Of the recent Fourth Plinth sculptures only Marc Quinn's Alison Lapper Pregnant has gone any way towards bending the square's rectilinear rigidity.
The model quantitatively correlates the microtubule bending rigidity, the surrounding filament network elasticity, and the cytosol viscosity with the buckling wavelength, the buckling growth rate, and the buckling amplitude of the microtubules.
The solutions require the knowledge of the bending rigidity of the bushing and the (out-of-plane) rotational stiffness of the cover plate.
The primary orthogrid stiffens the bending rigidity of the cylinder to resist the global instability while the sub-orthogrid stiffens the bending rigidity of the skin enclosed by the primary orthogrid to resist local buckling.
These three parameters are the mass per unit area, the bending rigidity and the out-of-plane shear rigidity.
The primary Isogrid improves the bending rigidity of the cylindrical wall to resist the global instability while the sub-Isogrid improves the bending rigidity of the skin enclosed by the primary Isogrid to resist local buckling.
This is due to the elastic properties of the membrane: the bending rigidity and the surface tension define a length ξ h = 1/2 (Schick, 2012), which sets the scale over which the membrane height deformations propagate (for our model parameters ξ h ∼ 100 nm).
The translational spring enforces the constraint that the endpoints of adjacent segments should be coincident, while a weighted sum of the torques from the translational spring and the torsional spring are used to approximate the bending rigidity of the filament (henceforce the endpoint and angular alignment constraints, respectively).
Indeed, according to Equation 2, the first term (which accounts for the bending rigidity of the layer) strongly depends on the sheet thickness, while the second one (which accounts for the initial pre-tension) is thickness independent.
Subsequently, the fitting procedure (Méléard et al., 2011) was applied, as displayed in Fig. 3b, resulting in the determination of both the bending rigidity and the membrane tension associated to the giant vesicle that was studied.
