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H.A. Mang, J. Eberhardsteiner, H. Walter:
"Development and Application of a Gradient-Dependent Fracture Criterion for Finite-Element Analysis of RC Surface Structures";
in: "Proceedings of the Europe-US Symposium on Finite Element Methods for Nonlinear Problems", P.G. Bergan, K.J. Bathe, W. Wunderlich (ed.); Springer, 1986, 603 - 621.

The modulus of rupture of concrete is not a material property in the classical sense of this term. Likewise, biaxial fracture stresses of concrete are not pure material properties. Criticism in the literature of a fixed failure envelope representing the geometric locus of all biaxial states of fracture stresses was the motivation for the development of a new fracture criterion for the analysis of reinforced-concrete structures by the Finite Element Method. This criterion is based on the well-known fact that critical values of physical quantities at a point of a given body frequently also depend on the gradients of these quantities at this point. For the limiting case of vanishing stress gradients, peak stresses from Kupfer's biaxial tests are taken as the biaxial tensile strength. For non-vanishing stress gradients, a magnifying factor for Kupfer's biaxial tensile strength at the considered point is determined with the help of a hypothesis of comparison. The influence of the new fracture criterion on the structural response of a hypar groined vault subjected to dead and snow load is discussed in the numerical investigation.