I am trying to implement a continuum damage mechanics based constitutive model in Abaqus using the user-defined subroutine UMAT. In that context, I am having hard time finding any available example UMAT subroutine which is modeling only damage elastic material (no plasticity).
In my model I am assuming isotropic scalar damage and single scale modeling (no multiscaling feature) framework. Once I get the updated damage for an increment or iteration, I update DDSDDE. The code works fine until peak stress, i.e. until softening happens. I am using viscous stabilization to complete the simulation. However, the overall strain vs. stress plot shows brittle pattern of failure due to localization (for all simulation having more than one element).
A snippet of my UMAT code is given below showing damage update and DDSDDE update.
I have 2 thoughts on modeling damage elastic material in Abaqus using UMAT:
- From my experience I have seen Abaqus examples related to snapping for structural geometry, but not snapping in damage elastic material. On the other hand, when I am using Riks method or Arclength method in Abaqus no localization happens. All the elements in my geometrical model fails and the strain vs. stress behavior is no longer brittle. Here is the dilemma, we are losing the physical insight to get energy consistent result. Is there any available technique for the commercial software Abaqus to handle material localization, especially when used with user subroutine UMAT ?
- The second possibility is that I am doing something wrong in my code? Do I need to get some other expression for consistent tangent stiffness matrix or DDSDDE update after damage accumulation?
Dear Rudraprasad,
I don't fully understand how you calculate the DDSDDE in your code
It looks like you divide the stress for a constant
In general for material damaging, the Jacobian is the same as for elastic material multiplied by a prefactor, for instance your (1-Omega)
If your damage parameter is a function of the strain, then you will need to take into account of the derivative of Omega with respect to the strain
If the model contains softening, localization is expected,
you should set a minimun value of the stiffness, not zero
You can look at models where a length scale for fracture is introduced,
Dr Martinez-Paneda has written a UEL for Abaqus that does this:
https://www.empaneda.com/codes/
The introduction of a length scale using UMAT is more problematic because spatial derivatives of the damage field cannot be easily calculated
I am not very familiar with the Abaqus implementation of Riks method, but if the constitutive model contains softening, the strain will localize for sure and result will be strongly mesh dependent. I don't see how you can avoid that.
Best Regards,
Nicolo'
Nicolò Grilli : Thank you for your response.
My damage evolution function is a function of strain. So I need to evaluate the derivative accordingly to calculate DDSDDE. I have missed that part in my code. This solves my question 2.
I'm still concerned about the problem as mentioned in my first question. I get same peak strength for 5 different meshes. But I can not see any dissipated energy after the peak reaches. So any quasi-brittle material behaves like a highly brittle material. If I use Riks method in Abaqus I don't observe any localization. Is there a bug in Abaqus. Why Riks method in Abaqus can't lead to localization ?
Just for completeness: Are you employing any kind of regularization, for instance by using a mesh-adjusted softening modulus? I cannot see anything like that in your screenshots. This would explain the overly brittle behavior.
Regarding the Riks: A 'non-localizing' solution is still a valid solution, although it is not a stable one. However, it occurs under perfect homogenous conditions. Try to introduce a 'weak' element to trigger localization?
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