LSC, ENAC, Swiss Federal Institute of Technology at Lausanne (EPFL),
Switzerland
Abstract
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
Conclusions
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:
shading effect of the notch and symmetric local correction of the
weight
function in the proximity of the boundary,
replacement of the notch by predamaged material.
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.