Peridynamics compatible with boundary conditions and its verification in plane elastic problems

Abstract

In the peridynamic (PD) theory established by Silling and his collaborates, the equation of motion is incompatible with the traction boundary conditions. In order to impose boundary conditions, a technique used is to set a fictitious boundary layer and transforming traction into a body force. This technique is easy to operate, but it is difficult to adapt to complex boundary constraints. To solve this problem, the new peridynamic governing equations with boundary conditions (PDBC) are introduced and simplified. In PDBC, the influence of the boundary conditions is confined to a boundary layer with finite thickness, by which, the surface correction can be shunned. A nonlinear implicit solver for PDBC is implemented. This solver is used to simulate the plane stress problems. The elastic deformations of a rectangular plate under three different boundary conditions, i.e., traction, displacement and mixed boundary conditions, are solved based on the bond-based and ordinary state-based constitutive models. Comparison of computational results between PDBC, the classical elastic theory and the original PD verifies the applicability and accuracy of PDBC and the implicit algorithm.