VUMAT for invariant-based hyperelastic model yield zig-zag shape under compression
I am trying in implement an invariant-based hyperelastic model (Holzapfel-Ogden 2009) in Abaqus using VUMAT. The constitutive model is modified to a slightly compressible form.
The subroutine with single element under biaxial testing and triaxial shear give expected results comparing to analytical solution. However, under compression test, the model start to have weird deformation (zig-zag) which happens in both single element and larger models. I have tried both C3D8 and C3D8R elements. In single element case, C3D8R with hourglass control and distortion control solved the issue. However, in larger models, both element types behave similarly with the zig-zag shape as shown below. I wonder if anyone can give any insight on how this could be solved? Thank you!
It looks like traditional hourglassing but since you see the same problem with C3D8 elements, that cannot be the reason for the behavior.
Another explanation could be that your implementation creates a material model that is softer in shear than what you think. In that case the block of elements would prefer to deform the way is shown in the figure, simply because that would reduce the total energy. I would check your equations and the implementation to see if there is a shear instability based on that.
Thanks for the quick response. Yes, I first thought this was hourglassing, shear locking, or volumetric locking but it doesn't seem like the case after a couple of checks.
I just checked the analytical solutions of biaxial and shear stress-strain curves. As shown below, the shear in all directions are much softer than the normal directions. However, it's likely that this is the nature of the tissue according to the literature. (I am using the parameters from papers that conducted experimental characterization.)
Interestingly, the abaqus built-in material (same constitutive model, nearly incompressible), which is written in vuanisohyper_inv does not have this zig-zag issue. (I have also compared my biaxial and shear results with the built-in material.) Therefore, it seems that the hyperelastic subroutine has some kind of tricks to prevent shear instability. (I did look into the user manual but couldn't find anything related to this.) I wonder if there is any method to prevent this instability in vumat if the material is much softer in shear?
Thank you very much for your help!