International Journal for Numerical and Analytical Methods in Geomechanics, 28 (2004), 653--670.


Milan Jirásek, Simon Rolshoven and Peter Grassl
LSC, ENAC, Swiss Federal Institute of Technology at Lausanne (EPFL), Switzerland


Experimental results available in the literature indicate that the nominal fracture energy of concrete (defined as total work of fracture divided by the ligament area) depends on the size of the specimen. Theoretical modeling of the size effect on nominal fracture energy based on a nonlocal  constitutive model is attempted in this paper. The influence of various details of the integral-type nonlocal formulation, e.g., of the specific form of nonlocal averaging in the vicinity of a physical boundary, is studied and a physical explanation is provided. The numerical results are compared to experimental data for notched compact tension specimens, and conclusions are drawn for individual formulations. It is shown that the best agreement with experimentally observed trends is achieved if the notch is modeled as a layer of completely damaged material. Fitting of the size effects on both strength and fracture energy permits a unique identification of the model parameters


This paper has presented an initial parametric study exploring the influence of various details of the nonlocal formulation on the nominal fracture energy and its size dependence. Trends consistent with experimental data for the compact tension specimen have been obtained with two formulations:
The latter formulation gives a clearly pronounced size effect on nominal fracture energy and the shape of the corresponding curve closely resembles those constructed in the literature from empirical formulas. It has been demonstrated that simultaneous fitting of the size effect on both nominal fracture energy and nominal strength is a viable method for calibration of nonlocal damage models. If the notch is replaced by completely damaged material, nonlocal formulation with averaging of damage energy release rate exhibits sensitivity to the notch thickness, while the formulation with averaging of equivalent strain does not suffer from this deficiency.

 CVUT / 26 November 2004 /