二维非局部埃舍尔比包容理论:特征应力驱动公式及应用

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-04-01 DOI:10.1098/rspa.2023.0842
Wei Ding, F. Semperlotti
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引用次数: 0

摘要

经典的 Eshelby 理论是基于局部线性弹性发展而来的,无法应用于微观机械系统中经常出现的涉及非局部(长程)弹性效应的包含问题。在本研究中,我们介绍了埃舍尔比包含理论在非局部弹性方面的扩展。从 Eringen 的非局部弹性积分公式出发,介绍了特征应力驱动的非局部 Eshelby 包容理论。在非局部包含问题的背景下,特征应力驱动方法被证明是经典特征应变驱动方法的有效数学扩展。我们开发并应用了两种单独的数值方法来模拟包容问题,并从数值上提取相应的非局部 Eshelby 张量。两种方法得出的数值结果都证实了推导出的非局部 Eshelby 张量的有效性及其捕捉椭圆包体内部非均匀特征应力分布的能力。这些结果还有助于揭示经典局部和非局部包含体问题的力学行为之间的根本区别。特征应力驱动的非局部包含理论可为非局部异质介质均质化方法的发展提供必要的理论基础。
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Two-dimensional nonlocal Eshelby’s inclusion theory: eigenstress-driven formulation and applications
The classical Eshelby’s theory, developed based on local linear elasticity, cannot be applied to inclusion problems that involve nonlocal (long range) elastic effects often observed in micromechanical systems. In this study, we introduce the extension of Eshelby’s inclusion theory to nonlocal elasticity. Starting from Eringen’s integral formulation of nonlocal elasticity, an eigenstress-driven nonlocal Eshelby’s inclusion theory is presented. The eigenstress-driven approach is shown to be a valid mathematical extension of the classical eigenstrain-driven approach in the context of nonlocal inclusion problems. Two individual numerical approaches are developed and applied to simulate inclusion problems and numerically extract the corresponding nonlocal Eshelby tensor. The numerical results obtained from both approaches confirm the validity of the derived nonlocal Eshelby tensor and its ability to capture the non-uniform eigenstress distribution within an elliptic inclusion. These results also help reveal the fundamental difference between the mechanical behaviour of the classical local and the nonlocal inclusion problems. The eigenstress-driven nonlocal inclusion theory could provide the necessary theoretical foundation for the development of homogenization methods of nonlocal heterogeneous media.
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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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