@article{jha2024nodal,
title = {Nodal finite element approximation of peridynamics},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {434},
pages = {117519},
year = {2025},
issn = {0045-7825},
doi = {10.1016/j.cma.2024.117519},
url = {https://www.sciencedirect.com/science/article/pii/S0045782524007734},
author = {Prashant K. Jha and Patrick Diehl and Robert Lipton},
keywords = {Nonlocal fracture theory, Peridynamics, Numerical analysis, Finite element method},
abstract = {This work considers the nodal finite element approximation of peridynamics, in which the nodal displacements satisfy the peridynamics equation at each mesh node. For the nonlinear bond-based peridynamics model, it is shown that, under the suitable assumptions on an exact solution, the discretized solution associated with the central-in-time and nodal finite element discretization converges to a solution in the L2 norm at the rate C1Δt+C2h2/ϵ2. Here, Δt, h, and ϵ are time step size, mesh size, and the size of the horizon or nonlocal length scale, respectively. Constants C1 and C2 are independent of h and Δt and depend on norms of the solution and nonlocal length scale. Several numerical examples involving pre-crack, void, and notch are considered, and the efficacy of the proposed nodal finite element discretization is analyzed.}
}