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Arash_Yavari's picture

On the stress singularities generated by anisotropic eigenstrains and the hydrostatic stress due to annular inhomogeneities

The problems of singularity formation and hydrostatic stress created by an inhomogeneity with eigenstrain in an incompressible isotropic hyperelastic material are considered. For both a spherical ball and a cylindrical bar with a radially-symmetric distribution of finite possibly anisotropic eigenstrains, we show that the anisotropy of these eigenstrains at the center (the center of the sphere or the axis of the cylinder) controls the stress singularity.

Arash_Yavari's picture

Nonlinear elastic inclusions in isotropic solids

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.

jsanz's picture

ISDMM11 - Upcoming Abstract Deadline January 30th 2011

5th International Symposium on Defect and Material Mechanics, Seville (Spain), from June 27 to July 1, 2011.

Scientific Committee: 

Modelling inclusion (second phase particles) by Ansys

Hi all

 

I am phd student and working on aluminium alloy 2214. i wanted to know if anyone here has experience of FE modelling of inclusions present in alloys by Ansys? i have characterized my material n i know inclusion distribution n size. can anyone help me in this regard?

 

 

Merci en avance

Mogadalai Gururajan's picture

Eshelby and his two classics (and some more on the side)

Eshelby and the inclusion/inhomogeneity problems

Any materials scientist interested in mechanical behaviour would be aware of the contributions of J.D. Eshelby. With 56 papers, Eshelby revolutionised our understanding of the theory of materials. The problem that I wish to discuss in this page is the elastic stress and strain fields due to an ellipsoidal inclusion/inhomogeneity - a problem that was solved by Eshelby using an elegant thought experiment.

In two papers published in the Proceedings of Royal Society (A) in 1957 and 1959 (Volume 241, p. 376 and Volume 252, p. 561) Eshelby solved the following problem ("with the help of a simple set of imaginary cutting, straining and welding operations"): In his own words,

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