An Advanced Numerical Differentiation Scheme for Plastic Strain-Rate Computation

Modern yield functions for orthotropic sheet metals are quite complex in a mathematical sense, mainly due to their non-quadratic character and/or the incorporation of eigenvalues of linearly transformed stress tensors (e.g. [5, 6]). In particular, the analytical computation of first and second order yield function gradients, which are, for instance, required in finite element codes, can become a very lengthy task. Thus, the numerical differentiation is a very convenient method to circumvent these difficulties. In the present article an advanced numerical differentation scheme is presented that exploits consequently the homogeneity property of the yield function