Deformation Gradient in UMAT

[petra]

Hi Jorgen,

I would like to incorporate a swelling stretch in a UMAT following the Arruda-Boyce example (2001) you mentioned in another post. To do this I need to calculate the total chain stretch from the deformation gradient (DFGRD1) that is supplied to the UMAT. I would like to back out the mechanical chain stretch by dividing the total chain stretch by the swelling stretch.

My question: Is the deformation gradient that ABAQUS passes INTO the UMAT the total deformation gradient (F=dx/dX) and not a modified deformation gradient (i.e. scaled by an average volume ratio J)? Or (as with the UHYPER), should we consider DFGRD1 to be the mechanical deformation gradient and then adjust by the swelling deformation gradient to get the total deformation gradient for each analysis step?

Thanks!

[Jorgen]

Hi Petra,

Yes, the deformation gradient provided by ABAQUS is the real total deformation gradient. You need to compensate for the swelling to get the mechancial deformation gradient.

- Jorgen

[Andy]

Hi, Jorgen,

I'm a little bit confused by your answer to this post. Here's what the ABAQUS User Subroutines Reference Manual-UMAT says about the deformation gradient:

"The deformation gradient is available for solid (continuum) elements, membranes, and finite-strain shells (S3/S3R, S4, S4R, SAXs, and SAXAs). It is not available for beams or small-strain shells. It is stored as a 3 × 3 matrix with component equivalence DFGRD0(I,J) . For fully integrated first-order isoparametric elements (4-node quadrilaterals in two dimensions and 8-node hexahedra in three dimensions) the selectively reduced integration technique is used (also known as the technique). Thus, a modified deformation gradient is passed into user subroutine UMAT."

Could you clarify? Thanks.

[Jorgen]

The original post was interested in swelling predictions. You can write a user-material model that captures swelling by decomposing the deformation gradient into a part that causes mechancial stress, and a part that causes swelling. Note that the swelling does not cause any stress. That was what I had in mind regarding the "total F" and the "mechanical F".

-Jorgen