Implementation of a Corner Theory Yield Surface Model Using a Novel Modulus Scaling Technique

Author(s):

Richard Becker

Abstract:

Closed-form integration of the J2-flow theory plasticity relation over a time step suggests a scaling of the shear modulus, which may be beneficial for integrating more challenging yield functions. The proposed scaling limits the elastic trial stress increment to less than the radius of the yield surface so that plastic return mapping along a prescribed path projects to a state on the yield surface. A numerical algorithm was developed and verified on a J2-flow theory model and was extended to a corner theory model, which has its plastic return path defined at the beginning of the time step. The algorithm proved stable and accurate on simple, nonproportional loading paths. Solutions were then obtained for right circular steel cylinders impacting finite aluminum targets. The corner theory results were similar to the J2-flow theory solution for initial penetration. As the penetrator neared the back surface, the corner theory model developed a clean cylindrical plug whereas the J2-flow model created a flared plug. Results were also obtained with a Tresca yield surface model for comparison.