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.

中文翻译：

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Unity 方法分区内近场动力学富集的裂缝多尺度模型：第 I 部分

统一方法的划分 (PUM) 属于域分解类型，为多尺度和多物理场数值建模提供了机会。不同的物理模型可以存在于 PUM 方案中，用于处理线性弹性区域和发生裂缝的区域的问题。在这里，近场动力学 (PD) 模型用于断裂区域，而平滑 PUM 用于周围的线性弹性介质。该方法是所谓的全局-局部富集策略。未损坏介质的弹性场为局部局部放电模拟提供了适当的边界数据。介绍了组合 PD/PUM 模拟器的第一步。在本系列的第一部分中，我们展示了局部 PD 近似可用于丰富全局 PUM 近似，以高效地捕获真实的材料响应。