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arXiv · 1409.6594

The plane stress state of residually stressed bodies: a stress function approach

Michael Moshe·Eran Sharon·Raz Kupferman
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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.

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Michael Moshe, Eran Sharon, Raz Kupferman. 2014-09-23. The plane stress state of residually stressed bodies: a stress function approach. https://arxiv.org/abs/1409.6594

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