Buckling of a stretched nanoplate with a nanohole incorporating surface energy

IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY International Journal of Engineering Science Pub Date : 2024-04-20 DOI:10.1016/j.ijengsci.2024.104075
M.A. Grekov, A.O. Bochkarev
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Abstract

The effect of a nanoplate buckling at a circular nanohole under the remote uniaxial tension is studied incorporating the surface energy in accordance with the Gurtin–Murdoch surface elasticity model. The hole surface within the framework of the plane problem and the faces of the plate within the framework of the Kirchhoff theory of the plate bending are characterized by both the surface elasticity properties and the residual surface tension. The full potential energy of the plate containing the surface tension with non-strain terms of the surface displacement gradient is derived. Based on the principle of virtual displacements, critical values of the load, corresponding symmetrical and asymmetrical forms of the buckling are found by the Ritz method. Numerical investigations reveal that allowing for the non-strain terms of the surface displacement gradient in the Gurtin–Murdoch constitutive relation leads to the essential increasing the rigidity of the plate and the critical Euler load. Two types of the size effect are detected. The nanoplate thickness and the ratio of the hole radius to the thickness influence independently the value of the critical load.

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含有表面能的纳米孔的拉伸纳米板的屈曲
根据 Gurtin-Murdoch 表面弹性模型,结合表面能研究了远程单轴拉力下圆形纳米孔处的纳米板屈曲效应。平面问题框架内的孔表面和基尔霍夫板弯曲理论框架内的板面均由表面弹性特性和残余表面张力表征。推导出了包含表面张力和表面位移梯度非应变项的板全势能。根据虚拟位移原理,通过里兹法找到了载荷的临界值以及相应的对称和非对称屈曲形式。数值研究表明,在 Gurtin-Murdoch 构成关系中考虑表面位移梯度的非应变项会导致板刚度和临界欧拉载荷的本质增大。检测到两种尺寸效应。纳米板厚度和孔半径与厚度之比会单独影响临界载荷值。
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来源期刊
International Journal of Engineering Science
International Journal of Engineering Science 工程技术-工程:综合
CiteScore
11.80
自引率
16.70%
发文量
86
审稿时长
45 days
期刊介绍: The International Journal of Engineering Science is not limited to a specific aspect of science and engineering but is instead devoted to a wide range of subfields in the engineering sciences. While it encourages a broad spectrum of contribution in the engineering sciences, its core interest lies in issues concerning material modeling and response. Articles of interdisciplinary nature are particularly welcome. The primary goal of the new editors is to maintain high quality of publications. There will be a commitment to expediting the time taken for the publication of the papers. The articles that are sent for reviews will have names of the authors deleted with a view towards enhancing the objectivity and fairness of the review process. Articles that are devoted to the purely mathematical aspects without a discussion of the physical implications of the results or the consideration of specific examples are discouraged. Articles concerning material science should not be limited merely to a description and recording of observations but should contain theoretical or quantitative discussion of the results.
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