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. 2016 Jun 8;9(6):456. doi: 10.3390/ma9060456

Table 3.

Utilized strain energy functions and their corresponding Cauchy stress expressions for an incompressible isotropic material under uniaxial tension.

Model	Strain Energy Function	Cauchy Stress
Mooney-Rivlin	$W = \sum_{i = 1}^{2} a_{i} (I_{i} - 3)$	$σ = (λ^{2} - \frac{1}{λ}) (a_{1} + \frac{a_{2}}{λ}$ )
Yeoh	$W = \sum_{i = 1}^{3} a_{i} {(I_{1} - 3)}^{i}$	$σ = a_{1} (I_{1} - 3) + a_{2} {(I_{1} - 3)}^{2} + a_{3} {(I_{1} - 3)}^{3}$
Fung	$W = \frac{a_{1}}{2 a_{2}} (e^{a_{2} (I_{1} - 3)} - 1)$	$σ = a_{1} (λ^{2} - \frac{1}{λ}) e^{a_{2} (I_{1} - 3)}$
Neo-Hookean	$W = a_{1} (I_{1} - 3)$	$σ = 2 a_{1} (λ^{2} - \frac{1}{λ})$
Humphrey	$W = a_{1} (e^{a_{2} (I_{1} - 3)} - 1)$	$σ = 2 a_{1} a_{2} (λ^{2} - \frac{1}{λ}) e^{a_{2} (I_{1} - 3)}$
Ogden	$W = \sum_{n = 1}^{3} \frac{a_{(2 n - 1)}}{a_{2 n}} (λ_{1}^{a_{2 n}} + λ_{2}^{a_{2 n}} + λ_{3}^{a_{2 n}} - 3)$	$σ = a_{1} (λ^{a_{2}} - 2^{a_{2} - 1} λ^{- a_{2} / 2}) + a_{3} (λ^{a_{4}} - 2^{a_{4} - 1} λ^{- a_{4} / 2}) + a_{5} (λ^{a_{6}} - 2^{a_{6} - 1} λ^{- a_{6} / 2})$
Veronda–Westmann	$W = a_{1} (e^{a_{2} (I_{1} - 3)} - 1) - \frac{a_{1} a_{2}}{2} (I_{2} - 3)$	$σ = 2 a_{1} a_{2} (λ^{2} - \frac{1}{λ}) (e^{a_{2} (I_{1} - 3)} - \frac{1}{2 λ})$