  The peridynamic theory brings advantages in dealing with discontinuities,
dynamic loading, and non-locality. The integro-differential formulation of
peridynamics poses challenges to numerical solutions of complicated and
practical problems. Some important issues attract much attention, such as the
computation of infinite domains, the treatment of softening of boundaries due
to an incomplete horizon, and time error accumulation in dynamic processes. In
this work, we develop the \textit{peridynamic boundary element method}
(PD-BEM). The numerical examples demonstrate that the PD-BEM exhibits several
features. First, for non-destructive cases, the PD-BEM can be one to two orders
of magnitude faster than the peridynamic meshless particle method (PD-MPM) that
directly discretizes the computational domains; second, it eliminates the time
accumulation error, and thus conserves the total energy much better than the
PD-MPM; third, it does not exhibit spurious boundary softening phenomena. For
destructive cases where new boundaries emerge during the loading process, we
propose a coupling scheme where the PD-MPM is applied to the cracked region and
the PD-BEM is applied to the un-cracked region such that the time of
computation can be significantly reduced.
