On The Convergence of the Discretized Linear Static State-Based Peridynamic Equations

In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply one-point-quadrature to the terms in the discrete equations. The resulting system coincides with the commonly used meshfree discretization using a regular lattice, including the possibility of using partial area algorithms to improve the numerical behavior. We again prove convergence, this time for fixed choices of a weighting function commonly used in literature and stronger assumptions on the input data. We note however, that these assumptions are not significantly restrictive for practical purposes. In particular, they still allow discontinuities in the material parameters and external body forces.