The simulation of two-dimensional plane problems using ordinary state-based peridynamics

The ordinary state-based peridynamics (OSB PD) model is an integral nonlocal continuum mechanics model. And the three-dimensional OSB PD model can deal with linear elastic solid problems well. But for plane problems, the calculation results of existing models have large deviations. In this paper, a set of OSB PD models for plane problems is established by theoretical derivation. First, through the strain energy density function equivalence of peridynamics and classical continuum mechanics, the equivalent coefficients of the plane strain and plane stress problems of OSB PD are deduced. Then, consider the cantilever beam deformation simulation under concentrated load. The simulation results show that the maximum displacements are in good agreement with the corresponding analytical solutions in all directions. Finally, in the simulation of the slab with a hole, the two cases of uniform displacement and uniform load are considered, respectively. The simulation results are consistent with the ANSYS analysis results, and the deviation is small, which verifies the validity of the model.