THE SURFACE- AND SIZE-DEPENDENT ELASTIC MODULI OF NANOSTRUCTURES

A theoretical model is presented to investigate the size-dependent elastic moduli of nanostructures with the effects of the surface relaxation surface energy taken into consideration. At nanoscale, due to the large ratios of the surface-to-volume, the surface effects, which include surface relaxation surface energy, etc., can play important roles. Thus, the elastic moduli of nanostructures become surface- and size-dependent. In the research, the three-dimensional continuum model of the nanofilm with the surface effects is investigated. The analytical expressions of five nonzero elastic moduli of the nanofilm are derived, and then the dependence of the elastic moduli is discussed on the surface effects and the characteristic dimensions of nanofilms.

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SIZE-DEPENDENT ELASTIC MODULUS AND FRACTURE TOUGHNESS OF THE NANOFILM WITH SURFACE EFFECTS

Surface Review and Letters ◽

10.1142/s0218625x08011901 ◽

2008 ◽

Vol 15 (05) ◽

pp. 599-603 ◽

Cited By ~ 15

Author(s):

JIAN-GANG GUO ◽

LI-JUN ZHOU ◽

YA-PU ZHAO

Keyword(s):

Fracture Toughness ◽

Elastic Modulus ◽

Surface Energy ◽

Size Effects ◽

Interatomic Potential ◽

Effective Elastic Modulus ◽

Surface Effects ◽

Surface Relaxation ◽

Ideal Crystal ◽

Size Dependent

The effective elastic modulus and fracture toughness of the nanofilm were derived with the surface relaxation and the surface energy taken into consideration by means of the interatomic potential of an ideal crystal. The size effects of the effective elastic modulus and fracture toughness were discussed when the thickness of the nanofilm was reduced. And the dependence of the size effects on the surface relaxation and surface energy was also analyzed.

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Size-Dependent Elasticity of Nanoporous Materials Predicted by Surface Energy Density-Based Theory

Journal of Applied Mechanics ◽

10.1115/1.4036345 ◽

2017 ◽

Vol 84 (6) ◽

Cited By ~ 1

Author(s):

Yin Yao ◽

Yazheng Yang ◽

Shaohua Chen

Keyword(s):

Energy Density ◽

Surface Energy ◽

Volume Fraction ◽

Surface Effect ◽

Compressive Strain ◽

Nanoporous Materials ◽

Surface Relaxation ◽

Surface Energy Density ◽

Closed Form Solutions ◽

Size Dependent

The size effect of nanoporous materials is generally believed to be caused by the large ratio of surface area to volume, so that it is also called surface effect. Based on a recently developed elastic theory, in which the surface effect of nanomaterials is characterized by the surface energy density, combined with two micromechanical models of composite materials, the surface effect of nanoporous materials is investigated. Closed-form solutions of both the effective bulk modulus and the effective shear one of nanoporous materials are achieved, which are related to the surface energy density of corresponding bulk materials and the surface relaxation parameter of nanomaterials, rather than the surface elastic constants in previous theories. An important finding is that the enhancement of mechanical properties of nanoporous materials mainly results from the compressive strain induced by nanovoid's surface relaxation. With a fixed volume fraction of nanovoids, the smaller the void size, the harder the nanoporous material will be. The results in this paper should give some insights for the design of nanodevices with advanced porous materials or structures.

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Analysis of Oxygen Exchange Between Arterioles and Surrounding Capillary-Perfused Tissue

Journal of Biomechanical Engineering ◽

10.1115/1.2891376 ◽

1992 ◽

Vol 114 (2) ◽

pp. 227-231 ◽

Cited By ~ 13

Author(s):

R. Hsu ◽

T. W. Secomb

Keyword(s):

Theoretical Model ◽

Flow Rate ◽

Oxygen Transport ◽

Continuum Model ◽

Capillary Flow ◽

Three Dimensional ◽

Continuum Approach ◽

Oxygen Loss ◽

Tissue Region ◽

The Continuum

A theoretical model is used to analyze oxygen transport in a three-dimensional tissue region containing an arteriole surrounded by an array of capillaries in planes perpendicular to the arteriole. Convective removal of oxygen from the vicinity of the arteriole by nearby capillaries is shown to increase diffusive oxygen loss from the arteriole. This effect depends on the locations of the capillaries, particularly those nearest to the arteriole. The arteriolar oxygen efflux is comparable to that predicted by a previous model which used a continuum approach, but the efflux does not increase with increasing perfusion as rapidly as predicted by the continuum model. Even a small capillary flow rate strongly influences the oxygen field surrounding the arteriole.

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SIZE-DEPENDENT ELASTIC PROPERTIES OF Ni NANOFILMS BY MOLECULAR DYNAMICS SIMULATION

Surface Review and Letters ◽

10.1142/s0218625x07010032 ◽

2007 ◽

Vol 14 (04) ◽

pp. 661-665 ◽

Cited By ~ 14

Author(s):

ZHENYU YANG ◽

YA-PU ZHAO

Keyword(s):

Molecular Dynamics ◽

Young’S Modulus ◽

Elastic Properties ◽

Young's Modulus ◽

Surface Effects ◽

Md Simulations ◽

Dynamics Simulation ◽

Surface Relaxation ◽

Size Dependent ◽

Embedded Atom

Size-dependent elastic properties of Ni nanofilms are investigated by molecular dynamics (MD) simulations with embedded atom method (EAM). The surface effects are considered by calculating the surface relaxation, surface energy, and surface stress. The Young's modulus and yield stress are obtained as functions of thickness and crystallographic orientation. It is shown that the surface relaxation has important effects on the the elastic properties at nanoscale. When the surface relaxation is outward, the Young's modulus decreases with the film thickness decreasing, and vice versa. The results also show that the yield stresses of the films increase with the films becoming thinner. With the thickness of the nanofilms decreasing, the surface effects on the elastic properties become dominant.

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Size-Dependent Elastic Moduli of FCC Crystal Nanofilms

MRS Proceedings ◽

10.1557/proc-0924-z03-22 ◽

2006 ◽

Vol 924 ◽

Author(s):

Shih-Hsiang Chang ◽

I-Ling Chang

Keyword(s):

Young’S Modulus ◽

Size Effects ◽

Continuum Model ◽

Elastic Moduli ◽

Young's Modulus ◽

Current Model ◽

Continuum Theory ◽

Thickness Direction ◽

Size Dependent ◽

Discrete Nature

ABSTRACTA semi-continuum model is constructed to study the size effects on the mechanical properties of face-cubic-center crystal structure nanofilms. Unlike the classical continuum theory, the current model directly takes the discrete nature in the thickness direction into consideration. In-plane and out-plane Poisson's ratios as well as in-plane Young's modulus are investigated with this model. It is found that the values of the Young's modulus and Poisson's ratio depend on the film thickness and approach the respective bulk values asymptotically.

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CALCULATION OF THE DEPENDENCE OF THE DISTANCE TO THE LOCATED OBJECT FROM THE CORNER POSITION OF THE VEHICLE LINE

Issues of radio electronics ◽

10.21778/2218-5453-2018-4-14-18 ◽

2018 ◽

pp. 14-18

Author(s):

V. V. Artyushenko ◽

A. V. Nikulin

Keyword(s):

Real Time ◽

Statistical Physics ◽

Angular Position ◽

Three Dimensional ◽

Line Of Sight ◽

Two Dimensional ◽

Radar Station ◽

Flight Mode ◽

Vector Algebra ◽

Analytical Expressions

To simulate echoes from the earth’s surface in the low flight mode, it is necessary to reproduce reliably the delayed reflected sounding signal of the radar in real time. For this, it is necessary to be able to calculate accurately and quickly the dependence of the distance to the object being measured from the angular position of the line of sight of the radar station. Obviously, the simplest expressions for calculating the range can be obtained for a segment or a plane. In the text of the article, analytical expressions for the calculation of range for two-dimensional and three-dimensional cases are obtained. Methods of statistical physics, vector algebra, and the theory of the radar of extended objects were used. Since the calculation of the dependence of the range of the object to the target from the angular position of the line of sight is carried out on the analytical expressions found in the paper, the result obtained is accurate, and due to the relative simplicity of the expressions obtained, the calculation does not require much time.

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Dopants Modulate Crystal Growth in Molten Salts Enabled by Surface Energy Tuning

Journal of Materials Chemistry A ◽

10.1039/d1ta02351a ◽

2021 ◽

Author(s):

Xiaoqiao Li ◽

Linming Zhou ◽

Han Wang ◽

Dechao Meng ◽

Guannan Qian ◽

...

Keyword(s):

Crystal Growth ◽

High Temperature ◽

Surface Energy ◽

Molten Salts ◽

Rational Approach ◽

Temperature Synthesis ◽

Crystalline Materials ◽

Size Dependent ◽

High Temperature Synthesis ◽

Energy Tuning

Crystalline materials are routinely produced via high-temperature synthesis and show size-dependent properties; however, a rational approach to regulating their crystal growth has not been established. Here we show that dopants...

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