I'm working with bulge tests of materials using biaxial loading (applying pressure from one side through a circular aperture). The materials are clamped on the edges.
The diameter of the aperture is >20 times the thickness of the material. Based on this, I expect membrane-like behavior, with almost uniform stress throughout the material, and the shape of a spherical cap. The experiments start with a flat sheet and proceed until displacements of the center are around >5-6 times the original thickness. Given this, I figured I could neglect bending and only focus on in-plane stresses.
instead of the actual spherical cap shape.
Why is this happening? I can't figure out why just looking at stress contours that are typically plotted -- usually the expected stress is largest at the center and less at the sides.
I have a theory that perhaps it's because in the center, there are "two directions" for stress to sustain the pressure, but at the clamped edges only one "direction" along the material experiences the stress due to the pressure. But I don't see anyone else having this issue online so I can't tell if my theory is total bogus/there's another reason this might be happening.
Any insight would be much appreciated. Thank you!