Convex polynomial yield functions

It is shown that some of the recently proposed orthotropic yield functions obtained through the linear transformation method are homogeneous polynomials. This simple observation has the potential to simplify considerably their implementation into finite element codes. It also leads to a general method for designing convex polynomial yield functions with powerful modeling capabilities. Convex parameterizations are given for the fourth, sixth and eighth order plane stress orthotropic homogeneous polynomials. Illustrations are shown for the modeling of biaxial and directional yielding properties of steel and aluminum alloy sheets. The parametrization method can be easily extended to general, 3D stress states.