Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions

In this paper, we study the linear bond-based nonlocal peridynamic models with a particular focus on problems associated with nonstandard nonlocal displacement loading conditions. Both stationary and time-dependent problems are considered for a one-dimensional scalar equation defined on a finite bar and for a two-dimensional system defined on a square. The related peridynamic operators and associated functional spaces are analyzed. Applications to the numerical analysis of the finite-dimensional approximations to peridynamic models are also illustrated.