{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:24:59Z","timestamp":1787325899707,"version":"build-2736575974"},"reference-count":66,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["P 27052"],"award-info":[{"award-number":["P 27052"]}],"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\/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. Math. Anal."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>We address a finite-plasticity model based on the symmetric tensor $P^\\top\\!P$ instead of the classical plastic strain $P$. Such a structure arises by assuming that the material behavior is invariant with respect to frame transformations of the intermediate configuration. The resulting variational model is lower-dimensional, symmetric, and based solely on the reference configuration. The constitutive model has been introduced in Part I [D. Grandi and U. Stefanelli, Contin. Mech. Thermodyn., 29 (2017), pp. 97--116], where the corresponding analysis at the material-point level has also been developed. Here, we combine the constitutive relation with the equilibrium system and prove the existence of quasi-static evolutions and convergence of time discretizations. Second, we investigate the linearization limit for small deformations via a rigorous evolution $\\Gamma$-convergence argument.<\/jats:p>","DOI":"10.1137\/16m1079440","type":"journal-article","created":{"date-parts":[[2017,4,18]],"date-time":"2017-04-18T11:58:42Z","timestamp":1492516722000},"page":"1356-1384","source":"Crossref","is-referenced-by-count":16,"title":["Finite Plasticity in $P^\\top\\!P$. Part II: Quasi-Static Evolution and Linearization"],"prefix":"10.1137","volume":"49","author":[{"given":"D.","family":"Grandi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"U.","family":"Stefanelli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,4,18]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.anihpc.2012.04.001"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202508002632"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/0322035"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/BF00279992"},{"key":"atypb5","series-title":"Lecture Notes in Phys","first-page":"1","volume-title":"Trends and Applications of Pure Mathematics to Mechanics (Palaiseau","author":"Ball J. M.","year":"1983"},{"key":"atypb6","first-page":"3","volume-title":"Geometry","author":"Ball J. M.","year":"2002"},{"key":"atypb7","volume-title":"Math Stud., 5","author":"Br\u00e9zis H.","year":"1973"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1115\/1.3153756"},{"key":"atypb9","volume-title":"Mathematical Elasticity, Volume 1: Three Dimensional Elasticity","author":"Ciarlet P. G.","year":"1988"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1023\/A:1016577431636"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2013081"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1142\/S021820251450016X"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2003.09.005"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1108\/02644409410799272"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620300602"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1007\/s00466-009-0381-8"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2717"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1515\/CRELLE.2006.044"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/S0065-2156(08)70388-0"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-5096(01)00049-7"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.10048"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/s00161-011-0221-x"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202513500097"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/s00161-016-0522-1"},{"key":"atypb26","volume-title":"Math. Sci. Engrg. 158","author":"Gurtin M. E.","year":"1981"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7225(71)90086-3"},{"key":"atypb28","volume-title":"Plasticity, Mathematical Theory and Numerical Analysis","author":"Han W.","year":"1999"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7683(94)90039-6"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(94)90096-5"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1137\/0315035"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1007\/BF00281393"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1115\/1.3564580"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620380509"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500022782"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1007\/BF01178397"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-008-9033-y"},{"key":"atypb38","first-page":"45","volume":"66","author":"Miehe C.","year":"1995","journal-title":"Arch. Appl. Mech."},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141003429906"},{"key":"atypb40","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1016\/S1874-5717(06)80009-5","volume-title":"Handbook of Differential Equations: Evolutionary Equations","volume":"2","author":"Mielke A.","year":"2004"},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.200510245"},{"key":"atypb42","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2009.25.585"},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2010054"},{"key":"atypb44","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4939-2706-7"},{"key":"atypb45","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-007-0119-4"},{"key":"atypb46","doi-asserted-by":"publisher","DOI":"10.4171\/JEMS\/381"},{"key":"atypb47","doi-asserted-by":"publisher","DOI":"10.1007\/s00030-003-1052-7"},{"key":"atypb48","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(97)00149-7"},{"key":"atypb49","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7683(91)90004-Y"},{"key":"atypb50","doi-asserted-by":"publisher","DOI":"10.1007\/BF00959986"},{"key":"atypb51","volume-title":"Proceedings of the IUTAM Symposium on Innovative Numerical Approaches for Coupled Multi-Scale Problems, arXiv:1410","author":"Neff P.","year":"2016"},{"key":"atypb52","volume-title":"Plasticity: A Treatise on Finite Deformation of Heterogeneous Inelastic Materials","author":"S.","year":"2004"},{"key":"atypb53","doi-asserted-by":"publisher","DOI":"10.1007\/s10659-009-9217-1"},{"key":"atypb54","doi-asserted-by":"publisher","DOI":"10.1007\/s00161-011-0184-y"},{"key":"atypb55","first-page":"299","volume-title":"Proceedings of the IUTAM Symposium on Finite Inelastic Deformations. Theory and Applications, D. Besdo and E. Stein, eds.","author":"Peri\u0107 D","year":"1991"},{"key":"atypb56","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(92)90156-E"},{"key":"atypb57","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2014.01.014"},{"key":"atypb58","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2015.12.022"},{"key":"atypb59","doi-asserted-by":"publisher","DOI":"10.1007\/s00161-008-0087-8"},{"key":"atypb60","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-2626-4_3"},{"key":"atypb61","volume-title":"Interdiscip. Appl. Math., 7","author":"Simo J. C.","year":"1998"},{"key":"atypb62","doi-asserted-by":"publisher","DOI":"10.1137\/070684574"},{"key":"atypb63","doi-asserted-by":"publisher","DOI":"10.1007\/BF00374241"},{"key":"atypb64","volume-title":"Variational Methods","author":"Struwe M.","year":"2008"},{"key":"atypb65","volume-title":"Handbuch der Physik","volume":"3","author":"Truesdell C.","year":"1965"},{"key":"atypb66","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2234"},{"key":"atypb67","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(90)90131-5"}],"container-title":["SIAM Journal on Mathematical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1079440","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:24:11Z","timestamp":1787322251000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1079440"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":66,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/16M1079440"],"URL":"https:\/\/doi.org\/10.1137\/16m1079440","relation":{},"ISSN":["0036-1410","1095-7154"],"issn-type":[{"value":"0036-1410","type":"print"},{"value":"1095-7154","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}