A three-invariant non-associative plasticity model for hard rocks: implicit integration and strain localization analysis

This paper describes a fully implicit return mapping algorithm for the numerical integration of a three-invariant non-associative plasticity model for hard rocks. Bifurcation analysis is performed to detect the onset of localization during the deformation process. A nonlinear Matsuoka-Nakai yield criterion along with an isotropic cohesive-softening law is employed to capture the inelastic material response. The integration algorithm guarantees a numerically stable and first-order accurate solution at the Gauss point level. The formulation of the model includes a consistent linearization of the weak form of the linear momentum balance to enable optimal convergence for Newton-Raphson iterations. The onset of strain localization is detected us-ing classical bifurcation theory by checking for the singularity of the elastoplastic constitutive operator at each step of the calculation process. The accuracy and convergence properties of the proposed algorithm are assessed through numerical simulations of single element tests and through a plane strain boundary value problem.