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P. Pivonka, J. Ozbolt, R. Lackner, H.A. Mang:
"Comparative Studies of 3D-Constitutive Models for Concrete: Application to Mixed-Mode Fracture";
International Journal for Numerical Methods in Engineering, 60 (2004), 2; 549 - 570.

This paper focusses on the predictive capabilities of 3D-constitutive
models for concrete when used for the simulation of mixed-mode
fracture in consequence of shear-tensile loading. For this purpose, two types of constitutive models are chosen. Models belonging to the first type such as the Extended Leon Model (ELM) and two multi-surface models are formulated within the framework of plasticity theory. The ELM (Etse and Willam: "Fracture energy formulation for inelastic behavior of plain concrete", Journal of Engineering Mechanics (ASCE) (120):1983-2011), a single-surface
model, accounts for the dependence of the concrete strength on the Lode angle. The first multi-surface model consists of a tension-cut-off (TC) for the description of tensile cracking of concrete and a Drucker-Prager (DP) surface for the description of compressive failure. To improve the description of concrete cracking, in the second multi-surface model the tension-cut-off function is replaced by three Rankine surfaces (RK).

The second type of material models considered in the presented
investigation is formulated on the basis of the microplane concept.

The performance of the material models is investigated on both the constitutive and the structural level. On the constitutive level, re-analyses of Willam's test are performed. For the assessment of the model performance on the structural level, a double-edge-notched concrete specimen is investigated.

http://aleph.ub.tuwien.ac.at/F?base=tuw01&func=find-c&ccl_term=AC04967014

http://www3.interscience.wiley.com/cgi-bin/abstract/108071180/ABSTRACT