Enhancing Computational Performance in Bond-Based Peridynamic Models through a Multi-Adaptive Framework
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Peridynamic (PD) models, commonly implemented via the particle-based standard mesh-free scheme, incur higher computational costs, particularly for large-scale three-dimensional problems, compared to classical theories. This is primarily due to the intricate quadrature schemes required by the nonlocal nature of PD and to inaccuracies in the standard scheme in case of non-uniform discretization. In this study, we introduce a framework to significantly enhance the numerical performance of PD models. The developed framework limits the use of the standard scheme to localized regions characterized by the presence of discontinuities and interfaces, employing a less demanding quadrature scheme for the remaining areas of the model domain. To further enhance PD model performance, this approach is applied in conjunction with a multi-grid strategy, utilizing fine grid spacing only in dynamically identified critical regions, resulting in the term multi-adaptive. The effectiveness of the approach is verified through two numerical examples: the Kalthoff-Winkler experiment and the bio-degradation of a magnesium-based bone implant screw. The proposed framework achieves comparable accuracy to a PD model with a very fine grid spacing using the standard scheme but at a significantly reduced computational cost.
