Willam-Warnke Yield Function
In the original paper, the three-parameter Willam-Warnke yield function was expressed as
where is the first invariant of the stress tensor, is the second invariant of the deviatoric part of the stress tensor, is the yield stress in uniaxial compression, and is the Lode angle given by
The locus of the boundary of the stress surface in the deviatoric stress plane is expressed in polar coordinates by the quantity which is given by
where
The quantities and describe the position vectors at the locations and can be expressed in terms of as
The parameter in the model is given by
The Haigh-Westergaard representation of the Willam-Warnke yield condition can be written as
where
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