Quantifying deformation of a shape

[gkiverm123]

TL;DR

Quantify deformation of a shape with single parameter

Hello all,

I hope this post is in the appropriate thread. Would anyone have any insight on a method to quantify deformation of a shape? For example, I attached two images of a white shape of interest at the center (one deformed and one undeformed). I'm trying to develop a metric/parameter (single number) that will quantify the degree to which the shape is being deformed.

One simple method would be to measure the reduction of area. However, this doesn't fully capture the deformation because sometimes the shape extends on the opposite side it is being deformed.

Thanks,
Vivek

 

[Dale]

I’m trying to develop a metric/parameter (single number) that will quantify the degree to which the shape is being deformed.

How about the Dice ratio?

https://en.m.wikipedia.org/wiki/Sørensen–Dice_coefficient

this doesn't fully capture the deformation

No single parameter will fully capture something as complicated as deformation. You need to set your goal a little lower. You just want something that seems reasonable for the task

 

[jrmichler]

I'm trying to develop a metric/parameter (single number) that will quantify the degree to which the shape is being deformed.

Here's an idea: If the black part is a homogeneous solid, then it is deformed along with the white inside shape. You could calculate (FEA) the strain in the black part, and average to get a mean strain for the entire black part. That mean strain would be both quantitative and nondimensional, and should reflect the degree to which the shape is deformed. Some work on your part is necessary to verify this.

Check for size effects of the white area. It may be necessary to scale by the size of the white area, or by some shape parameter such as the ratio of perimeter to white area. Or the white area raised to some power. More work on your part...

Another possibility is to treat the white area as a homogeneous solid, and calculate the mean strain of that area using FEA. And another possibility is to treat the white area as a homogeneous plastic solid of unit thickness, and calculate the total work to deform it. Divide by the volume or by the area to get a mean work. This would not be nondimensional, but would be quantitative.

Sounds like a fun project. Enjoy.