A Fourier series based generalized yield surface description for the efficient modelling of orthotropic sheet metals

Abstract

In the current state of the art, there exist a large number of different yield surface descriptions, which are well established in modelling particular types of materials. The success of a particular model is primarily related to its ability of accurately representing the material behaviour based on a limited number of experiments. In the present work, instead of defining a particular mathematical formulation, a generic yield surface is proposed based on a 2D Fourier series. Yield surfaces of increasing complexity can be effectively generated by increasing the number of terms in the series. The particular properties of the modelled materials are not derived from a predefined formulation, but enforced as a set of constraints. It is shown that both symmetric and asymmetric yield loci can be easily constructed using this approach. Furthermore the accuracy and computational efficiency of the proposed model is discussed in comparison to well established yield surface functions, using deep drawing simulations.