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Deriving the jacobian matrix for the Hill criterion
Wed, 2015-03-18 12:46 - hbh
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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Re: Deriving the jacobian matrix for the Hill criterion
One approach for anisotropic materials undergoing large rotations but moderate to small strains is as follows:
1) Keep track of the material principal directions (p.d.) and do stress updates in the material p.d. coordinate system by rotating and unrotating
2) Compute yield surface derivatives using df/dsigma_ij. The sigma_ij components should be with respct to the the starting material p.d.
3) Compute the derivative of the internal variables (hardening moduli)
4) Compute the continuum elastoplastic tangent modulus using the the flow rule and the consistency condition.
The basic procedure is the same as that shown in the examples in Ahmad Rafsanjani's blog post http://imechanica.org/node/7576
-- Biswajit