{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:21:15Z","timestamp":1740108075024,"version":"3.37.3"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2017,5,5]],"date-time":"2017-05-05T00:00:00Z","timestamp":1493942400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2017,5,5]],"date-time":"2017-05-05T00:00:00Z","timestamp":1493942400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["FCT-UTA_CMU\/MAT\/0005\/2009","UID\/MAT\/04561\/2013"],"award-info":[{"award-number":["FCT-UTA_CMU\/MAT\/0005\/2009","UID\/MAT\/04561\/2013"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["UID\/MAT\/04459\/2013"],"award-info":[{"award-number":["UID\/MAT\/04459\/2013"]}]},{"DOI":"10.13039\/100009112","name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","doi-asserted-by":"publisher","award":["Progetto di Ricerca GNAMPA- INdAM 2015 \u201cFenomeni critici nella meccanica dei materiali: un approccio variazionale\u201d"],"award-info":[{"award-number":["Progetto di Ricerca GNAMPA- INdAM 2015 \u201cFenomeni critici nella meccanica dei materiali: un approccio variazionale\u201d"]}],"id":[{"id":"10.13039\/100009112","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["DMS-0405343","DMS-0635983"],"award-info":[{"award-number":["DMS-0405343","DMS-0635983"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["290888","306274"],"award-info":[{"award-number":["290888","306274"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Arch Rational Mech Anal"],"published-print":{"date-parts":[[2017,9]]},"DOI":"10.1007\/s00205-017-1120-5","type":"journal-article","created":{"date-parts":[[2017,5,5]],"date-time":"2017-05-05T06:54:07Z","timestamp":1493967247000},"page":"1025-1072","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Second-Order Structured Deformations: Relaxation, Integral Representation and Applications"],"prefix":"10.1007","volume":"225","author":[{"given":"Ana Cristina","family":"Barroso","sequence":"first","affiliation":[]},{"given":"Jos\u00e9","family":"Matias","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3528-6152","authenticated-orcid":false,"given":"Marco","family":"Morandotti","sequence":"additional","affiliation":[]},{"given":"David R.","family":"Owen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,5,5]]},"reference":[{"key":"1120_CR1","doi-asserted-by":"crossref","unstructured":"Acharya, A., Fressengeas, C.: Continuum mechanics of the interaction of phase boundaries and dislocations in solids. Differential Geometry and Continuum Mechanics, Vol. 137 (Eds. Chen G.Q , Grinfeld M. and Knops R.J.) Springer Proceedings in Mathematics & Statistics, Berlin, 125\u2013168, 2015","DOI":"10.1007\/978-3-319-18573-6_5"},{"key":"1120_CR2","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1016\/j.jmps.2015.04.010","volume":"85","author":"V. Agrawal","year":"2015","unstructured":"Agrawal V., Dayal K.: Dynamic phase-field model for structural transformations and twinning: regularized interfaces with transparent prescription of complex kinetics and nucleation. Part I: formulation and one-dimensional characterization. J. Mech. Phys. Solids, 85, 270\u2013290 (2015)","journal-title":"J. Mech. Phys. Solids,"},{"key":"1120_CR3","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1016\/0022-1236(91)90104-D","volume":"100","author":"G. Alberti","year":"1991","unstructured":"Alberti G.: A Lusin type theorem for gradients. J. Funct. Anal., 100, 110\u2013118 (1991)","journal-title":"J. Funct. Anal.,"},{"key":"1120_CR4","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198502456.001.0001","volume-title":"Functions of Bounded Variation and Free Discontinuity Problems","author":"L. Ambrosio","year":"2000","unstructured":"Ambrosio L., Fusco N., Pallara D.: Functions of Bounded Variation and Free Discontinuity Problems. Oxford University Press, Oxford (2000)"},{"key":"1120_CR5","first-page":"269","volume":"70","author":"L. Ambrosio","year":"1991","unstructured":"Ambrosio L., Mortola S., Tortorelli V. M.: Functionals with linear growth defined on vector valued BV functions. J. Math. Pures Appl., 70, 269\u2013323 (1991)","journal-title":"J. Math. Pures Appl.,"},{"key":"1120_CR6","doi-asserted-by":"publisher","first-page":"185","DOI":"10.11606\/issn.2316-9028.v5i2p185-201","volume":"5","author":"M. Ba\u00eda","year":"2011","unstructured":"Ba\u00eda M., Matias J., Santos P. M.: A survey of structured deformations. S\u00e3o Paulo J. Math. Sci., 5, 185\u2013201 (2011)","journal-title":"S\u00e3o Paulo J. Math. Sci.,"},{"key":"1120_CR7","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1017\/S0308210510001460","volume":"142A","author":"M. Ba\u00eda","year":"2012","unstructured":"Ba\u00eda M., Matias J., Santos P.M.: A relaxation result in the framework of structured deformations. Proc. R. Soc. Edinb. Sect. A 142A, 239\u2013271 (2012)","journal-title":"Proc. R. Soc. Edinb. Sect. A"},{"issue":"2","key":"1120_CR8","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/S0294-1449(16)30304-3","volume":"7","author":"S. Baldo","year":"1990","unstructured":"Baldo S.: Minimal interface criterion for phase transitions in mixtures of Cahn\u2013Hilliard fluids. Ann. Inst. Henri Poincar\u00e9. Anal. Nonlin\u00e9aire 7(2), 67\u201390 (1990)","journal-title":"Inst. Henri Poincar\u00e9. Anal. Nonlin\u00e9aire"},{"key":"1120_CR9","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/BF02198453","volume":"135","author":"A.C. Barroso","year":"1996","unstructured":"Barroso A.C., Bouchitt\u00e9 G., Buttazzo G., Fonseca I.: Relaxation of bulk and interfacial energies. Arch. Ration. Mech. Anal., 135, 107\u2013173 (1996)","journal-title":"Arch. Ration. Mech. Anal.,"},{"key":"1120_CR10","first-page":"57","volume":"25","author":"M. Carriero","year":"1996","unstructured":"Carriero M., Leaci A., Tomarelli F.: A second order model in image segmentation: Blake and Zisserman functional. Prog. Nonlinear Diff. Equ., 25, 57\u201372 (1996)","journal-title":"Prog. Nonlinear Diff. Equ.,"},{"key":"1120_CR11","unstructured":"Carriero, M., Leaci, A., Tomarelli, F.: Second order variational problems with free discontinuity and free gradient discontinuity. Calculus of Variations: Topics from the Mathematical Heritage of E. De Giorgi, Quad. Mat., Vol. 14, Dept. Math., Seconda Univ. Napoli, Caserta, pp. 135\u2013186, 2004"},{"key":"1120_CR12","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1177\/108128659900400304","volume":"4","author":"R. Choksi","year":"1999","unstructured":"Choksi R., Del Piero G., Fonseca I., Owen D. R.: Structured deformations as energy minimizers in models of fracture and hysteresis. Math. Mech. Solids, 4, 321\u2013356 (1999)","journal-title":"Math. Mech. Solids,"},{"key":"1120_CR13","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/s002050050036","volume":"138","author":"R. Choksi","year":"1997","unstructured":"Choksi R., Fonseca I.: Bulk and interfacial energies for structured deformations of continus. Arch. Ration. Mech. Anal., 138, 37\u2013103 (1997)","journal-title":"Arch. Ration. Mech. Anal.,"},{"key":"1120_CR14","first-page":"199","volume":"82","author":"E. De Giorgi","year":"1988","unstructured":"De Giorgi E., Ambrosio L.: Un nuovo tipo di funzionale del calcolo delle variazioni. Atti. Accad. Naz. Lincei, 82, 199\u2013210 (1988)","journal-title":"Atti. Accad. Naz. Lincei,"},{"key":"1120_CR15","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1177\/108128650100600402","volume":"6","author":"G. Del Piero","year":"2001","unstructured":"Del Piero G.: The energy of a one-dimensional structured deformation. Math. Mech. Solids, 6, 387\u2013408 (2001)","journal-title":"Math. Mech. Solids,"},{"key":"1120_CR16","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/BF00375133","volume":"124","author":"G. Del Piero","year":"1993","unstructured":"Del Piero G., Owen D. R.: Structured deformations of continua. Arch. Ration. Mech. Anal., 124, 99\u2013155 (1993)","journal-title":"Arch. Ration. Mech. Anal.,"},{"key":"1120_CR17","doi-asserted-by":"crossref","unstructured":"Del Piero, D. R., Owen, D. R.: Multiscale Modeling in Continuum Mechanics and Structured Deformations. CISM Courses and Lecture Notes, Vol. 447, Springer, Berlin, 2004","DOI":"10.1007\/978-3-7091-2770-4"},{"key":"1120_CR18","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1023\/B:ELAS.0000005584.22658.b3","volume":"70","author":"L. Deseri","year":"2003","unstructured":"Deseri L., Owen D. R.: Toward a field theory for elastic bodies undergoing disarrangements. J. Elast., 70, 197\u2013236 (2003)","journal-title":"J. Elast.,"},{"key":"1120_CR19","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/s00161-012-0260-y","volume":"25","author":"L. Deseri","year":"2013","unstructured":"Deseri L., Owen D. R.: Moving interfaces that separate loose and compact phases of elastic aggregates: a mechanism for drastic reduction or increase in macroscopic deformation. Cont. Mech. Thermo., 25, 311\u2013341 (2013)","journal-title":"Cont. Mech. Thermo.,"},{"key":"1120_CR20","doi-asserted-by":"publisher","first-page":"2907","DOI":"10.1007\/s11012-014-0042-7","volume":"49","author":"L. Deseri","year":"2014","unstructured":"Deseri L., Owen D. R.: Stable disarrangement phases of elastic aggregates: a setting for the emergence of no-tension materials with non-linear response in compression. Meccanica, 49, 2907\u20132932 (2014)","journal-title":"Meccanica,"},{"key":"1120_CR21","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/j.ijengsci.2015.08.001","volume":"96","author":"L. Deseri","year":"2015","unstructured":"Deseri L., Owen D.R.: Stable disarrangement phases arising from expansion\/contraction or from simple shearing of a model granular medium. Int. J. Eng. Sci., 96, 111\u2013140 (2015)","journal-title":"Int. J. Eng. Sci.,"},{"key":"1120_CR22","unstructured":"Evans, L. C., Gariepy, R. F.: Measure theory and fine properties of functions. Studies in Advanced Mathematics, CRC Press, Boca Raton, 1992"},{"key":"1120_CR23","volume-title":"Geometric Measure Theory","author":"H. Federer","year":"1969","unstructured":"Federer H.: Geometric Measure Theory. Springer, Berlin (1969)"},{"key":"1120_CR24","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9486-0","volume-title":"Minimal Surfaces and Functions of Bounded Variation","author":"E. Giusti","year":"1984","unstructured":"Giusti E.: Minimal Surfaces and Functions of Bounded Variation. Birkh\u00e4user, Basel (1984)"},{"key":"1120_CR25","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/S1359-6454(99)00295-5","volume":"48","author":"R. D. James","year":"2000","unstructured":"James R. D., Hane K. F.: Martensitic transformations and shape-memorymaterials. Acta Mater., 48, 197\u2013222 (2000)","journal-title":"Acta Mater.,"},{"key":"1120_CR26","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1051\/cocv:2000120","volume":"5","author":"C. J. Larsen","year":"2000","unstructured":"Larsen C. J.: On the representation of effective energy densities. ESAIM Control Opt. Calc. Var., 5, 529\u2013538 (2000)","journal-title":"ESAIM Control Opt. Calc. Var.,"},{"issue":"3","key":"1120_CR27","first-page":"465","volume":"14","author":"J. Matias","year":"2007","unstructured":"Matias J.: Differential inclusions in $${SBV_0(\\Omega)}$$ and applications to the calculus of variations. J. Convex Anal., 14(3), 465\u2013477 (2007)","journal-title":"J. Convex Anal.,"},{"key":"1120_CR28","unstructured":"Owen, D. R.: Elasticity with gradient-disarrangements: a multiscale geometrical perspective for strain-gradient theories of elasticty and of plasticity. J. Elast. (submitted)"},{"key":"1120_CR29","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/s002050000111","volume":"155","author":"D. R. Owen","year":"2000","unstructured":"Owen D. R., Paroni R.: Second-order structured deformations. Arch. Ration. Mech. Anal., 155, 215\u2013235 (2000)","journal-title":"Arch. Ration. Mech. Anal.,"},{"issue":"3","key":"1120_CR30","doi-asserted-by":"publisher","first-page":"1633","DOI":"10.1007\/s00205-015-0890-x","volume":"218","author":"R. Owen","year":"2015","unstructured":"Owen R., Paroni R.: Optimal flux densities for linear mappings and the multiscale geometry of structured deformations. Arch. Ration. Mech. Anal., 218(3), 1633\u20131652 (2015)","journal-title":"Arch. Ration. Mech. Anal.,"},{"key":"1120_CR31","doi-asserted-by":"crossref","unstructured":"Paroni, R.: Second-order structured deformations: approximation theorems and energetics. Multiscale Modeling in Continuum Mechanics and Structured Deformations, Vol. 447 (Eds. Del Piero G. and Owen D.R.) Springer, Berlin, 2004","DOI":"10.1007\/978-3-7091-2770-4_5"},{"key":"1120_CR32","doi-asserted-by":"publisher","first-page":"1039","DOI":"10.1007\/BF02196453","volume":"9","author":"Y. G. Reshetnyak","year":"1968","unstructured":"Reshetnyak Y. G.: Weak convergence of completely additive vector functions on a set. Sib. Math. J., 9, 1039\u20131045 (1968)","journal-title":"Sib. Math. J.,"},{"key":"1120_CR33","doi-asserted-by":"publisher","first-page":"83","DOI":"10.2140\/memocs.2015.3.83","volume":"3","author":"M. \u0160ilhav\u00fd","year":"2015","unstructured":"\u0160ilhav\u00fd M.: On the approximation theorem for structured deformations from $${BV(\\Omega )}$$. Mech. Math. Complex. Syst., 3, 83\u2013100 (2015)","journal-title":"Mech. Math. Complex. Syst.,"},{"key":"1120_CR34","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1015-3","volume-title":"Weakly Differentiable Functions","author":"W. Ziemer","year":"1989","unstructured":"Ziemer W.: Weakly Differentiable Functions. Springer, Berlin (1989)"}],"container-title":["Archive for Rational Mechanics and Analysis"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00205-017-1120-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00205-017-1120-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00205-017-1120-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,23]],"date-time":"2024-06-23T23:17:28Z","timestamp":1719184648000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00205-017-1120-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,5]]},"references-count":34,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,9]]}},"alternative-id":["1120"],"URL":"https:\/\/doi.org\/10.1007\/s00205-017-1120-5","relation":{},"ISSN":["0003-9527","1432-0673"],"issn-type":[{"type":"print","value":"0003-9527"},{"type":"electronic","value":"1432-0673"}],"subject":[],"published":{"date-parts":[[2017,5,5]]},"assertion":[{"value":"9 July 2016","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 April 2017","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 May 2017","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}