Comparison of yield-vertex tangential loading and principal stress rotational loading

The yield-vertex tangential loading theory is a constitutive approach that accounts for the plastic straining induced by the part of a stress rate directed tangential to the yield surface. One of the important applications of this theory is in the study of geotechnical problems involving significant rotation of principal stress directions. However, it is inaccurate to simply regard the tangential loading as an equivalence to the principal stress rotation. For future reference, this paper presents an investigation into the difference between the tangential loading theory and a true purely principal stress rotational loading theory. Mathematical derivation shows that the tangential stress rate includes the rotational stress rate and an additional coaxial term that is associated with the variation of the Lode angle. Numerical applications of these two theories indicate that in shear dominated problems, such as simple shear, the two theories are almost identical and interchangeable, but in non-shear dominated circumstances, such as footing, the tangential loading theory produces considerably softer results than the rotational loading theory.