I am attempting to implement the St. Venant Kirchoff model in Ansys using the USERHYPER subroutine. I have expressed the strain energy density function in terms of the isochoric invariants of the right Cauchy-Green strain tensor (I1,I2) and elastic volume ratio (J). I would like to confirm the expression for the strain energy and its 9 derivatives (see below). I would also like to also clarify the differences between the linear elastic model w/large displacements and the St VK model.
Thanks
Strain Energy for the St. Venant Kirchoff Material (in terms of ischoric invariants of the Right Cauchy Green strain tensor):
Ws=0.5(lambda+2μ) {0.5(I1-3)}^2-0.5μ(I2-2I1+3)+(lambda+2μ/3)(J-1)^2
Derivative 1:
∂Ws/∂I1=0.5(lambda+2μ)(I1-3)+μ
Derivative 2:
∂Ws/∂I2=-0.5μ
Derivative 3:
(∂^2 Ws)/(∂I1^2 )=0.5(lambda+2μ)
Derivative 4:
(∂^2 Ws)/∂I1I2=0
Derivative 5:
(∂^2 Ws)/(∂I2^2 )=0
Derivative 6:
(∂^2 Ws)/∂I1J=0
Derivative 7:
(∂^2 Ws)/∂I2J=0
Derivative 8:
∂Ws/∂J=2(lambda+2μ/3)(J-1)
Derivative 9:
(∂^2 Ws)/(∂J^2 )=2(lambda+2μ/3)