implement the second piola kirchhoff stress for e Neo Hookean material.

[Carolina]

Hello,
I have a question regarding the implementation of the second piola kirchhoff stress as well as the corresponding constitutive tensor for a compresible for e Neo-Hookean material.

I would like to know how the computation of the Inverse of right Caochy Green deformation tensor is going to look like in FEAP?

CI=?

Thank you

[FEAP_Admin]

We perform the evaluation in the current configuration; likewise the tangent is assembled in the current configuration.
See the routine $FEAPHOME8_6/elements/material/finite/neoh3f.f for the constitutive evaluation.  The tangent is stored in aa(1:6,1:6)
and depends on U' and U'' is a simple way since we do not do this in the reference configuration.

See also the paper of Simo and Taylor 1991 Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms. CMAME; equation 3.29.

See also section 5.5.1 in Zienkiewicz and Taylor volume 2.

[FEAP_Admin]

Just notice you posted on the FEAPpv board.

In FEAPpv, look in elements/material/material.f which contains the subroutine stnh3f( ).  aa( , ) still contains the tangent.

[Prof. R.L. Taylor]

1. We always  compute the inverse of a 3x3 from the components C (or F) -- alternatively you can use the "invert.f" routine in ./program of feappv.

2. If you want the variation of the inverse then that can be done from variation (C * C^-1)_ = I -- using chain rule. 

[Prof. R.L. Taylor]

You need to study a book that describes how to do the development (in Voigt) notation.  One option is the book by Zienkiewicz, Taylor & Fox, The FEM for Solid and Structural Mechanics, 7th ed. Butterworth, 2013.