Abstract Nonlocal models provide accurate representations of physical phenomena ranging from fracture mechanics to complex subsurface flows, settings in which traditional partial differential equation models fail to capture effects caused by long-range forces at the microscale and mesoscale. However, the application of nonlocal models to problems involving interfaces, such as multimaterial simulations and fluid-structure interaction, is hampered by the lack of a physically consistent interface theory which is needed to support numerical developments and, among other features, reduces to classical models in the limit as the extent of nonlocal interactions vanish. In this paper, we use an energy-based approach to develop a formulation of a nonlocal interface problem which provides a physically consistent extension of the classical perfect interface formulation for partial differential equations. Numerical examples in one and two dimensions validate the proposed framework and demonstrate the scope of our theory.

中文翻译：

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非局部界面问题的基于能量的耦合方法

摘要 非局部模型提供了物理现象的准确表示，从断裂力学到复杂的地下流动，在这些设置中，传统的偏微分方程模型无法捕捉由微尺度和中尺度的长程力引起的影响。然而，非局部模型在涉及界面的问题上的应用，例如多材料模拟和流固耦合，由于缺乏物理一致的界面理论而受到阻碍，该理论需要支持数值发展，并且除其他特征外，还简化为经典模型随着非局部相互作用的范围消失，在极限中。在本文中，我们使用基于能量的方法来开发非局部界面问题的公式，该公式为偏微分方程的经典完美界面公式提供了物理上一致的扩展。一维和二维的数值例子验证了所提出的框架并证明了我们理论的范围。