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# Problem about Large volume changes with geometric nonlinearity

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(@at80)
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Joined: 16 years ago

Dear Jorgen,

I have to bother you again, on the problem of Large volume changes with geometric nonlinearity when I writing a UMAT of Drucker Prager constitutive model. My umat can run but the convergence rate is slow, so that some times I have to modify the convergence criterion a little bit. I suppose that the problem is due to the poor Jacobian Matrix when the stresses of an integration point approaches the apex, where I set a tensile strength. Thus there is only adjustment of the hydrastatic stresses. However, I am afraid that the Jacobian Matrix possibly casuses converange problem, if the large defromation exists at the same time.

The manual said that If the material model allows large volume changes and geometric nonlinearity is considered, the exact definition of the consistent Jacobian should be used to ensure rapid convergence. For the rate-form constitutive laws, which is commonly encountered by using pressure-dependent plasticity, the exact consistent Jacobian is given by

C=(1/J) * [Par (delta(J*stress)/Par (delta(strain))]

Based on manual, DFGRD0(3,3) and DFGRD1(3,3) provide deformation gradient at the beginning and the end of the increment. But how to calculate C using the DFGRD0(3,3) and DFGRD1(3,3)? I never read the discussion on this topic.

Thanks and waiting for your inspiration.

Best regards,

Willness

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Posts: 3998
(@jorgen)
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Joined: 5 years ago

Your question is not easy to answer since the calculation of the Jacobian is material model dependent. You have a few options. If you have a closed-form expression for the Jacobian for your material model then you can simply code that expression into the UMAT.

If you dont quite know the exact expression for the Jacobian then you might be able to approximate it and get reasonable convergence that way.

The last option is to approximate the Jacobian using a finite difference approach.

-Jorgen

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