Analytical return mapping for Mohr–Coulomb plasticity in rotated Haigh–Westergaard space with consistent tangent operator

Abstract This work presents an analytical construction of the stress projection onto the Mohr–Coulomb yield surface in Rotated Haigh–Westergaard (RHW) space. The solution is obtained through a Closest-Point Projection (CPP) procedure in which the distance to the yield surface is defined from the trial stresses using a complementary energy norm. A new regularization procedure is introduced to treat coincident principal stresses arising during projections onto the edges of the Mohr–Coulomb yield surface. Closed-form expressions are also derived for the Jacobian of the projection, which is used directly in the construction of the consistent tangent operator. In addition, a rotational correction is incorporated into the computation of the consistent tangent matrix. The resulting formulation is robust, accurate, and readily applicable to finite element implementations, and quadratic convergence is observed in the global Newton iterations. Although the methodology is presented for the associative Mohr–Coulomb model, it can be extended to other classical associative plasticity models, such as Drucker–Prager and von Mises, whenever the projection mapping admits an analytical expression in terms of the principal stresses.