An elastoplastic model with combined isotropic–kinematic hardening to predict the cyclic behavior of stiff clays

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This paper presents a kinematic hardening model for describing some important features of natural stiff clays under cyclic loading conditions, such as hysteretic loops, smooth transition between elastic and elastoplastic behavior, etc. The model includes two yield surfaces : an inner and a bounding surface. A non-associated flow rule and a kinematic hardening law are proposed for the inner surface. The adopted hardening law enables the plastic modulus to vary smoothly when the kinematic yield surface approaches the bounding surface and ensures the non-intersection of the two yield surfaces.The first loading, unloading, reloading stages are treated differently by applying distinct hardening parameters. The main feature of the model is that its constitutive equations can be simply formulated based on the consistency condition for the inner yield surface based on the proposed kinematic hardening law; this model can be easily implemented in a FE code using a classic stress integration scheme as for the modified CamClay model. The simulation results on the Boom Clay showed a good agreement with the experimental results under cyclic loading conditions. The model can satisfactorily describe the complex case of oedometric conditions where the deviator stress is positive upon loading but can become negative upon unloading.


Original languageEnglish
Pages (from-to)193-202
JournalComputers and Geotechnics
Issue number10
Publication statusPublished - Oct 2014


  • Natural stiff clay, kinematic hardening, cyclic loading, elastoplasticity, stress integration, validation

ID: 302657