Stored Energy Function of Rubberlike Materials Derived from Simple Tensile Data

Abstract

An explicit formulation to obtain the stored energy function W from simple tension experiments alone, based on the Valanis‐Landel separable symmetric stored energy function, W(λ1, λ2, λ3) = w(λ1) + w(λ2) + w(λ3), is developed. For a simple extension stress‐strain law of the form λσ=Eε, the analytical formula of W in the limited range 1≤λ≤2.5 is found to be W=E ∑ i=l 3 [λ i −1− ln λ i − 1 6 ( ln λ i ) 2 + 1 18 ( ln λ i ) 3 − 1 216 ( ln λ i ) 4 ] ,where the limitation originates with the stress‐strain law. The expression is used to verify the validity of the Valanis‐Landel postulation through prediction of the stress‐strain behavior in multiaxial deformations.