A multi-adaptive framework to enhance the computational performance of bond-based peridynamic models
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Peridynamic (PD) models are commonly implemented by exploiting a particle-based method referred to as standard scheme. PD models using the meshfree standard scheme are generally computationally more expensive, particularly for large-scale problems in three dimensions, than those based on classical theories (e.g., the finite element method) due to two major reasons. First, the nonlocal nature of PD leads to demanding quadrature schemes. Second, the standard scheme is inaccurate in case of non-uniform discretization and thus drastically inefficient when a very fine resolution is required only for a localized area (e.g., close to discontinuities and interfaces). The present work proposes a new framework to significantly enhance the numerical performance of PD models. The developed framework restricts the application of the standard scheme only to localized regions where discontinuities and interfaces emerge, while it employs a less demanding quadrature scheme for the remaining regions. To further enhance the performance of PD models, this strategy is applied in conjunction with a multi-grid approach that allows the usage of a fine grid spacing only in critical regions, which are identified dynamically over time. To this end, the proposed framework is referred to as multi-adaptive. The performance of the proposed approach is examined by means of two numerical examples, consisting respectively of the modeling of the Kalthoff-Winkler experiment and of the bio-degradation of a magnesium-based bone implant screw. It is demonstrated that the proposed framework yields the same accuracy as a PD model, discretized using the standard scheme and with a very fine grid spacing, at a significantly lower computational cost.
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