  In this paper, we propose two approaches to apply boundary conditions for
bond-based peridynamic models. There has been in recent years a renewed
interest in the class of so-called non-local models, which include peridynamic
models, for the simulation of structural mechanics problems as an alternative
approach to classical local continuum models. However, a major issue, which is
often disregarded when dealing with this class of models, is concerned with the
manner by which boundary conditions should be prescribed. Our point of view
here is that classical boundary conditions, since applied on surfaces of solid
bodies, are naturally associated with local models. The paper describes two
methods to incorporate classical Dirichlet and Neumann boundary conditions into
bond-based peridynamics. The first method consists in artificially extending
the domain with a thin boundary layer over which the displacement field is
required to behave as an odd function with respect to the boundary points. The
second method resorts to the idea that peridynamic models and local models
should be compatible in the limit that the so-called horizon vanishes. The
approach consists then in decreasing the horizon from a constant value in the
interior of the domain to zero at the boundary so that one can directly apply
the classical boundary conditions. We present the continuous and discrete
formulations of the two methods and assess their performance on several
numerical experiments dealing with the simulation of a one-dimensional bar.
