Hi all,

I have gone through the theory manual, subroutines manual and examples manual of ABAQUS documentation. There is an example of UMAT implementation for Neo-Hookean hyperelastic material at the following link starting on page L6.44. 

http://imechanica.org/files/Writing%20User%20Subroutines%20with%20ABAQUS.pdf

They give an explicit expression for material Jacobian C_ijkl for Neo-Hookean material on page L6.46. I tried to derive this expression based on the information provided in Abaqus Theory Manual Section 4.6.1. The problem I am facing in this derivation is that that I don't understand where does the term [(2/9)(delta_ij)(delta_kl)(BBAR_mm)] come from in the expression of C_ijkl. This is assuming that the strain energy density function is expressed in terms of the invariants of BBAR(left Cauchy-Green tensor of deviatoric deformation) and not B (left Cauchy-Green tensor). Can anyone throw some light on this derivation/issue? It will be really useful for me as well as the community.

Thanks in advance.

Mandar