The elastic potential function of slightly compressible rubberlike materials

In order to obtain an analytical expression for the stored energy function W of slightly compressible rubberlike materials, two recent results are used to obtain a unified expression where Γ_i are a new set of invariants, and H(Γ₁,Γ₂) is the shear part of the stored energy function which is now assumed to be a separate symmetric function of the modified stretch ratio, λ = λ_i/I, i.e., Various analytical forms of h(λ) are proposed. Also, a straightforward transformation technique is formulated such that one can easily relate the stress-strain relation in terms of modified stretch ratio λ to the new invariants Γ_i. Thus, by a combination of the above equations and the transformation technique, one may readily determine the elastic strain energy function of slightly compressible materials from careful measurements of the volume change in multiaxial deformations.