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

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Discussion Overview

The discussion revolves around the concept of strain in materials, particularly focusing on the differences between two expressions for strain: h/a and h/R. Participants explore definitions, applications, and the implications of strain in various geometries and dimensions.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant notes that strain is defined as h/a, where h is the height difference from the undeformed ball and a is the radius of the circle intersection with the surface, but questions whether it should instead be h/R, with R being the radius of the undeformed ball.
  • Another participant cautions against relying on Wikipedia for definitions, suggesting that strain should be understood as deformation per unit length, using the example of a rubber band to illustrate this concept.
  • A participant inquires about calculating strain for more complex objects, questioning why strain appears to differ based on shape and suggesting that for 2D and 3D objects, strain might be expressed as Δheight/height and ΔArea/Area, respectively.
  • One participant points out that the strain in a triangular sheet compressed against a surface involves more complexity than a rubber band, as it experiences changes in both length and width, indicating the presence of multiple strains in different dimensions.

Areas of Agreement / Disagreement

Participants express differing views on the definition and calculation of strain, with no consensus reached on the appropriate expressions or their applicability to different shapes and dimensions.

Contextual Notes

Some participants highlight the complexity of strain in three-dimensional deformations compared to simpler one-dimensional cases, indicating that the definitions and calculations may depend on specific conditions and geometries.

m00npirate
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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.
 
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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.
 

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