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# Trouble Writing Transversely Isotropic Hyperelastic UMAT in Abaqus (Ligament modeling

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(@PeggySchaefer)
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Joined: 11 years ago

**EDIT**

Hi,

I am currently attempting to change an existing Neo-Hooken UMAT from Abaquss documentation to add in the fiber response, which is a step-wise Cauchy stress-stretch function (Weiss et al, 1996, where W(total) = W(Neo-Hookean) + W(fiber):

fiber_stress = 0 stretch < 0
fiber_stress = non-linear function 1 < stretch stretch*

In the UMAT, the Right Cauchy-Green tensor is calculated (BBAR(1-6)) from the determinant of the deformation gradient, and then the Cauchy Stress (Stress(1-6)) is calculated from the Right-Cauchy Green Tensor.

Question: In order to add in fiber stress, I just added the fiber_stress to Stress(3), which is the stress in the fiber direction. Stress(3) is calculated as a function of determinant(F) and BBAR(3), the third value from the Cauchy-Green array, as well as the Neo-hookean properties.

Problem: This works for a single C3D8 element, but as soon as I make my cube a multi-element part, the solution will not converge. I believe this is due to the fact that Im adding a fiber stress to stress(3), and therefore the cauchy stress is too large. Does anyone have an idea of how to have the fiber stress effect translate to the other axial and shear stresses?

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Posts: 3998
(@jorgen)
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If your fibers are always located in the 3-direction, then adding a Stress(3) term seems right.
My guess is that your lack of convergence is caused by an incorrect or poor estimation of the Jacobian.

-Jorgen

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Topic starter
(@PeggySchaefer)
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Joined: 11 years ago

[QUOTE=Jorgen,12552]If your fibers are always located in the 3-direction, then adding a Stress(3) term seems right.
My guess is that your lack of convergence is caused by an incorrect or poor estimation of the Jacobian.

-Jorgen

Hi Jorgen,

I corrected the Jacobian (DDSDDE in Abaqus) to include the fiber response, and for my multi-brick element model, it converged perfectly and gave me almost identical values for published data in literature. However, when I apply this to the same cube with multiple tet 10 elements, convergence is not being reached. I doubled my C10 for the Neo-Hookean part, and updated the bulk modulus as well, and convergence was reached. My questions are:

1. Have you dealt with Tet 10 (10 nodes) quadratic elements in which convergence is not reached that would otherwise be reached in brick elements?
2. Why should raising the C10 value cause my solution to converge? The fiber stress (S11) is about 10 times higher than the non-fiber stress directions (S22 and S33) at 10% strain in the fiber direction.
3. More importantly, should the shear stress (S12, S13, S23) in my code somehow be updated to include the interaction between the fibers and the bulk material?

Thank you for your time, any insight is appreciated.

Jamie

Posts: 3998
(@jorgen)
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1. No, it should automatically work for all 3D element types.
2. That can happen if you Jacobian is not quite right.
3. That depends on how you calculate the stress. If the stress calculations are coupled, then the Jacobian should too.

-Jorgen

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