Implicit integration of a mixed isotropic-kinematic hardening plasticity model for structured clays

In recent years, a number of constitutive models have been proposed to describe mathematically the mechanical response of natural clays. Some of these models are characterised by complex formulations, often leading to non-trivial problems in their numerical integration in finite elements codes. The paper describes a fully implicit stress-point algorithm for the numerical integration of a single surface mixed isotropic-kinematic hardening plasticity model for structured clays. The formulation of the model stems from a compromise between its capability of reproducing the larger number of features characterising the behaviour of structured clays and the possibility of developing a robust integration algorithm for its implementation in a finite elements code. The model is characterised by an ellipsoid-shaped yield function, inside which a stress dependent reversible stiffness is accounted for by a non-linear hyperelastic formulation. The isotropic part of the hardening law extends the standard Cam-Clay one to include plastic strain-driven softening due to bond degradation, while the kinematic hardening part controls the evolution of the position of the yield surface in the stress space. The proposed algorithm allows the consistent linearization of the constitutive equations guaranteeing the quadratic rate of asymptotic convergence in the global level Newton-Raphson iterative procedure. The accuracy and the convergence properties of the proposed algorithm are evaluated with reference to the numerical simulations of single element tests and the analysis of a typical geotechnical boundary value problem.