User login

Navigation

You are here

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

Arash_Yavari's picture

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. If they are equal at the center no stress singularity develops but if they are not equal then stress always develops a logarithmic singularity.  In both cases, the energy density and strains are everywhere finite. As a related problem, we consider annular inclusions for which the eigenstrains vanish in a core around the center. We show that even for an anisotropic  distribution of eigenstrains, the stress inside the core is  always hydrostatic. We show how these general results are connected to recent claims on similar problems in the limit of small eigenstrains.

AttachmentSize
PDF icon AnnularInclusion_YaGo14.pdf374.33 KB
Subscribe to Comments for "On the stress singularities generated by anisotropic eigenstrains and the hydrostatic stress due to annular inhomogeneities"

Recent comments

More comments

Syndicate

Subscribe to Syndicate