  A methodology is presented for investigating the dynamics of heterogeneous
media using the nonlocal continuum model given by the peridynamic formulation.
The approach presented here provides the ability to model the macroscopic
dynamics while at the same time resolving the dynamics at the length scales of
the microstructure. Central to the methodology is a novel two-scale evolution
equation. The rescaled solution of this equation is shown to provide a strong
approximation to the actual deformation inside the peridynamic material. The
two scale evolution can be split into a microscopic component tracking the
dynamics at the length scale of the heterogeneities and a macroscopic component
tracking the volume averaged (homogenized) dynamics. The interplay between the
microscopic and macroscopic dynamics is given by a coupled system of evolution
equations. The equations show that the forces generated by the homogenized
deformation inside the medium are related to the homogenized deformation
through a history dependent constitutive relation
