Elastic/shear modulus relationship question

[dr_chickolas]

Dear All,

First of all, hi! I have just joined the forum and appreciate any help that people might be able to offer.

My question: I have test data for a type of rubber. In the shear tests, we observed that the shear stress/shear strain relationship is practically linear, up until shear strain of around 0.6. If the material were assumed linear elastic, this would give us a shear modulus (G) of about 0.6MPa. In separate uniaxial tensile tests, we observed a nonlinear hyperelastic relationship (as expected). It occurred to us to see whether the linear elastic assumptions hold for low strains: we took the initial elastic modulus (E) in the tensile test, which was found to be around 2.7MPa.

For a linear elastic material, assuming incompressibility, E=3G. In our case, E= approx 5G. My question is, I suppose, should hyperelastic materials, for small strains, obey the relationships of linear elastic materials, i.e. is there any cause for concern that E is not equal to 3G for small strains in our tests?

Apologies if this is a silly question! Thanks for any help,
Will

[Jorgen]

If your rubber is homogeneous (that is not full of void or "strange" particles) then it should be basically incompressible and E=3G to a very good approximation. If you don't get that experimentally then my guess is that you have some experimental errors.

-Jorgen