What is elastic stiffness? What about 2nd and 3rd order elastic stiffness

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SUMMARY

This discussion focuses on the concepts of elastic stiffness, specifically second- and third-order elastic stiffness as they relate to carbon nanotubes (CNTs) and graphene. The second-order elastic stiffness is quantified at 340 Newtons per meter (N m–1), while the third-order elastic stiffness is measured at –690 N m–1. The conversation clarifies that elastic stiffness is synonymous with Young's Modulus, and distinguishes between linear and nonlinear elastic stress-strain responses, with nonlinear responses incorporating higher-order terms in their equations.

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dkell
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I'm researching CNTs and am currently describing Graphene as I lead from carbon atoms to nano-tubes. I've come across this:

"The force-displacement behavior is interpreted within a framework of nonlinear elastic stress-strain response, and yields second- and third-order elastic stiffnesses of 340 Newtons per meter (N m–1) and –690 Nm–1, respectively." http://www.sciencemag.org/content/321/5887/385.full

The text says that the the "Elastic Stiffness" = Young's Modulus, but what about second- and third-order elastic stiffnesses?

I know elasticity is a materials ability to return to its previous shape, and stiffness is resistance to deformation or strain.

Thank you for your help.
 
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welcome to pf!

hi dkell! welcome to pf! :smile:
dkell said:
… nonlinear elastic stress-strain response …

linear elastic stress-strain response means that stress = constant times strain …

ie, hooke's law (and young's modulus) appplies​

non-linear elastic stress-strain response means that stress is a more complicated function of strain …

eg k1x + k2x2 + k3x3 + …

here, the constant k2 would be the second-order stiffness, the constant k3 would be the third-order stiffness, etc :wink:​
 

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