A two‐dimensional ordinary,state‐based peridynamic model for linearly elastic solids

Peridynamics is a non‐local mechanics theory that uses integral equations to include discontinuities directly in the constitutive equations. A three‐dimensional, state‐based peridynamics model has been developed previously for linearly elastic solids with a customizable Poisson's ratio. For plane stress and plane strain conditions, however, a two‐dimensional model is more efficient computationally. Here, such a two‐dimensional state‐based peridynamics model is presented. For verification, a 2D rectangular plate with a round hole in the middle is simulated under constant tensile stress. Dynamic relaxation and energy minimization methods are used to find the steady‐state solution. The model shows m‐convergence and δ‐convergence behaviors when m increases and δ decreases. Simulation results show a close quantitative matching of the displacement and stress obtained from the 2D peridynamics and a finite element model used for comparison. Copyright © 2014 John Wiley & Sons, Ltd.