Partition of unity methods (PUM) are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Different physical models can exist within a PUM scheme for handling problems with zones of linear elasticity and zones where fractures occur. Here, the peridynamic (PD) model is used in regions of fracture and smooth PUM is used in the surrounding linear elastic media. The method is a so-called global-local enrichment strategy. The elastic fields of the undamaged media provide appropriate boundary data for the localized PD simulations. The first steps for a combined PD/PUM simulator are presented. In part I of this series, we show that the local PD approximation can be utilized to enrich the global PUM approximation to capture the true material response with high accuracy efficiently. Test problems are provided demonstrating the validity and potential of this numerical approach.

翻译：统一方法的分区(PUM)是域分解类型,为多尺度和多物理数字模型提供了机会。在处理线性弹性区和骨折发生区的问题的PUM办法中,可以存在不同的物理模型。这里,在断裂区使用近地动力模型,在周围线性弹性介质中使用光滑的PUM。这种方法是一种所谓的全球-地方浓缩战略。未损坏介质的弹性场为本地PD模拟提供了适当的边界数据。介绍了PD/PUM联合模拟器的第一步。在这个系列的第一部分中,我们表明可以利用本地PD近地点来丰富全球PUM近地光度,以便高效地捕捉真实的物质反应。测试问题得到了证明这种数字方法的有效性和潜力的证明。