Plasticity model for concrete using the bounding surface concept

A rate-independent, plasticity-type bounding surface model is proposed for the multi-axial monotonic and cyclic behavior of concrete. The model adopts a bounding surface concept, in which the Ottosen model is modified to include the cyclic effect. In this model, the introduced bounding surface is a function of the maximum compressive strain experienced by the material, termed ε{lunate}_max. As anticipated, the bounding surface in stress space shrinks in size as ε{lunate}_max increases. The strain increment dε{lunate}_ij is decomposed into its deviatoric and volumetric components. The later strain components are calculated by using the plastic modulus which is a function of ε{lunate}_max and of the distance from the present stress point to the bounding surface along the deviatoric stress direction S_ij. The dependence of the plastic modulus on the distance defined above, and the functional form of the bounding surface, allows realistic modeling of the complex behavior of concrete. The model successfully captures the essential features of concrete behavior such as the nonlinearity, stiffness degradation, shear compaction-dilatancy, and the different behavior of concrete in tension and compression.