For the convenience of classification, let us introduce a parameter where and are the yield points in the uniaxial tension (compression) and shear, respectively.
However, as mentioned above, only the domains on the unit sphere where the local yield condition (4) is fulfilled, must be taken into account and therefore may never coincide with for
So the local yield condition (5.1) together with the global criterion (2) defines the Schmidt cylinder 3 or, in the case of (5.1) and (3), the yield condition (10) and does not correspond to the -flow theory.
Finally, we should note that the so called “microplane model version MP2” (5.8) was first put forward by Malmeister in 1955 4 and was further elaborated by him and by his collaborators and followers in numerous Russian and English papers. We have also considered a number of other models based on general integral representations of arbitrary second-rank tensors. For more details and references see our book 2.