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The extension of the Drucker-Prager material model is associated with the yield surface and not with the pressure stress. If you compare equations 4-98 and 4-101 of the Release 11.0 ANSYS Theory Manual, you see a different constant associated with the pressure term, SIGMAm, but the meaning for SIGMAm is the same for both equations. There is also a 3/2 factor in the extended Drucker-Prager equation where a 1/2 factor is present in the original Drucker-Prager equation which will change the meaning of the pressure stress factor. But if you use the same constant yield stress value for both formulations, you should get the same result. From this, then, the pressure stress factor ALPHA for the extended Drucker-Prager is equal to BETA * SQRT(3). The BETA value is documented in the original Drucker-Prager formulation and may be used for the extended, with the appropriate SQRT(3) modification.
As I mentioned, the extension of the Drucker-Prager for the linear formulation in ANSYS is to permit the modification of the yield stress value. Hence the notation in the extended Drucker-Prager formulation, sigy(epl), indicating that the yield stress is a function of the plastic strain. This is done by combining the extended Drucker-Prager with one of the isotropic hardening models. The hyperbolic and power forms are further extensions of the original Drucker-Prager formulation. For the original Drucker-Prager formulation, the yield stress is a constant. The yield stress will also be a constant in the extended Drucker-Prager unless the extended Drucker Prager is combined with an isotropic hardening plasticity model.
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