The science of behavior of stretch fabrics

I’ve been wanting to ask this for a while but was trying to find a picture to help with my explanation. I can’t so I’ll ask anyway.

When someone wears tight stretch fabric it tends to want to conform to the body’s curves even when it looses contact with the body. For example if someone is wearing a tight fitting T-shirt the fabric tends to dip into the belly button ‘well’. Or in the case of a tight fitting dress or panties the fabric attempts to try to follow the contour of the buttocks. This makes no sense to me. Why wouldn’t the fabric take the path straight across the depression? If I hold a T-shirt in my hands and stretch it the fabric makes a straight line between them.

What is the science that makes stretch fabric deform into body cavities instead of stretching straight point to point? And why not deform out?

Never seen the belly-button thing, that doesn’t make any sense to me at all.

The buttocks thing i think is fairly straight forward though. The fabric takes the path that provides least stretch (i.e tensile force) exactly as you assume. What you are perhaps overlooking though is that the fabric stretches in all directions, and depending on the original shape of the garment the required ‘stretch’ across the cheeks as it were is less than the required stretch through the crotch.

I think that pretty much covers most scenarios i’ve seen. Bear in mind that a garment can be shaped such that such things are intended to happen. I would assume it is even possible to make some parts more stretchy than others in order to achieve the desired fitted shape.

Not my area of expertise, but fairly confident in this answer. I don’t believe there is any more complicated physics at work here.

Belly button thing stumps me though, was that an actual example you’ve seen or just a theoretical?

I think rocksolid is right. I’ve done a little work with web deformation, though not with clothing in particular. In lots of cases the curvature is negative, in the sense that radii taken along paths at right angles to each other extend from opposite faces of the fabric. That is, the shape is like the surface of a saddle.

But not in the case of the belly button. It might be that the eye and brain are creating the impression of a dip based on how curved the fabric is everywhere else nearby. But other than that guess, I got nothing.

On a molecular scale, polymers that stretch are made up of molecules that are curled and kinked. When you stretch the material, you “straighten” them out. These molecules act like a spring and pull the molecules tight.

Of course this doesn’t answer your bellybutton question. Most springs in a limited fashion behave according to Hooks Law so F =kx. Actually, materials are not necessarily so linear. As always, the material will try to find the lowest energy configuration available to it. It is possible that a material will find that the energy of stretching lots is not much different from stretching medium, but much more energy is relieved by not stretching much at all. In this case following the curve of the bellybutton, might actually be the easiest way to go. This would be a more common phenomenon when a material is being stretched to it’s limit.

Of course, maybe your just really sweaty. In which case, something else is going on.

Here is a clear example of the belly button being visible under a shirt.

Upon further investigation of that image, it seems like the reason is because the belly is actually a curved surface and so the shirt is actually lying flat across the belly button which minimises surface area. That it appears to dip inward is a perceptual illusion.

The shortest distance between two points on a convex surface isn’t an arc over the surface, it’s a chord that reaches some depth within the surface.
Stretched cloth over a belly button doesn’t follow the curve of the bellybutton, it follows the shortest distance chord between the two sides of the belly button.

Actual example. Here in Santa Cruz you see it all the time. I’ll keep my eye out for a better example.

Thanks for the responses.

I’m sorry, I don’t think I understand what you are saying. Certainly the shortest distance between the edges of a concave (isn’t the belly button concave rather than convex) surface is the straight line from one edge to the next.

My point in my previous post is that modern fabrics don’t have to take the shortest distance between two points. If you want to design a garmet that form fits the body you can by choosing the right weeve of the right polymer. Nothing has to be linear.

Maybe the belly button in Shalmanene’s example isn’t perfect, but look at the way her shirt form fits her breasts. You better believe the people that designed that shirt designed it to do exactly that, and it isn’t taking the shortest distance between two points there.

Yes, the belly button is a concavity in a convex surface. Stretchy cloth doesn’t conform to the belly button, it merely takes the shortest path from one side of the button to the other.

Yes it is. It’s just not the shortest distance from nipple to nipple, it’s the shortest distance from below the breasts to above the breasts. It’s the same as what rocksolid mentioned about the buttocks.

There might also be some form fitting design involved, but that wouldn’t work for the belly button where the fabric could as easily go out as in and you’d just get an extra loose patch of fabric.

>On a molecular scale, polymers that stretch are made up of molecules that are curled and kinked. When you stretch the material, you “straighten” them out. These molecules act like a spring and pull the molecules tight.

You’re describing elastomers like polyisoprene or polyurethane. Stretch fabrics work by a different mechanism. They either use fibers that are curled, or they use a weaving pattern that would require the straight fibers to bend with zero radius at single points, or both. The beam strength of the fiber makes it follow a longer path to avoid tight kinking, and stretching the fabric, while it does not stretch the fibers enough to matter, pulls them into more jagged shapes so they extend further. Stretch fabrics can be made of polypropylene, nylon, polyethylene teraphthalate (sp?), and so on. Those things generally have molecules with substantially straight backbones aligned with the length of the fiber, because they are oriented while being spun from the melt.