A constitutive model to describe the triaxial load-response spectrum of plain concrete in both tension and shear was developed. The inelastic phenomena are described using the plastic flow with direction determined by the gradient of the plastic potential. A new plastic potential is introduced and experimentally fitted to ensure better estimate of the load direction. This approach allows to control the inelastic dilatancy in terms of the inelastic deformation of the material. By overlaying the plastic potential on modified Etse and Willam's yield surface (both defined on the Haigh–Westergaard coordinates), the results showed that the two curves do not undergo similar stress states for a given strength level. It is, therefore, necessary that each surface goes through the current stress state to ensure adequate evaluation of normal vectors. A closed-form solution to accurately predict the triaxial stress state in concrete has been proposed. The predictive capabilities of the proposed model are evaluated by comparing predicted and measured stresses. The proposed model is shown to be accurate in predicting stress state of concrete.
Hammoud, R., Boukhili, R., & Yahia, A. (2013). Unified Formulation for a Triaxial Elastoplastic Constitutive Law for Concrete. Materials, 6(9), 4226–4248. https://doi.org/10.3390/ma6094226