Jacobian

The implicit implementation of creep in abaqus requires dh/d(\delta \epsilon_c ) as Jacobian in Newton-Raphson's iteration. The derivative can be expanded as shown in the figure attached. The term dh/dq, the one underlined by a green stroke, is expected to be provided by users through specifying DECRA, whereas the term dq/d(\delta \epsilon), underlined by a red one, is confusing me. It seems that that term is computed by Abaqus but I have no idea how it is done. The same question applies to the last derivative on the right hand side.

Thank you very much !

Hello all, 

I am a beginner in UMAT implementation. I want to implement a Umat soubroutine for a kinematic hardening model using Hill's yield criterion. However, after looking in different courses and books, I remarked that the jacobian matrix derivation steps from the constitutive equations are not explicitaly defined.

Can anyone help me to understand this derivation step so that I can apply it for the Hill's criterion ?

Thank you in advance,

Regards,
Haithem