Hyperelastic, elastic, hypoelastic

[Trying2Learn]

TL;DR Summary

What is the difference between these words: Hyperelastic, elastic, hypoelastic

Could someone explain to me the difference in these words: Hyperelastic, elastic, hypoelastic? But first...

I understand the terms (in and of themselves), with regard to large deformation, recoverable, strain energy functions, etc. ;, but, instead words like "x-elastic, y-elastic, z-elastic," I would have been equally fine: just words.

But those prefixes "hyper" and "hypo" mean things. And I cannot put those three types of elasticity in a 'hyper' or 'hypo' ranking, while, at the same time, getting a feeling that distinguishes (or, relates) the words to (or from) each other. So, could somone help me out?

Anyone?

 

[FEAnalyst]

I guess that by elastic you actually mean linear elastic. In simple words, without going into details:
- linear elastic material - exhibits elastic behavior at all levels of strain (all deformations are reversible) and this behavior is linear (stress directly proportional to strain)
- hyperelastic material - exhibits elastic behavior even at very high levels of strain (for example rubber can be stretched significantly and it still goes back to its initial shape) and this behavior is nonlinear (nonlinear relationship between stress and strain)
- hypoelastic material - exhibits nonlinear elastic behavior even at very low levels of strain

 

[Trying2Learn]

I guess that by elastic you actually mean linear elastic. In simple words, without going into details:
- linear elastic material - exhibits elastic behavior at all levels of strain (all deformations are reversible) and this behavior is linear (stress directly proportional to strain)
- hyperelastic material - exhibits elastic behavior even at very high levels of strain (for example rubber can be stretched significantly and it still goes back to its initial shape) and this behavior is nonlinear (nonlinear relationship between stress and strain)
- hypoelastic material - exhibits nonlinear elastic behavior even at very low levels of strain

Hi! THANK YOU! This helps a LOT. Now may I push my luck and ask for a bit more?

Within the context of elastic behavior with regard to large and small strain...

Why is there a strain energy function for hyperelastic materils and NOT for hypoelastic materials.

Next:

Why is it that with the Jaumann stress rate, we REMOVE rotations from hypoelastic materials. I would have imagined we do that for hyperelastic materials.