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Exponential behavior in elasticity?

  1. Sep 23, 2015 #1
    Hi!
    I know some constitutive models for elastic materials like Neo-Hooke or Mooney-Rivlin, which give a relation between elongation ##\lambda=y/y_o## (where ##y## and ##y_o## are the length of the elastic material in a uniaxial compression test in the direction of the compression at stress ##P## and ##P=0##, respectively).

    I propose the next model of elasticity:

    1) Using the differential definition of strain ##d\epsilon \equiv \frac{dy}{y}##

    2) Using the equality ##-\frac{dP}{E} = d\epsilon##, assuming ##E## is the 'Young's modulus' of the material.

    3) Using this two equations, taking ##E## constant, and using the boundary conditions ##y(P=0)=y_o## we get ##y(P)=y_o e^{-P/E}##.

    This exponential curve fits very well for many of my elastic materials.

    My question is: Is wrong this model? (conceptually speaking).

    Best regards.
     
    Last edited by a moderator: Sep 23, 2015
  2. jcsd
  3. Sep 23, 2015 #2

    Andy Resnick

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    Perhaps I'm not understanding your idea (the text is somewhat garbled), but I don't see where you are proposing a 'new' constitutive relation- you simply used Hooke's law (sort of generalized to 3-D, I suppose).
     
  4. Sep 23, 2015 #3
    Use ## for inline latex
     
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