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

SUMMARY: 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.