Stress Integration of the Drucker–prager Material Model with Kinematic Hardening

This paper presents a method for implicit stress integration of the Drucker–Prager material model with kinematic hardening. The stress integration of the material model is conducted using the incremental plasticity method, while the kinematic hardening of material is defined using nonlinear Armstrong–Frederick hardening. This type of granular material hardening occurs as a consequence of the cyclic loading effects, such as the seismic load. For this reason, this material model is used for the earthquake analysis in the soil mechanics. Yield surface of the material model changes its position under the cyclic loads in the stress space, whereas there is no change in the size of the yield surface in deviatoric plane. The developed algorithm of the material model has been implemented in the software package PAK. Nomenclature σ stress tensor σm mean stress e total strain e elastic strain e plastic strain f yield function g plastic potential function dλ plastic parameter C elastic constitutive matrix C elastic-plastic constitutive matrix α Drucker–Prager material parameter β Drucker–Prager material parameter k Drucker–Prager material parameter I1 first stress invariant J2D second deviatoric stress invariant t time s deviatoric stress 2010 Mathematics Subject Classification: 74S05, 65Z05.