  Nonlocal models provide exceptional simulation fidelity for a broad spectrum
of scientific and engineering applications. However, wider deployment of
nonlocal models is hindered by several modeling and numerical challenges. Among
those, we focus on the nontrivial prescription of nonlocal boundary conditions,
or volume constraints, that must be provided on a layer surrounding the domain
where the nonlocal equations are posed. The challenge arises from the fact
that, in general, data are provided on surfaces (as opposed to volumes) in the
form of force or pressure data. In this paper we introduce an efficient,
flexible and physically consistent technique for an automatic conversion of
surface (local) data into volumetric data that does not have any constraints on
the geometry of the domain and on the regularity of the nonlocal solution and
that is not tied to any discretization. We show that our formulation is
well-posed and that the limit of the nonlocal solution, as the nonlocality
vanishes, is the local solution corresponding to the available surface data.
Quadratic convergence rates are proved for the strong energy and L-2
convergence. We illustrate the theory with one dimensional numerical tests
whose results provide the ground work for realistic simulations.
