In this work, we develop a dynamic hybrid local/nonlocal continuum model to study wave propagations in a linear elastic solid. The developed hybrid model couples, in the dynamic regime, a classical continuum mechanics model with a bond-based peridynamic model using the Morphing coupling method that introduced in a previous study (Lubineau et al., J Mech Phys Solids 60(6):1088–1102, 2012). The classical continuum mechanical model is known as a local continuum model, while the peridynamic model is known as a nonlocal continuum model. This dynamic hybrid model aims to introduce the nonlocal model into the key structural domain, in which the dispersions or crack nucleations may occur due to flaws, while applying the local model to the rest of the structural domain. Both the local and nonlocal continuum domains are overlapped in the coupled subdomain. We study the speeds and angular frequencies of the plane waves, with small and large wavenumbers obtained by the hybrid model and compare them to purely local and purely nonlocal solutions. The error of the hybrid model is discussed by analyzing the ghost forces, and the work done by the ghost forces is considered equivalent to the energy of spurious reflections. One- and two-dimensional numerical examples illustrate the validity and accuracy of the proposed approach. We show that this dynamic hybrid local/nonlocal continuum model can be successfully applied to simulate wave propagations and crack nucleations induced by waves.

中文翻译：

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波传播的动态混合局部/非局部连续介质模型

在这项工作中，我们开发了一个动态混合局部/非局部连续介质模型来研究线弹性固体中的波传播。开发的混合模型在动态范围内将经典连续介质力学模型与基于键的近场动力学模型结合使用，该模型使用先前研究中引入的 Morphing 耦合方法（Lubineau 等人，J Mech Phys Solids 60(6):1088） –1102, 2012)。经典的连续介质力学模型被称为局部连续介质模型，而近场动力学模型被称为非局部连续介质模型。这种动态混合模型旨在将非局部模型引入关键结构域，其中可能由于缺陷而发生弥散或裂纹成核，同时将局部模型应用于结构域的其余部分。局部和非局部连续域在耦合子域中重叠。我们研究平面波的速度和角频率，以及混合模型获得的大小波数，并将它们与纯局部​​和纯非局部解进行比较。通过分析鬼力讨论了混合模型的误差，认为鬼力所做的功等效于杂散反射的能量。一维和二维数值例子说明了所提出方法的有效性和准确性。我们表明，这种动态混合局部/非局部连续介质模型可以成功地应用于模拟波浪传播和由波浪引起的裂纹成核。通过分析鬼力讨论了混合模型的误差，认为鬼力所做的功等效于杂散反射的能量。一维和二维数值例子说明了所提出方法的有效性和准确性。我们表明，这种动态混合局部/非局部连续介质模型可以成功地应用于模拟波浪传播和由波浪引起的裂纹成核。通过分析鬼力讨论了混合模型的误差，认为鬼力所做的功等效于杂散反射的能量。一维和二维数值例子说明了所提出方法的有效性和准确性。我们表明，这种动态混合局部/非局部连续介质模型可以成功地应用于模拟波浪传播和由波浪引起的裂纹成核。