Effects of higher-order interface stresses on the elastic states of two-dimensional composites

Chen, Tungyang; Chiu, Min Sen

doi:10.1016/j.mechmat.2011.02.003

Cited by 26 publications

(5 citation statements)

References 42 publications

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“…Noting the curvature κ = −(n · ∇ s ) = d 2 w/dx 2 and δu n ≈ δw [16,50], the variation of the energy induced by the normal surface-induced traction γ n can be expressed as…”

Section: Deflection Equation Of Nanowiresmentioning

confidence: 99%

Buckling behavior of nanowires predicted by a new surface energy density model

Yao

Chen

2016

Acta Mech

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The axial buckling behavior of nanowires is investigated with a new continuum theory, in which the surface effect of nanomaterials is characterized by the surface energy density. Only the surface energy density of bulk materials and the surface relaxation parameter are involved, instead of the surface elastic constants in the classical surface elasticity theory. Two kinds of nanowires with different boundary conditions are discussed. It is demonstrated that the new continuum theory can predict the buckling behavior of nanowires very well. Similar to the prediction of the classical elasticity theory, the critical compressive load of axial buckling of nanowires predicted by the new continuum theory increases with an increasing characteristic length, such as the diameter or height of nanowires. With the same aspect ratio, a nanowire with a rectangular cross section possesses a larger critical buckling load than that with a circular one. However, the surface effect could enhance the critical buckling load not only for a fixed-fixed nanowire but also for a cantilevered one in contrast to the classical elastic model. All the results predicted by the new continuum theory agree well with predictions by the surface elasticity models. The present research not only verifies the validation of the new continuum theory, but also gives a much more convenient characterization of buckling behaviors of nanowires. This should be helpful for the design of nanodevices based on nanomaterials, for example, nanobeams in NEMS or high-precision instruments.

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“…Noting the curvature κ = −(n · ∇ s ) = d 2 w/dx 2 and δu n ≈ δw [16,50], the variation of the energy induced by the normal surface-induced traction γ n can be expressed as…”

Section: Deflection Equation Of Nanowiresmentioning

confidence: 99%

Buckling behavior of nanowires predicted by a new surface energy density model

Yao

Chen

2016

Acta Mech

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show abstract

“…Besides the interfacial strength, the interfacial stiffness is one of the most important parameters since it has a great effect on the overall mechanical properties and stress distributions of the composites. Benveniste and Miloh [4] suggested that the interface conditions could be classified into four distinct regimes including "membrane type", "inextensible membrane type", "inextensible shell type" and "rigid contact type" depending on the stiffness of the interphase with respect to the neighboring media, which were further verified by Chen et al [5] defining suitable material parameters about the stiffness and length scales of the interphase. Du et al [6] examined several basic issues related to the interface stiffness and especially determined the interface stiffness in particular directions.…”

Section: Introductionmentioning

confidence: 80%

Study of Interfacial Stiffness by Using the Structural Interface Model Based on Elastic Mechanics

Xie

Chai

Weng

et al. 2013

AMM

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The recently proposed structural interface model is a realistic model of thick interfaces, but the bars of the structure are assumed iso-stiffness. In the present work, the structural interface consisting of pairs of bars with different stiffness is developed. Based on the neutral inclusion concept and elastic mechanics, the stiffness of bars of the structural interface is studied. It is found that all the bars have the same stiffness in a special loading condition of equal-biaxial tension. The finite element simulations for glass fiber-reinforced epoxy composite reveal that the fiber does not alter the prescribed stress due to the presence of the structural interface. Compared with the iso-stiffness-bar interface, the developed structure interface is more suitable for characterizing a multi-component interface and more flexible to be designed.

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“…This mathematical equation is referred to as the generalized Young-Laplace (YL) equation. A more refined model in 2D, the membrane could sustain not only in-plane stress but also surface moment, was recently proposed by Chen and Chiu [9], which is referred to as high-order surface stress. The jump condition across the interface Γ for the surface stresses s α σ and surface moments s m α can be derived as [9] 2 2…”

Section: High-order Surface Stressmentioning

confidence: 99%

“…[4][5][6][7][8]. Chen and Chiu [9] have recently proposed a more rigorous approach to simulate the effects of different orders of surface stress, including in-plane surface stress as well as surface moments. Surface moments can be induced from the non-uniform stress variation across the thickness of the thin surface layer, and thus can be viewed as high-order surface stress effects.…”

Section: Introductionmentioning

confidence: 99%

Timoshenko Beam Model for Buckling of Nanowires with High-Order Surface Stresses Effects

Chiu

Chen

2012

AMR

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High-order surface effects can have a significant effect in the mechanical behavior of micro- and nano-sized materials and structures. In the literature the mathematical framework of surface/interface stresses are generally described by generalized Young-Laplace equations based on membrane theory. A refined model of surface stress, counting into surface stresses as well as surface moments, collectively referred to as high-order surface stress, was recently derived by the authors. This framework allows us to simulate the interface between two neighboring media which may have varying in-plane stress through the thickness of the thin membrane. To illustrate surface stress effects, we consider the critical force of axial buckling of nanowires by accounting various degrees of surface stresses. Using the refined Timoshenko beam theory, we incorporate the high-order surface effect in the simulation of axial buckling of nanowires. The results are compared with the solutions based on conventional surface stress model as well as existing experimental data. This study might be helpful to characterize the mechanical properties of nanowires in a wide range of applications.

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Effects of higher-order interface stresses on the elastic states of two-dimensional composites

Cited by 26 publications

References 42 publications

Buckling behavior of nanowires predicted by a new surface energy density model

Buckling behavior of nanowires predicted by a new surface energy density model

Study of Interfacial Stiffness by Using the Structural Interface Model Based on Elastic Mechanics

Timoshenko Beam Model for Buckling of Nanowires with High-Order Surface Stresses Effects

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