I am seeking to implement a hyperelastic material whose Cauchy stress (T) is defined as:
T = 2.87(3.28/det(F))2.5I
where I and F are Identity and deformation gradient tensors, respectively. I have used the UMAT subroutine to implement it. Unfortunately, Abaqus Standard cannot converge the result even for a single cubic continuum element. I think the trouble is caused by DDSDDE computation.
I have attached a photo of this derivation. Please take a look, and find the problem, if possible.
Waiting for your kind advice.
Dear Seyed,
See appendix A.2 of my thesis
http://doc.utwente.nl/82517/1/thesis_M_Niazi.pdf
1) You are mixing up indices during derivation. First decide if it is pre-derivative (Eq A.50) or post derivative (Eq A.51) in appendix. I would say use post derivative. Then remain consistent with indices.
2) Actually you don't need to use indices. You can get the derivative directly in tensorial form.
dawaC-1/dawaC = -C-1.I4.C-T see Eq A.56 in appendix
and
dawa(det C)/dawaC = det(C) [C-1]T This you can find in any tensor calculus book.
kind regards
Thank you for your response but I found that the error caused by the instability of the material, not by its DDSDDE derivation. Therefore the DDSDDE is correct.
- Badges
- Science topic