A gradient approach to localization of deformation. I. Hyperelastic materials
dc.contributor.author | Triantafyllidis, Nicolas | en_US |
dc.contributor.author | Aifantis, Elias C. | en_US |
dc.date.accessioned | 2006-09-08T20:35:53Z | |
dc.date.available | 2006-09-08T20:35:53Z | |
dc.date.issued | 1986-09 | en_US |
dc.identifier.citation | Triantafyllidis, N.; Aifantis, Elias C.; (1986). "A gradient approach to localization of deformation. I. Hyperelastic materials." Journal of Elasticity 16(3): 225-237. <http://hdl.handle.net/2027.42/42674> | en_US |
dc.identifier.issn | 0374-3535 | en_US |
dc.identifier.issn | 1573-2681 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/42674 | |
dc.description.abstract | By utilizing methods recently developed in the theory of fluid interfaces, we provide a new framework for considering the localization of deformation and illustrate it for the case of hyperelastic materials. The approach overcomes one of the major shortcomings in constitutive equations for solids admitting localization of deformation at finite strains, i.e. their inability to provide physically acceptable solutions to boundary value problems in the post-localization range due to loss of ellipticity of the governing equations. Specifically, strain-induced localized deformation patterns are accounted for by adding a second deformation gradient-dependent term to the expression for the strain energy density. The modified strain energy function leads to equilibrium equations which remain always elliptic. Explicit solutions of these equations can be found for certain classes of deformations. They suggest not only the direction but also the width of the deformation bands providing for the first time a predictive unifying method for the study of pre- and post-localization behavior. The results derived here are a three-dimensional extension of certain one-dimensional findings reported earlier by the second author for the problem of simple shear. | en_US |
dc.format.extent | 732742 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Martinus Nijhoff, The Hague/Kluwer Academic Publishers; Martinus Nijhoff Publishers ; Springer Science+Business Media | en_US |
dc.subject.other | Physics | en_US |
dc.subject.other | Mechanics | en_US |
dc.subject.other | Automotive and Aerospace Engineering | en_US |
dc.title | A gradient approach to localization of deformation. I. Hyperelastic materials | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | MM Program, Dept. of Mechanical Engineering and Engineering Mechanics, Michigan Technological University, 49931, Houghton, MI, USA; Dept. of Aerospace Engineering, The University of Michigan, 48109, Ann Arbor, MI | en_US |
dc.contributor.affiliationother | MM Program, Dept. of Mechanical Engineering and Engineering Mechanics, Michigan Technological University, 49931, Houghton, MI, USA | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/42674/1/10659_2004_Article_BF00040814.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/BF00040814 | en_US |
dc.identifier.source | Journal of Elasticity | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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