A three-invariant cap model with isotropic–kinematic hardening rule and associated plasticity for granular materials

In this paper, a three-invariant cap model is developed for the isotropic–kinematic hardening and associated plasticity of granular materials. The model is based on the concepts of elasticity and plasticity theories together with an associated flow rule and a work hardening law for plastic deformations of granulars. The hardening rule is defined by its decomposition into the isotropic and kinematic material functions. The constitutive elasto-plastic matrix and its components are derived by using the definition of yield surface, material functions and non-linear elastic behavior, as function of hardening parameters. The model assessment and procedure for determination of material parameters are described. Finally, the applicability of proposed plasticity model is demonstrated in numerical simulation of several triaxial and confining pressure tests on different granular materials, including: wheat, rape, synthetic granulate and sand.