Weak Form of Peridynamics

Abstract

This chapter presents the weak form of the peridynamic (PD) governing field equations. They specifically concern the Poisson’s equation and Navier’s equation under in-plane loading conditions. Their weak forms derived based on the variational approach enable the direct imposition of nonlocal essential and natural boundary conditions. The numerical solution to these equations can be achieved by considering either a uniform or a nonuniform discretization.