- #1
mresimulator
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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.
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.
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