For a while our research group has been using a constitutive model, namely, Drucker-Prager/Cap implemented in Abaqus. It is a plasticity model with multiple yield surfaces. One of these surfaces is implemented with no hardening (perfect plasticity). But we have observed that for some granular materials, this behavior is not physically representative. For example, a compacted alumina specimen has hardening under uniaxial compression:
Article Identification of dilatancy in green compacted ceramic powde...
Thus, we would like to know if there are some numerical or physical meaning for the implementation of a yield surface (Drucker-Prager) with no hardening?
Hi Caiuã,
suitability of a material model depends on the problem under consideration and is often a trade-off between model complexity and the degree to which the model should represent the real world from the perspective of the intended use.
According to the Abaqus manual, the addition of the cap yield surface to the Drucker-Prager shear failure surface serves two main purposes: providing a mechanism to represent plastic compaction and controling volume dilatancy when the material yields in shear. The Drucker-Prager shear failure surface, on the other hand, is perfectly plastic (i.e. no hardening). Therefore, it represents a "classical" yield surface for limit state (shear failure) analysis of granular materials. It was not intended for realistic modeling of deformation during failure; you would need more "elaborate" material models for that.
Regards,
Daniel
Hi Daniel Aubram, thank you for your response!
"suitability of a material model depends on the problem under consideration and is often a trade-off between model complexity and the degree to which the model should represent the real world from the perspective of the intended use."
I totally agree. In constitutive modeling, we may always consider a domain of validity as models, generally, cannot represent all cases of the real world.
"It was not intended for realistic modeling of deformation during failure; you would need more "elaborate" material models for that."
We are searching for new models to represent this behavior. For example, we have considered:
- Crook et al. model Article Predictive modelling of structure evolution in sandbox experiments
- Bigoni-Piccolroaz model
Article Yield criteria for quasibrittle and frictional materials
Also, we have considered adding this behavior to DPC model using Fortran subroutines.
Thank you again,
Caiuã.
The perfectly plastic representation of the Drucker-Prager surface is only a numerical simplification. The DP cap model dates back to the 1970s for practical numerical implemention, but the theory and other similar models were available earlier. The DP cap model likely can give realistic limit solutions for soil and rock mechanics problems, but likely does not adequately describe the stress-strain response and thus the deformations/displacement predictions can be poor. There are many other material models developed since the late 1970s through 2000 or so, that perform better. The calibration of the newer/advanced models requires more detailed material test results. As of a 2-3 years ago, none of these models were available in Abaqus.
Hello William McCarron, thank you for collaborating with this topic!
"There are many other material models developed since the late 1970s through 2000 or so, that perform better."
Can you please tell us a little bit more about this? What are these models and why they perform better in describing the stress-strain response?
Thank you again.
Caiuã Melo , The most useful models available now are single-surface models with closed yield/plastic surfaces in the stress space. There are many references by C. S. Desai and his colleagues. You can likely find him and several reference papers on ResearchGate. Look for the so-called HISS (hierarchical single surface) models. You can find a background in his book "Mechanics of Materials and Interfaces; the disturbed state concept". The HISS models have the flexibility to account for non-associated flow as well as a shape in the deviatoric plane that well represents geomaterials. When bounding-surface methods are included, the models better represent the sub-failure inelastic responses that may be important for accurate deformation predictions and load-unload responses. The Abaqus model you referred to does not include these characteristic responses. Additionally, as I recall, the cap surface on the DP cap model implemented in Abaqus does not retract when loading is on the DP surface (so it only hardens), and thus does not control dilation very well and the strength may be over-predicted depending on your calibration/application.
Additionally, you might look at models developed by P. Lade. His models are not single-surface, but might be easier to calibrate.
The single-surface models are easier to implement, in my opinion, since you are concerned with coding a single numerical representation of the yield surface. For models like the DP cap model, you in-fact need to implement two models/surfacea and then handle situations where the stress path intersects both surface.
Regards, Bill
- Badges
- Science topic