Why did the toilet roll in the previous image buckle non-axisymmetrically, producing a post-buckled pattern of diamond-shaped buckles ( the familiar Yoshimura pattern), whereas this toilet roll has an axistmmetric post-buckled state?
Perhaps because of the particular way the outer layers of the toiet roll adhere to eachother. Or perhaps the material has a non-linear softening stress-strain curve much like that of an elastic-plastic metal.
Post-buckled states of elastic-plastic cylindrical shells are often partly axisymmetric, especially adjacent to the supported ends of the cylindrical shell.
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