  The convergence of a peridynamic model for solid mechanics inside
heterogeneous media in the limit of vanishing nonlocality is analyzed. It is
shown that the operator of linear peridynamics for an isotropic heterogeneous
medium converges to the corresponding operator of linear elasticity when the
material properties are sufficiently regular. On the other hand, when the
material properties are discontinuous, i.e., when material interfaces are
present, it is shown that the operator of linear peridynamics diverges, in the
limit of vanishing nonlocality, at material interfaces. Nonlocal interface
conditions, whose local limit implies the classical interface conditions of
elasticity, are then developed and discussed. A peridynamics material interface
model is introduced which generalizes the classical interface model of
elasticity. The model consists of a new peridynamics operator along with
nonlocal interface conditions. The new peridynamics interface model converges
to the classical interface model of linear elasticity.
