Nonlinear elastic inclusions in isotropic solids

A. Yavari, A. Goriely

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)20130415
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2160
StatePublished - Oct 16 2013
Externally publishedYes


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