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

[dkell]

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.

 

[tiny-tim]

welcome to pf!

hi dkell! welcome to pf!

… 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 ​