A novel and effective way to impose boundary conditions and to mitigate the surface effect in state-based Peridynamics

Peridynamics is a nonlocal continuum theory capable of modeling effectively crack initiation and propagation in solid bodies. However, the nonlocal nature of this theory is the cause of two main problems near the boundary of the body: an undesired stiffness fluctuation, the so-called surface effect, and the difficulty of defining a rational method to properly impose the boundary conditions. The surface effect is analyzed analytically and numerically in the present paper in a state-based peridynamic model. The authors propose a modified fictitious node method based on an extrapolation with a truncated Taylor series expansion. Furthermore, a rational procedure to impose the boundary conditions is defined with the aid of the fictitious nodes. In particular, Neumann boundary conditions are implemented via the peridynamic concept of force flux. The accuracy of the proposed method is assessed by means of several numerical examples for a state-based peridynamic model: with respect to the peridynamic model adopting no corrections, the results are significantly improved even if low values of the truncation order for the Taylor expansion are chosen.