非局部弹性理论概述及在当代材料背景下的一些进展

局部作用原理在发展经典连续介质力学的本构关系中起着重要的作用,由此导出的简单物质理论得到了广泛的应用.然而,随着科技的发展,各种具有微结构的新材料不断涌现,理论和实验表明,非局部理论可以更好地刻画这些材料的宏观力学行为.本文简要介绍了一些传统的非局部弹性理论,包括Eringen理论、Kunin理论、Mindlin理论;阐述了针对复合材料发展的,具有时间-空间非局部特征的Willis方程、最新的时间-空间耦合非局部弹性动力学理论以及近场动力学理论.时间-空间非局部理论反映了复合材料宏观性能固有的非局部特征,而具有空间非局部特征的近场动力学理论便于处理具有不连续性的问题.最后,本文讨论了非局部理论的发展中值得关注的一些问题.

An Overview and Advances of Nonlocal Elasticity Theories in the Background of Contemporary Materials

The principle of local action plays an important role in the development of constitutive relations of classical continuum mechanics, and the theory of simple materials that is derived from this principle has been widely applied. However, with the development of science and technology, various new materials which have microstructures are emerging. It has been theoretically and experimentally demonstrated that nonlocal theories may better depict the macroscopic behavior of these materials. In this article, we briefly review some traditional nonlocal elasticity theories, including the Eringen theory, the Kunin theory, the Mindlin theory, and the Willis theory that is developed for composite materials and is characterized by temporal and spatial nonlocality, the newly developed spatiotemporal nonlocal elastodynamic theory, and the peridynamic theory. The spatiotemporal nonlocal theory reflects the inherent nonlocal characteristics of the macroscopic properties of composite materials, and the spatially nonlocal peridynamic theory facilitates processing problems with discontinuities. Finally, we point out some issues that may deserve consideration in the development of nonlocal theories.