Nodal finite element approximation of peridynamics
<|reference_start|>Nodal finite element approximation of peridynamics: 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 the exact solution in $L^2$ norm at the rate $C_1 \Delta t + C_2 h^2/\epsilon^2$. Here, $\Delta t$, $h$, and $\epsilon$ are time step size, mesh size, and the size of the horizon or nonlocal length scale, respectively. Constants $C_1$ and $C_2$ are independent of $h$ and $\Delta t$ and depend on the norms of the exact solution. Several numerical examples involving pre-crack, void, and notch are considered, and the efficacy of the proposed nodal finite element discretization is analyzed.<|reference_end|>
@article{jha2024nodal,
    title={Nodal finite element approximation of peridynamics},
    author={Prashant K. Jha and Patrick Diehl and Robert Lipton},
    journal={arXiv preprint arXiv:2403.05501},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.05501},
    primaryClass={math.NA cs.NA}
}