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

  1. Nov 23, 2012 #1
    I'm researching CNTs and am currently describing Graphene as I lead from carbon atoms to nano-tubes. I've come accross 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.
     
  2. jcsd
  3. Nov 24, 2012 #2

    tiny-tim

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    welcome to pf!

    hi dkell! welcome to pf! :smile:
    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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