  This paper assesses the accuracy and convergence of the linear-elastic,
bond-based Peridynamic model with brittle failure, known as the prototype
micro-brittle (PMB) model. We investigate the discrete equations of this model,
suitable for numerical implementation. It is shown that the widely used
discretization approach incurs rather large errors. Motivated by this
observation, a correction is proposed, which significantly increases the
accuracy by cancelling errors associated with the discretization. As an
additional result, we derive equations to treat the interactions between
differently sized particles, i.e., a non-homogeneous discretization spacing.
This presents an important step forward for the applicability of the PMB model
to complex geometries, where it is desired to model interesting parts with a
fine resolution (small particle spacings) and other parts with a coarse
resolution in order to gain numerical efficiency. Validation of the corrected
Peridynamic model is performed by comparing longitudinal sound wave propagation
velocities with exact theoretical results. We find that the corrected approach
correctly reproduces the sound wave velocity, while the original approach
severely overestimates this quantity. Additionally, we present simulations for
a crack growth problem which can be analytically solved within the framework of
Linear Elastic Fracture Mechanics Theory. We find that the corrected
Peridynamics model is capable of quantitatively reproducing crack initiation
and propagation.
