An invariant basis for natural strain which yields orthogonal stress response terms in isotropic hyperelasticity

By John C. Criscione, Jay D. Humphrey, A. Douglas, W. Hunter. 2000

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Rivlin's Representation Formula is Ill-Conceived for the Determination of Response Functions via Biaxial Testing (2003, methodology): “In fact, Criscione et al. [ 11 ] developed an approach using natural strain ln V which minimizes the covariance amongst response terms.”
Geometry of Logarithmic Strain Measures in Solid Mechanics (2015, background): “Note that while every isotropic elastic energy W can be expressed as W (F ) = h(K1,K2,K3) with Criscione’s invariants 52 [46, 45, 51, 208]”
An explicit, direct approach to obtaining multiaxial elastic potentials that exactly match data of four benchmark tests for rubbery materials—part 1: incompressible deformations (2012, background): “Recent results for applications of Hencky strain to finite elasticity are given in [1–3,15–17,19,20,23,45,52,54,91,94], and many others.”
Fitting hyperelastic models to experimental data (2004, methodology): “In the analysis of the Jones–Treloar data conducted in [5] the value N 1⁄4 3 is suggested.”