Hi David,

I have reproduced some single elements test on ABAQUS using the UMAT to compare with Triax Hypoplasticity. So far, my stiffness curve (q vs ea) and my stress paths (q vs p’) are perfect matches. However, I cannot get matching shear stiffness curves.

Thus my question is; how is G calculated for Hypoplastic Model or Triax? I have all the principal stresses and strains from Abaqus as well as all the Hypo Intergranular input parameters.

I used equations 6.16 and 3.131 from your book and still could not get a decent match.. Please advise.



  1. David Mašín
    David Mašín 5 years ago

    Hi Hashmi, are you sure you calculate tangent stiffness Gtan=dq/depsh/3 and not secant stiffness Gsec=q/epsh/3? In my papers tangent stiffness is always presented. Regards David

  2. Hashmi Sohawon
    Hashmi Sohawon 5 years ago

    Hi again David,

    Thanks for the quick response. I have added a picture to my post to show you my current results.

    I had already calculated Gtan the same you mentioned and got the above curve. So i thought, I should try a different formula instead and thus tried a few that I have found from your new hypo textbook to investigate the predictions of G. These did not lead to any improvement unfortunately.

    I am now trying to increase the number on increments in the undrained single element Abaqus analysis. However, ABAQUS cae seems to be crashing about half way into the analysis.

    Please advise if possible.

    Thank you,

  3. David Mašín
    David Mašín 5 years ago

    Hi Hashmi,
    I see,

    Actually, the problem is that to correctly track tangent stiffness using increments Deltaq/Deltaepsh, you need to run your simulation using extremely small increments as the model is highly non-linear in the small strain range.

    When running in Abaqus, the increments are quite large. Because umat uses accurate Rung-Kutta integration scheme, your stress-strain curve is correct, but stiffness is calculated using too large increments, so it looks incorrect. But still – be aware that the results are correct! You just do not have enough points to visualise the G curve…

    To resolve, either run Abaqus with extremely small step size (but you write you get crash), or run umat using element test driver.

    Actually, I suggest you evaluate Abaqus using secant stiffness and not tangent stiffness, than your simulations should be OK. You would need to generate reference secant stiffness curve using element test driver, however, as I do not present them in papers.

    Regards David

  4. Hashmi Sohawon
    Hashmi Sohawon 5 years ago

    ok, thank you for this insight David!

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