Convex plastic potentials of fourth and sixth rank for anisotropic materials

Abstract

It is briefly reminded how the theory of dual plastic potentials has been used in the past to generate analytical expressions for plastic potentials of anisotropic polycrystalline materials with a known crystallographic texture. Such constitutive models are fairly general, and the identification of their parameters can readily be done on the basis of data obtained from a texture measurement. As a result, they are suitable for engineering applications such as elastic–plastic finite element models for forming processes. However, the yield loci generated in this way are not automatically convex. Therefore, a new variant of the method has now been developed, which preserves the advantages of the old method, but for which convexity can at least been tested by means of a mathematical criterion. In addition, it has turned out to be possible to slightly modify plastic potentials which do not satisfy the criterion, in order to achieve convexity. An example of a plastic potential modified in this way is discussed. After modification, it was still a good analytical approximation of the plastic potential directly derived from the Taylor–Bishop–Hill theory on the basis of the crystallographic texture of the material.