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G. Hofstetter, H.A. Mang, G. Meschke:
"3D Inelastic Constitutive Modelling for FE Analyses of Concrete Structures";
in: "Nonlinear Computational Mechanics - State of the Art", Springer, Berlin-Heidelberg-New York-Toronto, 1991, 606 - 626.

In this paper two constitutive models for consideration of plastic deformations of concrete cased by 3D states os stress are presented. The first model is a modified cap model, serving as an example for nonsmooth multisurface plasticity. For this model a return mapping algorithm is presented. Tangent operators are derived, which are consistent with the integration algorithm. Hence, the quadratic rate of asymptotic convergence in the Newton solution procedure is preserved. The second constitutive model belongs to a special category of bounding surface models, characterized by the vanishing of the elastic range. This model is a so-called hypoplastic model. In contrast to ordinary plasticity, the tangent elasto-plastic material stiffness matrix also depends on the stress rate direction. In the theoretical part of the paper the mechanical function of the two material models are described. Subsequently, these constitutive models are applied to finite element analysis of a cylindrical concrete specimen subjected to a concentrated compressive force of the form of a steel punch. The results allow a comparison with experimental results and demonstrate advantages as well as disadvantages of the two constitutive models relative to one another.