Derivation of higher order gradient continuum theories in 2,3-d non-linear elasticity from periodic lattice models
dc.contributor.author | Bardenhagen, S. | en_US |
dc.contributor.author | Triantafyllidis, Nicolas | en_US |
dc.date.accessioned | 2006-04-10T18:26:44Z | |
dc.date.available | 2006-04-10T18:26:44Z | |
dc.date.issued | 1994-01 | en_US |
dc.identifier.citation | Bardenhagen, S., Triantafyllidis, N. (1994/01)."Derivation of higher order gradient continuum theories in 2,3-d non-linear elasticity from periodic lattice models." Journal of the Mechanics and Physics of Solids 42(1): 111-139. <http://hdl.handle.net/2027.42/31886> | en_US |
dc.identifier.uri | http://www.sciencedirect.com/science/article/B6TXB-46PYMG2-2W/2/9f520912174c2a56321c41b2e316f0ce | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/31886 | |
dc.description.abstract | localization of deformation (in the form of shear bands) at sufficiently high levels of strain, are frequently modeled by gradient type non-local constitutive laws, i.e. continuum theories that include higher order deformation gradients. These models incorporate a length scale for the localized deformation zone and are either postulated or justified from micromechanical considerations. Of interest here is the consistent derivation of such models from a given microstructure and the subsequent investigation of their localization and stability behavior under finite strains.In the interest of simplicity, the microscopic model is a discrete, periodic, non-linear elastic lattice structure in two or three dimensions. The corresponding macroscopic model is a continuum constitutive law involving displacement gradients of all orders. Attention is focused on the simplest such model, namely the one whose energy density includes gradients of the displacements only up to the second order. The relation between the ellipticity of the resulting first (local) and second (non-local) order gradient models at finite strains, the stability of uniform strain solutions and the possibility of localized deformation zones is discussed. The investigations of the resulting continuum are done for two different microstructures, the second one of which approximates the behavior of perfect monatomic crystals in plane strain. Localized strain solutions based on the continuum approximation are possible with the first microstructurc but not with the second. Implications for the stability of three-dimensional crystals using realistic interaction potentials are also discussed. | en_US |
dc.format.extent | 2118954 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Elsevier | en_US |
dc.title | Derivation of higher order gradient continuum theories in 2,3-d non-linear elasticity from periodic lattice models | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Mechanical Engineering | en_US |
dc.subject.hlbtoplevel | Engineering | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, U.S.A. | en_US |
dc.contributor.affiliationum | Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, U.S.A. | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/31886/1/0000838.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1016/0022-5096(94)90051-5 | en_US |
dc.identifier.source | Journal of the Mechanics and Physics of Solids | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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