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

2017 ◽  
Vol 84 (6) ◽  
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.

scholarly journals Elastic Theory of Nanomaterials Based on Surface-Energy Density

2014 ◽  
Vol 81 (12) ◽  
Author(s):  
Shaohua Chen ◽  
Yin Yao
Keyword(s):  
Energy Density ◽  
Surface Energy ◽  
Elastic Constants ◽  
Surface Effect ◽  
Relaxation Parameter ◽  
Elastic Theory ◽  
Surface Relaxation ◽  
Surface Energy Density ◽  
Lagrangian Surface ◽  
Bulk Surface

Recent investigations into surface-energy density of nanomaterials lead to a ripe chance to propose, within the framework of continuum mechanics, a new theory for nanomaterials based on surface-energy density. In contrast to the previous theories, the linearly elastic constitutive relationship that is usually adopted to describe the surface layer of nanomaterials is not invoked and the surface elastic constants are no longer needed in the new theory. Instead, a surface-induced traction to characterize the surface effect in nanomaterials is derived, which depends only on the Eulerian surface-energy density. By considering sample-size effects, residual surface strain, and external loading, an explicit expression for the Lagrangian surface-energy density is achieved and the relationship between the Eulerian surface-energy density and the Lagrangian surface-energy density yields a conclusion that only two material constants—the bulk surface-energy density and the surface-relaxation parameter—are needed in the new elastic theory. The new theory is further used to characterize the elastic properties of several fcc metallic nanofilms under biaxial tension, and the theoretical results agree very well with existing numerical results. Due to the nonlinear surface effect, nanomaterials may exhibit a nonlinearly elastic property though the inside of nanomaterials or the corresponding bulk one is linearly elastic. Moreover, it is found that externally applied loading should be responsible for the softening of the elastic modulus of a nanofilm. In contrast to the surface elastic constants required by existing theories, the bulk surface-energy density and the surface-relaxation parameter are much easy to obtain, which makes the new theory more convenient for practical applications.

Surface effect on deformation around an elliptical hole by surface energy density theory

2019 ◽  
Vol 25 (2) ◽  
pp. 337-347
Author(s):  
Liyuan Wang
Keyword(s):  
Energy Density ◽  
Surface Energy ◽  
Hoop Stress ◽  
Surface Effect ◽  
Plane Deformation ◽  
Surface Elasticity ◽  
Closed Form Solution ◽  
Elliptical Hole ◽  
External Loading ◽  
Surface Energy Density

The finite plane deformation of nanomaterial surrounding an elliptical hole subjected to remote loading is systematically investigated using a recently developed continuum theory. A complex variable formulation is utilized to obtain a closed-form solution for the hoop stress along the edge of the hole. The results show that when the size of the hole reduces to the same order as the ratio of the surface energy density to the applied remote stress, the influence of the surface energy density plays an even more significant role, and the shape of the hole coupled with surface energy density has a significant effect on the elastic state around the hole. Surprisingly, in the absence of any external loading, the hoop stress induced solely by surface effects is identical to that for a hole with surface energy in a linearly elastic solid derived by the Gurtin–Murdoch surface elasticity model. The results in this paper should be useful for the precise design of nanodevices and helpful for the reasonable assessment of test results of nano-instruments.

Effect of Surface Energy on the Size-Dependent Yield Criterion of Nanoporous Materials under Complex Stress States

2011 ◽  
Vol 121-126 ◽  
pp. 15-19
Author(s):  
Liu Juan Zhu ◽  
Wen Zhong Cai ◽  
Shan Tung Tu
Keyword(s):  
Surface Energy ◽  
Nanostructured Materials ◽  
Surface Effect ◽  
Yield Criterion ◽  
Complex Stress ◽  
Nanoporous Materials ◽  
Octahedral Plane ◽  
Size Dependent ◽  
Stress States ◽  
Effect Of Surface

Within a micromechanical framework, the effect of surface energy is taken into account to explore the size-dependent yield criterion of nanoporous materials under complex stress states. A theoretical picture of the yield behavior on an octahedral plane is illustrated as functions of the surface properties and void size. The prominent size dependence of the yield criterion of nanoporous materials highlights the importance of the surface effect in analyzing the strength of nanostructured materials. The results demonstrate a fundamental framework to extend continuum strength theories to the nanoscale with substantial surface effect, which may be useful for evaluating the mechanical integrity of nanostructured materials.

Surface Energy Density

2012 ◽  
pp. 2573-2573
Author(s):  
Yimei Zhu ◽  
Hiromi Inada ◽  
Achim Hartschuh ◽  
Li Shi ◽  
Ada Della Pia ◽  
...  
Keyword(s):  
Energy Density ◽  
Surface Energy ◽  
Surface Energy Density

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

2008 ◽  
Vol 15 (05) ◽  
pp. 599-603 ◽  
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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