The Finite Element Method for the Analysis of Non-Linear and ...

Hyperelastic Material
Hyperelastic Material Models
Saint Venant-Kirchhoff model
W (ɛ) = λ 2 [tr(ɛ)]2 + µtr(ɛ 2 )
and the second Piola-Kirchhoff stress can be derived as
S = λ[tr(ɛ)]I + 2µɛ
λ, µ are the Lamé constants
Mooney-Rivlin model
W (ɛ) = C 1 (I 1 − 3) + C 2 (I 2 − 3)
where C1 and C2 are empirically determined material constants and
I 1 = tr(C) = C 11 + C 22 + C 33
where C is the Cauchy-Green deformation tensor (see Lecture 4) and
I 2 = 1 2 [(I 1) 2 − tr(C) 2 ]
Institute of Structural Engineering Method of Finite Elements II 19