  Nonlocal models provide accurate representations of physical phenomena
ranging from fracture mechanics to complex subsurface flows, where traditional
partial differential equations fail to capture effects caused by long-range
forces at the microscale and mesoscale. However, the application of nonlocal
models to problems involving interfaces such as multimaterial simulations and
fluid-structure interaction, is hampered by the lack of a rigorous nonlocal
interface theory needed to support numerical developments. In this paper, we
use an energy-based approach to develop a mathematically rigorous nonlocal
interface theory which provides a physically consistent extension of the
classical perfect interface PDE formulation. Numerical examples validate the
proposed framework and demonstrate the scope of our theory.
