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    Nonlinear elastic inclusions in isotropic solids

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    Type
    Article
    Authors
    Yavari, A.
    Goriely, A.
    KAUST Grant Number
    KUK C1-013-04
    Date
    2013-10-16
    Online Publication Date
    2013-10-16
    Print Publication Date
    2013-10-16
    Permanent link to this record
    http://hdl.handle.net/10754/598989
    
    Metadata
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    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.
    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.
    Publisher
    The Royal Society
    Journal
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
    DOI
    10.1098/rspa.2013.0415
    PubMed ID
    24353470
    PubMed Central ID
    PMC3857869
    ae974a485f413a2113503eed53cd6c53
    10.1098/rspa.2013.0415
    Scopus Count
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