This paper proves that existing implicit integration schemes for the modified cam-clay (MCC) cannot handle the dependency of critical state stress ratio on Lode angle, because the coaxiality between the deviatoric strain rate tensor and the deviatoric stress tensor, on which these algorithms are built, no longer holds when the Lode angle effect is considered. A more appropriate algorithm is proposed based on closet point return mapping, and a consistent tangent modulus is calculated. After detailed mathematical derivations, the proposed method is examined via four computational examples. The first example includes a series of numerical triaxial tests, for demonstrating the appropriateness of the employed constitutive equations. The second and third examples are convergence tests at the material (integration point) level and finite element (FE) level, respectively. The resulting quadratic converging rate proves that the Jacobian matrix for return mapping and the consistent tangent modulus for finite element implementation are correctly computed. The last example concerns drained penetration of a surface footing. The proposed method is demonstrated to be more efficient and robust in this case than the Abaqus built-in MCC model, which aborted halfway when simulating the same problem.
Peng et al. (Fri,) studied this question.