Peridynamic stress is the static first Piola–Kirchhoff Virial stress

The peridynamic stress formula proposed by Lehoucq and Silling (2008) is cumbersome to be implemented in numerical computations. In this paper, we show that the tensor has exact mathematical expression as of first Piola–Kirchhoff static Virial originated from Irving–Kirkwood–Noll formalism (Irving Kirkwood, 1905; Noll, 1955) through Hardy–Murdoch procedure (Hardy, 1982; Murdoch, 1983), which offers a simple clear for calculations stress. Several verifications have been carried out validate accuracy predicting states vicinity crack tip other sources concentration. By evaluating prototype microelastic brittle (PMB) material model bond-based peridynamics, it found PMB may exhibit nonlinear constitutive behaviors at large deformations. fields calculated good agreements with these using finite element methods, analytical solutions, well experimental data, demonstrating merit failure problems.