-number":["I 2375"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["P27052"],"award-info":[{"award-number":["P27052"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001821","name":"Vienna Science and Technology Fund","doi-asserted-by":"publisher","award":["MA14-009"],"award-info":[{"award-number":["MA14-009"]}],"id":[{"id":"10.13039\/501100001821","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>We discuss a topology optimization problem for an elastoplastic medium. The distribution of material in a region is optimized with respect to a given target functional taking into account compliance. The incremental elastoplastic problem serves as a state constraint. We prove that the topology optimization problem admits a solution. First-order optimality conditions are obtained by considering a regularized problem and passing to the limit.<\/jats:p>","DOI":"10.1137\/20m1331275","type":"journal-article","created":{"date-parts":[[2021,1,20]],"date-time":"2021-01-20T09:54:08Z","timestamp":1611136448000},"page":"339-364","source":"Crossref","is-referenced-by-count":12,"title":["Topology Optimization for Incremental Elastoplasticity: A Phase-Field Approach"],"prefix":"10.1137","volume":"59","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7308-221X","authenticated-orcid":true,"given":"Stefano","family":"Almi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3969-2716","authenticated-orcid":true,"given":"Ulisse","family":"Stefanelli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,1,20]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1080\/02331934.2015.1111364"},{"key":"atypb2","first-page":"101","author":"Allaire G.","year":"1997","journal-title":"Vienna"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"G. Allaire,\n                      Shape Optimization by the Homogenization Method\n                      . Appl. Math. Sci. 146. Springer-Verlag, New York, 2002.","DOI":"10.1007\/978-1-4684-9286-6"},{"key":"atypb4","first-page":"1","author":"Allaire G.","year":"2004","journal-title":"Dordrecht"},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"L. Ambrosio, N. Fusco, and D. Pallara,\n                      Functions of Bounded Variation and Free Discontinuity Problems\n                      , Oxford Math. Monogr., Oxford University Press, New York, 2000.","DOI":"10.1093\/oso\/9780198502456.001.0001"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-016-1618-8"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(88)90086-2"},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"M. P. Bends\u00f8e and O. Sigmund,\n                      Topology Optimization: Theory, Methods and Applications\n                      , Springer-Verlag, Berlin, 2003.","DOI":"10.1007\/978-3-662-05086-6"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2014006"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/140989066"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:2002070"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2013.18.331"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2138"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/05062723X"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2015.02.003"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1007\/s00466-019-01736-w"},{"key":"atypb17","doi-asserted-by":"crossref","unstructured":"G. Dal Maso,\n                      An Introduction to $\\Gamma$-Convergence\n                      , Progr. Nonlinear Differential Equations Appl. 8, Birkh\u00e4user Boston, Boston, MA, 1993.","DOI":"10.1007\/978-1-4612-0327-8"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-011-9435-x"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1137\/130920861"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-013-0956-z"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.3934\/eect.2014.3.411"},{"key":"atypb22","doi-asserted-by":"crossref","first-page":"369","DOI":"10.3934\/dcdss.2013.6.369","volume":"6","author":"Eleuteri M.","year":"2013","journal-title":"Discrete Contin. Dyn. Syst. Ser. S"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2020.01.006"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/BF01442860"},{"key":"atypb25","doi-asserted-by":"crossref","unstructured":"W. Han and B. D. Reddy,\n                      Plasticity\n                      , Interdiscip. Appl. Math. 9, Springer, New York, 2013.","DOI":"10.1007\/978-1-4614-5940-8"},{"key":"atypb26","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/BF00273705","volume":"1","author":"Haslinger J.","year":"1986","journal-title":"Comput. Mech."},{"key":"atypb27","first-page":"29","author":"Haslinger J.","year":"1986","journal-title":"New York"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.200900378"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2011.04.074"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1137\/100809325"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.21136\/AM.1986.104226"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.21136\/AM.1987.104269"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.21136\/AM.1991.104483"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2014.11.012"},{"key":"atypb35","first-page":"107","volume":"33","author":"Kaliszky S.","year":"1989","journal-title":"Period. Polytech. Civil Engrg."},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1080\/13923730.2004.9636293"},{"key":"atypb37","first-page":"175","volume":"9","author":"Khanzadi M.","year":"2011","journal-title":"Int. J. Civil Engrg."},{"key":"atypb38","doi-asserted-by":"crossref","unstructured":"J. Lemaitre, J.L. Chaboche,\n                      Mechanics of Solid Materials\n                      , Cambridge University Press, Cambridge, UK, 1990.","DOI":"10.1017\/CBO9781139167970"},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-017-1670-z"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1002\/nme.5427"},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1080\/0305215X.2016.1141203"},{"key":"atypb42","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-018-1940-4"},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.1137\/17M1128940"},{"key":"atypb44","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1521-4001(199910)79:10<651::AID-ZAMM651>3.0.CO;2-O"},{"key":"atypb45","doi-asserted-by":"publisher","DOI":"10.1007\/BF00251230"},{"key":"atypb46","first-page":"285","volume":"14","author":"Modica L.","year":"1977","journal-title":"Boll. Un. Mat. Ital. B (5)"},{"key":"atypb47","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2016.01.003"},{"key":"atypb48","doi-asserted-by":"publisher","DOI":"10.1007\/s00466-015-1159-9"},{"key":"atypb49","doi-asserted-by":"publisher","DOI":"10.1002\/nme.787"},{"key":"atypb50","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2010045"},{"key":"atypb51","first-page":"503","author":"Petersson J.","year":"1998","journal-title":"NJ"},{"key":"atypb52","doi-asserted-by":"publisher","DOI":"10.21136\/AM.1990.104419"},{"key":"atypb53","doi-asserted-by":"publisher","DOI":"10.1137\/080718711"},{"key":"atypb54","doi-asserted-by":"publisher","DOI":"10.1137\/080744050"},{"key":"atypb55","unstructured":"J. C. Simo and T. J. R. Hughes,\n                      Computational Inelasticity\n                      , Interdiscip. Appl. Math. 7, Springer-Verlag, New York, 1998."},{"key":"atypb56","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012901384430"},{"key":"atypb57","doi-asserted-by":"crossref","unstructured":"J. Soko\u0142owski and J.P. Zolesio,\n                      Introduction to Shape Optimization. Shape Sensitivity Analysis\n                      , Springer Ser. Comput. Math. 16, Springer-Verlag, Berlin, 1992.","DOI":"10.1007\/978-3-642-58106-9"},{"key":"atypb58","doi-asserted-by":"crossref","first-page":"1467","DOI":"10.3934\/dcdss.2017076","volume":"10","author":"Stefanelli U.","year":"2017","journal-title":"Discrete Contin. Dyn. Syst. Ser. S"},{"key":"atypb59","doi-asserted-by":"publisher","DOI":"10.5802\/afst.531"},{"key":"atypb60","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0207(19971030)40:20<3785::AID-NME240>3.0.CO;2-V"},{"key":"atypb61","unstructured":"R. Temam,\n                      Probl\u00e8mes math\u00e9matiques en plasticit\u00e9\n                      , Math. Methods Inform. Sci. 12, Gauthier-Villars, Paris, 1983."},{"key":"atypb62","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-014-1074-2"},{"key":"atypb63","doi-asserted-by":"publisher","DOI":"10.1137\/110839187"},{"key":"atypb64","doi-asserted-by":"publisher","DOI":"10.4171\/ZAA\/1546"},{"key":"atypb65","doi-asserted-by":"publisher","DOI":"10.4171\/ZAA\/1556"},{"key":"atypb66","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-014-1141-8"},{"key":"atypb67","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-013-0991-9"},{"key":"atypb68","doi-asserted-by":"crossref","unstructured":"X. Zhang and B. Zhu,\n                      Topology Optimization of Compliant Mechanisms\n                      , Springer, New York, 2018.","DOI":"10.1007\/978-981-13-0432-3"},{"key":"atypb69","doi-asserted-by":"publisher","DOI":"10.1007\/s11831-015-9151-2"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1331275","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:42:29Z","timestamp":1787316149000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1331275"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":69,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/20M1331275"],"URL":"https:\/\/doi.org\/10.1137\/20m1331275","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}