On the modeling of asymmetric yield functions

In the context of metal plasticity, the yield function of a metal polycrystal is its most complex macro-characteristic. Letting aside the questions of kinematic or distortional hardening, the basic problem is geometric in nature: to design a family of convex surfaces capable of reproducing a wide range of experimental, or theoretically predicted data. While many satisfactory solutions have been proposed for the modeling of symmetric (with respect to the origin of the stress space) yield functions, the more general case of asymmetric functions has not witnessed comparable progress. The topic has significant practical relevance because many lightweight metals are from the hcp-class, thus featuring tension-compression asymmetry. The attached paper proposes a general approach to the problem, based on simple geometrical concepts, trigonometric polynomials and linear transformations.