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dc.contributor.authorYavari, A.
dc.contributor.authorGoriely, A.
dc.date.accessioned2016-02-25T13:50:42Z
dc.date.available2016-02-25T13:50:42Z
dc.date.issued2013-10-16
dc.identifier.citationYavari A, Goriely A (2013) Nonlinear elastic inclusions in isotropic solids. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469: 20130415–20130415. Available: http://dx.doi.org/10.1098/rspa.2013.0415.
dc.identifier.issn1364-5021
dc.identifier.issn1471-2946
dc.identifier.pmid24353470
dc.identifier.doi10.1098/rspa.2013.0415
dc.identifier.urihttp://hdl.handle.net/10754/598989
dc.description.abstractWe introduce a geometric framework to calculate the residual stress fields and deformations of nonlinear solids with inclusions and eigenstrains. Inclusions are regions in a body with different reference configurations from the body itself and can be described by distributed eigenstrains. Geometrically, the eigenstrains define a Riemannian 3-manifold in which the body is stress-free by construction. The problem of residual stress calculation is then reduced to finding a mapping from the Riemannian material manifold to the ambient Euclidean space. Using this construction, we find the residual stress fields of three model systems with spherical and cylindrical symmetries in both incompressible and compressible isotropic elastic solids. In particular, we consider a finite spherical ball with a spherical inclusion with uniform pure dilatational eigenstrain and we show that the stress in the inclusion is uniform and hydrostatic. We also show how singularities in the stress distribution emerge as a consequence of a mismatch between radial and circumferential eigenstrains at the centre of a sphere or the axis of a cylinder.
dc.description.sponsorshipThis publication was based on work supported in part by award no. KUK C1-013-04, made by King Abdullah University of Science and Technology (KAUST). A.Y. was partially supported by AFOSR (grant no. FA9550-12-1-0290) and NSF (grant nos. CMMI 1042559 and CMMI 1130856). A.G. is a Wolfson/Royal Society Merit Award Holder and acknowledges support from a Reintegration Grant under EC Framework VII.
dc.publisherThe Royal Society
dc.subjectResidual Stresses
dc.subjectInclusions
dc.subjectGeometric Elasticity
dc.titleNonlinear elastic inclusions in isotropic solids
dc.typeArticle
dc.identifier.journalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
dc.identifier.pmcidPMC3857869
dc.contributor.institutionSchool of Civil and Environmental Engineering, The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA.
dc.contributor.institutionOCCAM, Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK.
kaust.grant.numberKUK C1-013-04


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