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Size effect of the elastic modulus of rectangular nanobeams:Surface elasticity effect

Chinese Physics B 2013年第10期22卷 424-428页

作者：姚海燕云国宏范文亮 College of Ordos Inner Mongolia University Inner Mongolia Key Laboratory of Nanoscience and Nanotechnology College of Physical Science and Technology Inner Mongolia University College of Physics and Electronic Information Inner Mongolia Normal University

The size-dependent elastic property of rectangular nanobeams （nanowires or nanoplates） induced by the surface elas- ticity effect is investigated by using a developed modified core-shell model. The effect of surface elasticity on the elastic modulus of nanobeams can be characterized by two surface related parameters, i.e., inhomogeneous degree constant and surface layer thickness. The analytical results show that the elastic modulus of the rectangular nanobeam exhibits a distinct size effect when its characteristic size reduces below 1 O0 nm. It is also found that the theoretical results calculated by a mod- ified core-shell model have more obvious advantages than those by other models （core-shell model and core-surface model） by comparing them with relevant experimental measurements and computational results, especially when the dimensions of nanostructures reduce to a few tens of nanometers.

关键词： size effects elastic modulus nanobeams surface elasticity

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A review on the application of modified continuum models in modeling and simulation of nanostructures

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Acta Mechanica Sinica 2016年第1期32卷 83-100页

作者： K.F.Wang B.L.Wang T.Kitamura Graduate School at Shenzhen Harbin Institute of Technology Department of Mechanical Engineering Kyoto University

Analysis of the mechanical behavior of nanos- tructures has been very challenging. Surface energy and non- local elasticity of materials have been incorporated into the traditional continuum analysis to create modified continuum mechanics models. This paper reviews recent advancements in the applications of such modified continuum models in nanostructures such as nanotubes, nanowires, nanobeams, graphenes, and nanoplates. A variety of models for these nanostructures under static and dynamic loadings are men- tioned and reviewed. Applications of surface energy and nonlocal elasticity in analysis of piezoelectric nanomateri- als are also mentioned. This paper provides a comprehensive introduction of the development of this area and inspires fur- ther applications of modified continuum models in modeling nanomaterials and nanostructures.

关键词： Surface elasticity Nonlocal continuum Nanotubes nanobeams Nanoplates Modeling andsimulations

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SURFACE STRESS EFFECT IN MECHANICS OF NANOSTRUCTURED MATERIALS

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Acta Mechanica Solida Sinica 2011年第1期24卷 52-82页

作者： Jianxiang Wang Zhuping Huang Huiling Duan Shouwen Yu Xiqiao Feng Gangfeng Wang Weixu Zhang Tiejun Wang LTCS and Department of Mechanics and Aerospace Engineering College of Engineering Peking University Beijing 100871 China AML Department of Engineering Mechanics Tsinghua University Beijing 100084 China SV Lab Deparment of Engineering Mechanics School of Aerospace Engineering Xi＇an Jiaotong University Xi＇an 710049 China

This review article summarizes the advances in the surface stress effect in mechanics of nanostructured elements, including nanoparticles, nanowires, nanobeams, and nanofilms, and heterogeneous materials containing nanoscale inhomogeneities. It begins with the fundamental formulations of surface mechanics of solids, including the definition of surface stress as a surface excess quantity, the surface constitutive relations, and the surface equilibrium equations. Then, it depicts some theoretical and experimental studies of the mechanical properties of nanostructured elements, as well as the static and dynamic behaviour of cantilever sensors caused by the surface stress which is influenced by adsorption. Afterwards, the article gives a summary of the analytical elasto-static and dynamic solutions of a single as well as multiple inhomogeneities embedded in a matrix with the interface stress prevailing. The effect of surface elasticity on the diffraction of elastic waves is elucidated. Due to the difficulties in the analytical solution of inhomogeneities of complex shapes and configurations, finite element approaches have been developed for heterogeneous materials with the surface stress. Surface stress and surface energy are inherently related to crack propagation and the stress field in the vicinity of crack tips. The solutions of crack prob- lems taking into account surface stress effects are also included. Predicting the effective elastic and plastic responses of heterogeneous materials while taking into account surface and interface stresses has received much attention. The advances in this topic are inevitably delineated. Mechanics of rough surfaces appears to deserve special attention due to its theoretical and practical implications. Some most recent work is reviewed. Finally, some challenges are pointed out. They include the characterization of surfaces and interfaces of real nanomaterials, experimental mea- surements and verification of mechanical parameters o

关键词： surface/interface stress size-effect nanowires nanobeams nanofilms nanoinhomogeneities cantilevers elastic wave crack elastic constants rough surface effective surface stress

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