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Souhayl Sadik

Nonlinear Elasticity in a Deforming Ambient Space

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Nonlinear Elasticity in a Deforming Ambient Space. / Yavari, Arash; Ozakin, Arkadas; Sadik, Souhayl.
In: Journal of Nonlinear Science, Vol. 26, No. 6, 12.2016, p. 1651-1692.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Harvard

Yavari, A, Ozakin, A & Sadik, S 2016, 'Nonlinear Elasticity in a Deforming Ambient Space', Journal of Nonlinear Science, vol. 26, no. 6, pp. 1651-1692. https://doi.org/10.1007/s00332-016-9315-8

APA

Yavari, A., Ozakin, A., & Sadik, S. (2016). Nonlinear Elasticity in a Deforming Ambient Space. Journal of Nonlinear Science, 26(6), 1651-1692. https://doi.org/10.1007/s00332-016-9315-8

CBE

Yavari A, Ozakin A, Sadik S. 2016. Nonlinear Elasticity in a Deforming Ambient Space. Journal of Nonlinear Science. 26(6):1651-1692. https://doi.org/10.1007/s00332-016-9315-8

MLA

Yavari, Arash, Arkadas Ozakin, and Souhayl Sadik. "Nonlinear Elasticity in a Deforming Ambient Space". Journal of Nonlinear Science. 2016, 26(6). 1651-1692. https://doi.org/10.1007/s00332-016-9315-8

Vancouver

Yavari A, Ozakin A, Sadik S. Nonlinear Elasticity in a Deforming Ambient Space. Journal of Nonlinear Science. 2016 Dec;26(6):1651-1692. doi: 10.1007/s00332-016-9315-8

Author

Yavari, Arash ; Ozakin, Arkadas ; Sadik, Souhayl. / Nonlinear Elasticity in a Deforming Ambient Space. In: Journal of Nonlinear Science. 2016 ; Vol. 26, No. 6. pp. 1651-1692.

Bibtex

@article{3dc69c996e0a4bcf9ad7d59b008afcfe,
title = "Nonlinear Elasticity in a Deforming Ambient Space",
abstract = "In this paper, we formulate a nonlinear elasticity theory in which the ambient space is evolving. For a continuum moving in an evolving ambient space, we model time dependency of the metric by a time-dependent embedding of the ambient space in a larger manifold with a fixed background metric. We derive both the tangential and the normal governing equations. We then reduce the standard energy balance written in the larger ambient space to that in the evolving ambient space. We consider quasi-static deformations of the ambient space and show that a quasi-static deformation of the ambient space results in stresses, in general. We linearize the nonlinear theory about a reference motion and show that variation of the spatial metric corresponds to an effective field of body forces.",
keywords = "Deforming ambient space, Geometric mechanics, Nonlinear elasticity",
author = "Arash Yavari and Arkadas Ozakin and Souhayl Sadik",
year = "2016",
month = dec,
doi = "10.1007/s00332-016-9315-8",
language = "English",
volume = "26",
pages = "1651--1692",
journal = "Journal of Nonlinear Science",
issn = "0938-8974",
publisher = "Springer",
number = "6",

}

RIS

TY - JOUR

T1 - Nonlinear Elasticity in a Deforming Ambient Space

AU - Yavari, Arash

AU - Ozakin, Arkadas

AU - Sadik, Souhayl

PY - 2016/12

Y1 - 2016/12

N2 - In this paper, we formulate a nonlinear elasticity theory in which the ambient space is evolving. For a continuum moving in an evolving ambient space, we model time dependency of the metric by a time-dependent embedding of the ambient space in a larger manifold with a fixed background metric. We derive both the tangential and the normal governing equations. We then reduce the standard energy balance written in the larger ambient space to that in the evolving ambient space. We consider quasi-static deformations of the ambient space and show that a quasi-static deformation of the ambient space results in stresses, in general. We linearize the nonlinear theory about a reference motion and show that variation of the spatial metric corresponds to an effective field of body forces.

AB - In this paper, we formulate a nonlinear elasticity theory in which the ambient space is evolving. For a continuum moving in an evolving ambient space, we model time dependency of the metric by a time-dependent embedding of the ambient space in a larger manifold with a fixed background metric. We derive both the tangential and the normal governing equations. We then reduce the standard energy balance written in the larger ambient space to that in the evolving ambient space. We consider quasi-static deformations of the ambient space and show that a quasi-static deformation of the ambient space results in stresses, in general. We linearize the nonlinear theory about a reference motion and show that variation of the spatial metric corresponds to an effective field of body forces.

KW - Deforming ambient space

KW - Geometric mechanics

KW - Nonlinear elasticity

UR - http://www.scopus.com/inward/record.url?scp=84976515263&partnerID=8YFLogxK

U2 - 10.1007/s00332-016-9315-8

DO - 10.1007/s00332-016-9315-8

M3 - Journal article

VL - 26

SP - 1651

EP - 1692

JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

SN - 0938-8974

IS - 6

ER -