  Integral-type nonlocal damage models describe the fracture process zones by
regular strain profiles insensitive to the size of finite elements, which is
achieved by incorporating weighted spatial averages of certain state variables
into the stress-strain equations. However, there is no consensus yet how the
influence of boundaries should be taken into account by the averaging
procedures. In the present study, nonlocal damage models with different
averaging procedures are applied to the modelling of fracture in specimens with
various boundary types. Firstly, the nonlocal models are calibrated by fitting
load-displacement curves and dissipated energy profiles for direct tension to
the results of mesoscale analyses performed using a discrete model. These
analyses are set up so that the results are independent of boundaries. Then,
the models are applied to two-dimensional simulations of three-point bending
tests with a sharp notch, a V-type notch, and a smooth boundary without a
notch. The performance of the nonlocal approaches in modelling of fracture near
nonconvex boundaries is evaluated by comparison of load-displacement curves and
dissipated energy profiles along the beam ligament with the results of
meso-scale simulations. As an alternative approach, elastoplasticity combined
with nonlocal or over-nonlocal damage is also included in the comparative
study.
