A generalized calculation of the rate independent single crystal yield surface

In this paper, we discuss a method to calculate the topology of the rate independent single crystal yield surface for materials with arbitrary slip systems and arbitrary slip strengths. We describe the general problem, as motivated by Schmid's law, and detail the calculation of hyperplanes in deviatoric stress space, $\mathbb{D}^5$, which describe the criteria for slip on individual slip systems. We focus on finding the intersection of five linearly independent hyperplanes which represent stresses necessary to satisfy the criteria for general plastic deformation. Finally, we describe a method for calculating the inner convex hull of these intersection points, which describe the vertices of the five dimensional polytope that represents the single crystal yield surface. Our method applies to arbitrary crystal structure, allowing for an arbitrary number and type of slip systems and families, considers plastic anisotropy via inter- and intra-family strength anisotropy, and further considers strength anisotropy between slip in the positive and negative direction. We discuss the calculation and possible applications, and share a computational implementation of the calculation of the single crystal yield surface.