Anisotropic hardening – numerical application of a cubic yield theory and consideration of variable r-values for sheet metal

The first part of this paper contains a polynomial yield condition of third order connected with evolution equations for material tensors of higher orders. They are formulated by formal generalisation of an approach by Danilov. The second part presents a possibility of taking into account the rotation of the yield surface as a result of a variable planar anisotropy (r-value) in sheet metal. This is done by an extension of the evolution equations, based on a quadratic yield function. The corresponding deformation law and the set of evolution equations are numerically integrated for selected loading paths in the subspaces σ1,σ2 and σ,τ. Some of the experimentally observed effects, such as the increasing curvature of the yield locus curve in the loading direction or the specific rotation of the yield surface, are correctly reproduced.