Abstract The classical continuum mechanics assumes that a material is a composition of an infinite number of particles each of which is a point that can only move and interact with its nearest neighbors. This classical mechanics has limited applications where it fails to describe the discrete structure of the material or to reveal many of the microscopic phenomena, e.g., micro-deformation and micro-dislocation. This observation motivated the need for a general point of view that instills the fact that the material particle is a volume element that would deform and rotate, and the material is generally a multiscale material. In addition, the particle's equilibrium should not be considered in isolation from its nonlocal interactions with other particles of the material. Material models with these features are the nonlocal microcontinuum theories. Whereas review articles and books on microcontinuum theories and nonlocal mechanics would be found in the literature, no review that extensively deals with the fundamentals of nonlocal mechanics from the physics, material, and mathematical points of view has been presented so far. There is a current scientific debate on the benefits of applying nonlocal theories to various fields of mechanics. This is due to a lack of understanding of the physics behind these theories. In addition, questions on the applicability of nonlocal mechanics for various materials are not answered yet. Furthermore, mathematicians revealed paradoxes and complications of finding solutions of nonlocal field problems. In this review, we shed light on these folders. We give extensive interpretations on the physics of nonlocal mechanics of particles and elastic continua, and the applicability of nonlocal mechanics to multiscale materials and single-scale materials is interpreted. In addition, the existing complications of solving nonlocal field problems, and the various methods and approaches to overcome these complications are collected and discussed from the physical and material points of view. Furthermore, we define the open forums that would be considered in future studies on nonlocal mechanics.

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非局部连续介质力学综述：物理学、材料适用性和数学

摘要 经典连续介质力学假设材料是由无数个粒子组成的组合，每个粒子都是一个只能移动并与其最近邻相互作用的点。这种经典力学的应用有限，因为它不能描述材料的离散结构或揭示许多微观现象，例如微变形和微位错。这一观察激发了对一般观点的需求，该观点灌输了以下事实：材料粒子是会变形和旋转的体积元素，并且材料通常是多尺度材料。此外，不应将粒子的平衡与其与材料的其他粒子的非局部相互作用分开考虑。具有这些特征的材料模型是非局部微连续介质理论。虽然在文献中可以找到关于微连续介质理论和非局域力学的评论文章和书籍，但迄今为止还没有从物理学、材料和数学的角度广泛讨论非局域力学基础的评论。目前存在关于将非局部理论应用于力学各个领域的好处的科学辩论。这是由于缺乏对这些理论背后的物理学的理解。此外，关于非局部力学对各种材料的适用性的问题尚未得到解答。此外，数学家揭示了寻找非局部域问题解的悖论和复杂性。在本次审查中，我们阐明了这些文件夹。我们对粒子的非局域力学和弹性连续体的物理学进行了广泛的解释，并解释了非局部力学对多尺度材料和单尺度材料的适用性。此外，还从物理和材料的角度收集和讨论了解决非局部场问题的现有复杂性，以及克服这些复杂性的各种方法和途径。此外，我们定义了在未来非局部力学研究中将考虑的开放论坛。