The Valanis–Landel strain energy function Elasticity of incompressible and compressible rubber-like materials. (1st March 2022) - Valanis, Kirk C.
Abstract: The paper revisits the original article by Valanis and Landel on the strain energy density function W = w(λ1 ) + w(λ2 ) + w(λ3 ), where λi are the stretch ratios. The main new results and findings are: (i) An extension of the above algebraic form of W to compressible rubber-like materials (ii) Proof that the Cauchy-Green stress tensor t, as a function of the Left Stretch tensor V, has the same analytical form as the function λw′(λ), within a hydrostatic pressure. (iii) The determination of the form of the constitutive equation t (V ) from a single experiment, the plane strain test. (iv) Comparison with experimental data of several empirical algebraic forms of w′(λ) in the literature. (v) Findings of a study of the Mooney-Rivlin and Ogden models of the Valanis- Landel function, in axial compression.