The plane stress state of residually stressed bodies: a stress function approach
Abstract
The stressed state of flattened thin elastic sheet, as well as that of translationally symmetric 3D solids, are effectively 2D problems. This paper study equilibrium state-of-stress in metrically-incompatible 2D elastic materials. The solution is represented by a scalar stress function, generalizing the Airy stress function, which is determined by geometric compatibility conditions. We develop a perturbative approximation method for solving this stress function, valid for any constitutive relation. We apply the method for the case of a Hookean solid to solve prototypical examples in which the classical Airy approach is either inaccurate or inapplicable. Results are shown to agree well with numerical results obtained in previous works.
Keywords
Cite
@article{arxiv.1409.6594,
title = {The plane stress state of residually stressed bodies: a stress function approach},
author = {Michael Moshe and Eran Sharon and Raz Kupferman},
journal= {arXiv preprint arXiv:1409.6594},
year = {2015}
}
Comments
9 pages, 5 figures