Analytical CPP in Rotated Energy-Mapped Stress Space: A Finite-Element Implementation in Mathematica Software

Abstract

This study describes step-by-step analytical closest-point projection (CPP) implicit return mapping solutions for von Mises, Drucker-Prager, and Hyperbolic Drucker-Prager yield surfaces in rotated energy-mapped stress space (REMSS) along with discussion, nonlinear finite-element implementation and examples within the Wolfram Mathematica environment. The CPP in conventional stress space does not give the closest point in the Euclidean norm, but in the energy norm. In REMSS, the correct return trajectory is a closest-point return, allowing the constitutive relations to be simplified and turning the determination of a CPP solution in a systematic task. The obtained finite-element results are in excellent agreement with the analytical solutions.