Request for Guidance on Plastic Multiplier Calculation for Constitutive Model in FLAC3D

FLAC3D
1

Dear Colleagues,
I am currently developing a new constitutive model that incorporates a curved yield surface, conceptually similar to the Drucker-Prager criterion. My current challenge lies in determining the plastic multiplier for this nonlinear yield surface within FLAC3D, as the manual does not provide explicit guidance for such cases.
I understand that a Newton-Raphson iterative scheme is a potential approach for estimating the plastic multiplier. However, I am concerned about the potential for numerical instability and significantly increased computational time that this method might introduce.
Therefore, I would greatly appreciate any guidance or insights you could offer on the most effective and stable methods for calculating the plastic multiplier in this context. If anyone has experience with a similar implementation or could provide a relevant code snippet, it would be immensely helpful.

Thank you for your time and assistance.
Sincerely,

Mojtaba

2

In FLAC3D, usually the time step is small due to the requirement of global level (the level higher than the constitutive level) of an explicit algorithm. So even the yield surface is non-linear, one iteration Newton-Raphson scheme is usually okay with a balance between numerical accuracy and computational time. However, this is not absolutely right but depending on the specific constitutive model.

Another approach is using the tangent surface at the current stress state also based on the assumption that time step is small sufficient. An example is the Hoek-Brown model implementation.

You can still use multiple-iteration of Newton-Raphson scheme if you think the numerical accuracy is more important. The best way is to examine if the iteration number is sensitive. If not, just set iteration number to one to save calculation time.