Implicit numerical integration of a three-invariant, isotropic/kinematic hardening cap plasticity model for geomaterials

The mechanical constitutive behavior of geomaterials is quite complex, involving pressure-sensitive yielding, differences in strength in triaxial extension vs. compression, the Bauschinger effect, dependence on porosity, and other factors. Capturing these behaviors necessitates the use of fairly complicated and expensive non-linear material models. For elastically isotropic materials, such models usually involve three-invariant plasticity formulations. Spectral decomposition has been used to increase the efficiency of numerical simulation for such models for the isotropically hardening case. We modify the spectral decomposition technique to models that include kinematic hardening. Finally, we perform some numerical simulations to demonstrate quadratic convergence.