STRESS-STRAIN RELATIONSHIPS IN RUBBER (I) PRAGMATIC ELASTIC CONSTANTS OF RUBBER-LIKE MATERIAL

Abstract

Theoretically the value of elastic constants for isotropic materials can be determined with the knowledge of any two elastic constants, from either of the following equation (1).
ν=1/2-E/6B, E=2G(1+ν) (1) when, E: Young′s modulus, E=σ/ε, σ: Stress, ε: Strain, G: Shear modulus, B: Bulk modulus, ν: Poisson′s ratio.
The rubber deformation takes place without change in volumes so that obtained equation (2).
ν=0.5, E=3G (2)
Bartenev shows equation (3) when large deformation of the rubber.
σ=E(1-λ^-1), λ=1+ε (3)
But from (2) and (3) obtained equation (4) σ=3G(1-λ^-1) did not fit for experimental data by Treloar stress-strain curve. σ=G(λ-λ^-2) also famous equation but the experiment failed of success at tensile side to Treloar data.
My idea is defined rubber-like Poisson′s ratio (ν_R) and rubber-like Young′s modulus (E_R), (ν_R)=ε′/ε =(1-1/√<λ>)/(λ-1), (E_R)=2G(1+(ν_R))…(5), and (E_R) relation input Bartenev equation (3), gained σ-λ formula (6), σ=2G(1-λ^-1.5).
This equation (6) shows very close agreement to the Treloar tensile and compression data in the pragmatic strain region from about 2>λ>0.5.