I implemented a tension cut-off criterion for the Drucker Prager (DP) model. It limits tensile stresses to a user-defined tensile strength. This is a next step towards modelling reinforced concrete (getting closer
). I browsed the literature and find that DP tension cut-offs are usually (if not always) applied to pressure; not principal stress. The simple reason is that the DP model itself is formulated in terms of pressure. A cut-off on principal stress is therefore much more difficult to formulate.
Anyway, IMHO putting a cut-off on pressure makes no sense for concrete. Cracks occur as a result of tensile principal stresses and not pressure. I therefore decided to go the extra mile and formulate a tension cut-off on principal stress as well as on pressure.
Tension cut-off is also relevant for the study of soil bodies. Clay, for example, can accommodate tensile stress under short term loading. The reason is that clay is rather impermeable and water cannot easily drain from it. This means that in clay under tension the water prevents the clay matrix from expanding and therefore carries the tension as suction. In the long term, however, water will flow towards areas of suction and the soil loses its tensile strength. This is the reason cracks appear at the crest of earth dams and embankments.
So lets see how the trench responds with the two versions of tension cut-off (tensile strength = 0.0):
In the foreground the model with tension cut-off on pressure and in the background the model with tension cut off on principal stress. The failure modes are completely different. In the first a normal slip surface develops, but in the second the soil wedge slides and topples into the trench due to lack of tension tying it back to the "hinterland".
The limit loads for the two mechanisms are also completely different. The model with tension cut-off on pressure predicts a limit load which is only 2.9% below the failure load without tension cut-off:
However, the model with tension cut off on principal stress predicts a limit load which is 43% lower !
So a trench which is stable in the short term can easily collapse when drainage occurs.
Next step: reinforcement steel.