Algorithmic issues for three-invariant hyperplastic Critical State models

Implicit stress integration and the consistent tangents are presented for Critical State hyperplasticity models which include a dependence on the third invariant of stress. An elliptical deviatoric yielding criterion [43] is incorporated within the family of geotechnical models first proposed by Collins and Hilder [8]. An alternative expression for the yield function is proposed and the consequences of different forms of that function are revealed in terms of the stability and efficiency of the stress return algorithm. Errors associated with the integration scheme are presented. It is shown how calibration of the two new material constants is achieved through examining one-dimesional consolidation tests and undrained triaxial compression data. Material point simulations of drained triaxial compression tests are then compared with established experimental results. Strain probe analyses are used to demonstrate the concepts of energy dissipation and stored plastic work along with the robustness of the integration method. Over twenty finite element boundary value problems are then simulated. These include single three-dimensional element tests, plane strain footing analyses and cavity expansion tests. The rapid convergence of the global Newton–Raphson procedure using the consistent tangent is demonstrated in small strain and finite deformation simulations.