Check out this video I found online whilst uploading last week’s Friday fold:

This video was produced and published on YouTube by Markus Beckers, Michael Ketterman, Dennis Laux and Janos Urai.

It’s a nice demonstration of how multiple layers of material of different properties and different thicknesses can yield up different flavors of folds. In the movie, there are two materials present: white silicone and gray foam. The silicone layers are stronger (“more competent”) than the foam. But the two silicone layers are different thicknesses. It turns out that this ends up being a decisive factor in determining the way they fold.

We can explain this behavior using the Ramberg-Biot equation:

L = 2 π t (η / 6η_o)^⅓

where L is the wavelength of the fold (in other words, the distance from one antiform fold hinge to the next antiform fold hinge); t is the thickness of the folded layer; η is the viscosity (resistance to flow) of the silicone layer (or, in general, the more competent of the two layers); and η_o is the viscosity of the foam layers.

In other words, the (η / 6η_o)^⅓ part of the equation reflects the viscosity contrast between the affected layers. In the video, this viscosity contrast is a constant, since we’re looking at two layers of the same stuff surrounded by the same matrix of other stuff.

As far as our video up top is concerned, pay attention to the t value and the L value: the thicker the layer is, the larger the wavelength of the resulting fold. The thin layer has a lower t value, and so it ends up with a shorter wavelength: i.e., there are more folds packed into the same amount of vertical space as its stouter neighbor. The thick layer’s higher t value means it will have a longer wavelength, and fewer undulations will fit into the available vertical space.

Happy Friday, everyone!