Newbie: UMAT and incompressibilty

[Ratatosk]

Dear users,

I am a graduating student working on a viscohyperelastic constitutive law for a biologic tissue. I found your forum and am very enthousiastic about it.

I have three weeks left to give my repport, any I still have to implement my law in ABAQUS/standard. Which is really stressfull, since I am a newbie in ABAQUS. I have some probably simple questions for you.

I plan to do quasi-static simulations of an axissymmetric geometrie.

I am planning to write an UMAT subroutine (never done before..) to relate de Stress to the deformation and its rate of deformation.

My model is of the form S=Se + Sv (S= Second Piola-Kirschoff Stress tensor, Se = elastic contribution, Sv= viscous contributions)

Having the Jacobian of the cauchy stress tensor is not problematic.

First. Since I am in large deformations are the increments of the deformation gradient and the rate of the deformation gradient simply

dF = DFGRD1 - DFGRD0
dFpoint = dF/DTIME ?

Secondly. I supposed an incompressible material det(F)=1, therefore a static pressure, p, was introduced (as a Lagrangian multiplier) in my constitutive relation. This was used to liberate de stresses on thes sufaces orthogonal to the uniaxial traction of my experiments in order to identify the parameters of my law.

=> T = -pI + ...; T is the Cauchy Stress tensor, and I the identity tensor.

How do I implement this condition of incompressibility in ABAQUS?

Thank you for replying, I would be very gratefull!!

Arne

[Jorgen]

Hello Arne,

Here are my comments:

First. Since I am in large deformations are the increments of the deformation gradient and the rate of the deformation gradient simply

dF = DFGRD1 - DFGRD0
dFpoint = dF/DTIME ?

Yes, the increments in the deformation gradient and the rate of change of the deformation gradient can be approximated from those equations.

Secondly. I supposed an incompressible material det(F)=1, therefore a static pressure, p, was introduced (as a Lagrangian multiplier) in my constitutive relation. This was used to liberate de stresses on thes sufaces orthogonal to the uniaxial traction of my experiments in order to identify the parameters of my law.

=> T = -pI + ...; T is the Cauchy Stress tensor, and I the identity tensor.

How do I implement this condition of incompressibility in ABAQUS?

If it is a possibility for you, I would recommend that you add a small amount of compressibility to your model. That way it will be easier to implement the equations, and unless you have very high hydrostatic stresses, you will get virtually the same results as a fully incompressible model.

If that is not possible, you can use the incompressible portion of the deformation gradient, and then "drive" the flow and statevariables to be incompressible. This approach should work for implicit FE simulations.

Best of luck,
Jorgen

[Ratatosk]

Hello Jorgen,

thank you for replying as quick as you did!!

Unfortunatly I can not add a bit of compressibility, I surely would like to... but in case of compressibility I did not find a valuable strain function satisfying my conditions (convexity and fit).

But, as I wandered through the ton of ABAQUS manuals, I read about hybrid elements with constant pressure. It seems that these elements are used for the incompressible case. I have to read the corresponding pages tomorrow, do you have any suggestion for which element to use?

Another thing, if I don't abuse of your time, can I use the VISCO option with a user defined material?

Again, thank you for your help, I really appreciate it!!

Regards,

Arne

[Jorgen]

You are right, if you implement an incompressible UMAT then you will need to use hybrid elements in your simulations. Any hybrid elements should work for you.

I don't think that you can use *VISCO with UMATS, but I don't quite see why you would be interested in doing that.

Cheers,
Jorgen

[Ratatosk]

Hello,

I think that I have all the elements to implement properly my law, thanks to your help and suggestions!!

regards,

Arne