Hello,
I'm trying to implement a UMAT for an incompressible Mooney-Rivlin (MR) material model (strain energy = c10*(inv1-3)+c01*(inv2-3)). I know that I need to use hybrid elements since I have incompressibility. What I cannot understand is how to incorporate the hydrostatic pressure within my subroutine.
The Kirchhoff stress tensor (KST) looks something like this:
KST = KST_MR - p I, where KST_MR is the Kirchhoff stress that stems from the MR strain energy, p is the hydorstatic pressure and I is the second order identity.
How should I define the pressure in the subroutine such that, as stated in the UMAT manual, "Abaqus/Standard replaces the pressure stress calculated from your definition of STRESS with that derived from the Lagrange multiplier and will modify the Jacobian appropriately."?
Thank you very much in advance and please let me know if there's anything I can clarify further.
PS: The reason I'm using a UMAT instead of a UHYPER is that I'm going to extend the MR with additional terms such that I have transversely isotropic material model at the end.
I figured that I don't really need to anything but just define the stress!..
it's been a while since i last worked on this topic, but the pressure p is a lagrange multiplier to impose incompressibility and creates an extra equation to be solved for, so it's an unknown. therefore, you shouldn't define any value for it.
good luck!
you have to add the bulk response to your model and use a large value for the compressibility parameter (D) with hybrid element as it is explained in the Abaqus User subroutines reference guide. Worked fine for me
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