  Peridynamic (PD) theories have gained widespread diffusion among various
research areas, due to the ability of modeling discontinuities formation and
evolution in materials. Bond-Based Peridynamics (BB-PD), notwithstanding some
modeling limitations, is widely employed in numerical simulations, due to its
easy implementation combined with physical intuitiveness and stability. In the
present paper, several aspects of bond-based peridynamic models have been
reviewed and investigated. A detailed description of peridynamics theory,
applications and numerical models has been presented. Employed BB-PD integral
kernels have been displayed, together with their differences and commonalities;
then, some consequences of their mathematical structure have been discussed.
The kinematic role of nonlocality, the relation between kernel structure and
material impenetrability, and the role of PD kernel nonlinearity in cracks
formation prediction have been critically analyzed and commented. Finally the
idea of extending BB-PD to fluids is proposed and presented in the framework of
fading memory material, drawing some perspectives for a deeper and more
comprehensive understanding of the peridynamics in fluids.
