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：单位分解法（PUM）属于区域分解类方法，为多尺度和多物理场数值建模提供了可能。在PUM框架下，可共存不同物理模型，用于处理包含线弹性区域和断裂区域的问题。本文采用近场动力学模型描述断裂区，并在周围线弹性介质中应用光滑PUM。该方法是一种全局-局部富集策略：无损伤介质的弹性场为局部近场动力学模拟提供合适的边界数据。我们提出了结合PD/PUM模拟器的初步步骤。本系列的第一部分表明，局部近场动力学近似可用于富集全局PUM近似，从而高效、高精度地捕捉真实材料响应。文中给出了验证性算例，证明了该数值方法的有效性与潜力。