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

2014/09/23 by Michael Moshe, Moshe, Michael, Eran Sharon +3 · 1 citation
Engineering · #Advanced Materials and Mechanics #Composite Material Mechanics #Elasticity and Material Modeling #FOS: Physical sciences #Mathematical Physics (math-ph) #Soft Condensed Matter (cond-mat.soft) #Structural Analysis and Optimization

paper · pdf · doi:10.48550/arxiv.1409.6594

openalex publication_date 2014/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The stressed state of flattened thin elastic sheet, as well as that of\ntranslationally symmetric 3D solids, are effectively 2D problems. This paper\nstudy equilibrium state-of-stress in metrically-incompatible 2D elastic\nmaterials. The solution is represented by a scalar stress function,\ngeneralizing the Airy stress function, which is determined by geometric\ncompatibility conditions. We develop a perturbative approximation method for\nsolving this stress function, valid for any constitutive relation. We apply the\nmethod for the case of a Hookean solid to solve prototypical examples in which\nthe classical Airy approach is either inaccurate or inapplicable. Results are\nshown to agree well with numerical results obtained in previous works.\n

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