期刊
出版社
ROYAL SOC
DOI: 10.1098/rspa.2013.0415
关键词
geometric elasticity; inclusions; residual stresses
资金
- King Abdullah University of Science and Technology (KAUST) [KUK C1-013-04]
- AFOSR [FA9550-12-1-0290]
- NSF [CMMI 1042559, CMMI 1130856]
- Wolfson/Royal Society Merit Award Holder
- EC
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [1130856] Funding Source: National Science Foundation
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.
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