A four parameter in-plane isotropic yield function

We take a general plane stress, orthotropic, sixth order homogeneous polynomial and impose upon it conditions for in-plane isotropy. We obtain a four parameter yield function that takes as input the yield stress along the rolling direction, the average r-value of the sheet, the balanced-biaxial yield stress and a shape parameter. This last parameter can be easily tuned so that the plane strain data point, if available, can be better predicted. In particular, the function proposed here can be a useful tool for limit strain prediction.