An optimization algorithm applied to the Morrey conjecture in nonlinear elasticity

dc.contributor.authorGutierrez, Sergio
dc.contributor.authorVillavicencio, Jorge
dc.date.accessioned2024-01-10T13:45:53Z
dc.date.available2024-01-10T13:45:53Z
dc.date.issued2007
dc.description.abstractFor a long time it has been studied whether rank-one convexity and quasiconvexity give rise to different families of constitutive relations in planar nonlinear elasticity. Stated in 1952 the Morrey conjecture says that these families are different, but no example has come forward to prove it. Now we attack this problem by deriving a specialized optimization algorithm based on two ingredients: first, a recently found necessary condition for the quasiconvexity of fourth-degree polynomials that distinguishes between both classes in the three dimensional case, and secondly, upon a characterization of rank-one convex fourth-degree polynomials in terms of infinitely many constraints.
dc.description.abstractAfter extensive computational experiments with the algorithm, we believe that in the planar case, the necessary condition mentioned above is also necessary for the rank-one convexity of fourth-degree polynomials. Hence the question remains open. (c) 2006 Elsevier Ltd. All rights reserved.
dc.fechaingreso.objetodigital26-03-2024
dc.format.extent10 páginas
dc.fuente.origenWOS
dc.identifier.doi10.1016/j.ijsolstr.2006.09.017
dc.identifier.eissn1879-2146
dc.identifier.issn0020-7683
dc.identifier.urihttps://doi.org/10.1016/j.ijsolstr.2006.09.017
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/79093
dc.identifier.wosidWOS:000246273100005
dc.information.autorucIngeniería;Gutiérrez S;S/I;100336
dc.issue.numero10
dc.language.isoen
dc.nota.accesocontenido completo
dc.pagina.final3186
dc.pagina.inicio3177
dc.publisherPERGAMON-ELSEVIER SCIENCE LTD
dc.revistaINTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
dc.rightsacceso abierto
dc.subjectrank-one convexity
dc.subjectquasiconvexity
dc.subjectMorrey conjecture
dc.subjectcutting-plane method
dc.subjectconstitutive relations in nonlinear elasticity
dc.subjectQUASICONVEXITY
dc.subject.ods11 Sustainable Cities and Communities
dc.subject.odspa11 Ciudades y comunidades sostenibles
dc.titleAn optimization algorithm applied to the Morrey conjecture in nonlinear elasticity
dc.typeartículo
dc.volumen44
sipa.codpersvinculados100336
sipa.indexWOS
sipa.trazabilidadCarga SIPA;09-01-2024
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