Exponential behavior in elasticity?

[mresimulator]

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.

 

[Andy Resnick]

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).

 

[Greg Bernhardt]

Best regards

Use ## for inline latex