Strain: What is the Difference Between h/a and h/R?

[m00npirate]

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?
Thank you in advance.

 

[PhanthomJay]

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.

 

[m00npirate]

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?

 

[Subductionzon]

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.