(

*A*) Representative ligament (

*Center*) extracted from the Buckliball, and a simplified curved column model (

*Right*). (

*B*) Narrowest cross-section of the ligament. (

*C* and

*D*) Phase diagram of the two design parameters

. The color-shaded region indicates on-sphere buckling and the white region represents the out-of-sphere buckling. The magnitude of the critical pressure for the onset of the on-sphere buckling is shown as a contour map with the adjacent color bar; (

*C*) for 12 holes and (

*D*) for 24 holes. The dotted marked lines indicate the analytical criterion from , based on the second moment of area. (

*E*) Linear approximation of the normalized effective width of the ligament (

*α* =

*w*_{e}/

*R*_{i}, see ) in terms of effective solid volume fraction (

*ψ*_{c} -

*ψ*). This linear approximation is valid up to the width ratio of

*α* ≈ 0.15. (

*F*) Master curve obtained from the buckling of the simplified ligament shapes. Regardless of the hole arrangements, the normalized critical pressure (

*ρ* =

*p*/

*E*) for the onset of on-sphere buckling has a distinctive relation with the two design variables

,

*ρ* ≈

*Aτ*(

*ψ*_{c} -

*ψ*)

^{2}, with the prefactor

*A* = 0.556 and a coefficient of determination of

.

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