Handle URI:
http://hdl.handle.net/10754/598989
Title:
Nonlinear elastic inclusions in isotropic solids
Authors:
Yavari, A.; Goriely, A.
Abstract:
We 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.
Citation:
Yavari 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.
Publisher:
The Royal Society
Journal:
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
KAUST Grant Number:
KUK C1-013-04
Issue Date:
16-Oct-2013
DOI:
10.1098/rspa.2013.0415
PubMed ID:
24353470
PubMed Central ID:
PMC3857869
Type:
Article
ISSN:
1364-5021; 1471-2946
Sponsors:
This 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.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorYavari, A.en
dc.contributor.authorGoriely, A.en
dc.date.accessioned2016-02-25T13:50:42Zen
dc.date.available2016-02-25T13:50:42Zen
dc.date.issued2013-10-16en
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.en
dc.identifier.issn1364-5021en
dc.identifier.issn1471-2946en
dc.identifier.pmid24353470en
dc.identifier.doi10.1098/rspa.2013.0415en
dc.identifier.urihttp://hdl.handle.net/10754/598989en
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.en
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.en
dc.publisherThe Royal Societyen
dc.subjectResidual Stressesen
dc.subjectInclusionsen
dc.subjectGeometric Elasticityen
dc.titleNonlinear elastic inclusions in isotropic solidsen
dc.typeArticleen
dc.identifier.journalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciencesen
dc.identifier.pmcidPMC3857869en
dc.contributor.institutionSchool of Civil and Environmental Engineering, The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA.en
dc.contributor.institutionOCCAM, Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK.en
kaust.grant.numberKUK C1-013-04en
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