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Jacobian

Question about implicit creep subroutine in Abaqus

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.

hbh's picture

Deriving the jacobian matrix for the Hill criterion

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  

hbh's picture

Deriving the jacobian matrix for the Hill criterion

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  

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