# What is strain?

In class we discussed a force exerted on a soft ball against a rigid surface. We were told that the strain (of the order: we are doing dimensional analysis) h/a where h is the height difference from the undeformed ball, and a is the radius of the circle intersection of the ball with the surface. However, on wikipedia it says that strain is the "measure of how much a given displacement differs locally from a rigid-body displacement." Wouldn't this be h/R (Radius of the undeformed ball.) Can someone give a more clear definition of strain?

Related Other Physics Topics News on Phys.org
PhanthomJay
Homework Helper
Gold Member
Be careful using Wiki ....its explanations tend to be quite complex. But the ball/rigid surface example of strain is also not a good start point for understanding strain, because it involves 3 dimensional deformations. Instead, consider strain as the amount of deformation per unit length. Take a rubber band about 10 cm long and stretch it 2 cm so that it is now 12 cm long. The deformation, or stretch, is 2 cm, and the strain is 2 cm/10 cm = 0.2, a dimensionless quantity.

how does one go about finding the strain for more complex objects? My professor pretty much just told us it was h/a with little explanation.

For example in 2 dimensions compressing a soft triangular sheet against a rigid surface (on its point). Isn't the strain again just Δheight/height? Why is it different in different shapes?
For 2D and 3D is it ΔArea/Area and ΔV/V?

Last edited:
The triangle is more complex than a rubber band which has strain in one direction only (of course in the real world it is a bit more complicated than that). Not only does it get shorter, but it will also get wider. So you have two different strains in two different dimensions.