scholarly journals Large Deformation and Instability of Soft Hollow Cylinder With Surface Effects

2021 ◽  
Vol 88 (4) ◽  
Author(s):  
Qitao Wang ◽  
Mingchao Liu ◽  
Zhenyu Wang ◽  
Changqing Chen ◽  
Jian Wu
Keyword(s):  
Surface Energy ◽  
Large Deformation ◽  
Hollow Cylinder ◽  
Surface Stress ◽  
Uniform Pressure ◽  
Pressure Loading ◽  
Residual Surface Stress ◽  
Buckling Behavior ◽  
Global Buckling ◽  
Hyper Elastic

Abstract Surface stress, which is always neglected in classical elastic theories, has recently emerged as a key role in the mechanics of highly deformable soft solids. In this paper, the effect of surface stress on the deformation and instability of soft hollow cylinder is analyzed. By incorporating surface energy density function into the constitutive model of a hyper-elastic theory, explicit solutions are obtained for the large deformation of soft hollow cylinder under the uniform pressure loading and geometric everting. The surface tension and the residual surface stress have a significant effect on the large deformation and instability of the soft cylinder. When the pressure loading and geometric everting are applied on the soft hollow cylinder, significant changes in the critical condition of the creases are found by varying the surface parameters. Two models of instability, surface crease and global buckling behavior, will be generated on the soft hollow cylinder with the uniform pressure, and the formed instability model is dependent on the ratio of the thickness to the radius. The results in this work reveal that surface energy obviously influences both the deformation and the instability of soft hollow cylinder at finite deformation and will be helpful for understanding and predicting the mechanical behavior of soft structures accurately.

Surface Effects on the Buckling of Piezoelectric Nanobeams

2012 ◽  
Vol 486 ◽  
pp. 519-523 ◽  
Author(s):  
Kai Fa Wang ◽  
Bao Lin Wang
Keyword(s):  
Shear Deformation ◽  
Electric Potential ◽  
Surface Stress ◽  
Surface Elasticity ◽  
Beam Theory ◽  
Surface Effects ◽  
Residual Surface Stress ◽  
Buckling Behavior ◽  
Stress Surface ◽  
Piezoelectric Nanobeam

In this paper, we analyze the influence of surface effects including residual surface stress, surface piezoelectric and surface elasticity on the buckling behavior of piezoelectric nanobeams by using the Timoshenko beam theory and surface piezoelectricity model. The critical electric potential for buckling of piezoelectric nanobeams with different boundary condition is obtained analytically. From the results, it is found that the surface piezoelectric reduces the critical electric potential. However, a positive residual surface stress increases the critical electric potential. In addition, the shear deformation reduces the critical electric potential, and the influence of shear deformation become more significant for a stubby piezoelectric nanobeam.

Surface Effects on Large Deflection of Nanobeams Subjected to a Follower Load

2020 ◽  
Vol 12 (06) ◽  
pp. 2050067
Author(s):  
Yun Xing ◽  
Yi Han ◽  
Hua Liu ◽  
Jialing Yang
Keyword(s):  
Large Deformation ◽  
Surface Stress ◽  
Large Deflection ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Surface Residual Stress ◽  
Residual Surface Stress ◽  
Deformation Problem ◽  
Cross Sectional Dimension

As a basic element of the micro/nanodevices, nanobeams have remarkable physical properties and have attracted considerable attention in the previous studies. However, previous publications did not study the large deformation problem of nanobeams under follower loading when the surface effect becomes significant and especially for the influence of surface effect on mechanical behaviors of the nanobeams under follower loading remains unclear. In this paper, we investigated the large deformation behavior of nanobeams subjected to follower loads in consideration of the surface effects. The mechanical model of large deflection of extensible cantilever nanobeams under follower loading is presented in combination with the surface elasticity and residual surface stress, and then a MATLAB program of shooting method with a technique for determining the initial value was developed to solve the problems. The results indicate that the surface effects have an important influence on the large deflection of nanobeams under follower loading: when the surface residual stress is positive, the maximums of displacement in horizontal and vertical directions and the rotation angle of the free end become lager, but the corresponding follower force related to those maximums becomes smaller. When the residual surface stress is negative, the results are the opposite. In addition, the influence of the cross-sectional dimension of the nanobeams under follower loading on surface effects was discussed. This work is beneficial to understand the mechanism of large deformation of nanobeams with surface effects subjected to follower loads, and can also provide inspirations to design advanced nanomaterials and nanoscaled devices.

Elastic Energy of Surfaces and Residually Stressed Solids: An Energy Approach for the Mechanics of Nanostructures

2015 ◽  
Vol 82 (1) ◽  
Author(s):  
Xiang Gao ◽  
Daining Fang
Keyword(s):  
Surface Energy ◽  
Elastic Energy ◽  
Surface Stress ◽  
Strain Energy ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Small Deformation ◽  
Energy Approach ◽  
Residual Surface Stress ◽  
The Impact

The surface energy plays a significant role in solids and structures at the small scales, and an explicit expression for surface energy is prerequisite for studying the nanostructures via energy methods. In this study, a general formula for surface energy at finite deformation is constructed, which has simple forms and clearly physical meanings. Next, the strain energy formulas both for isotropic and anisotropic surfaces under small deformation are derived. It is demonstrated that the surface elastic energy is also dependent on the nonlinear Green strain due to the impact of residual surface stress. Then, the strain energy formula for residually stressed elastic solids is given. These results are instrumental to the energy approach for nanomechanics. Finally, the proposed results are applied to investigate the elastic stability and natural frequency of nanowires. A deep analysis of these two examples reveals two length scales characterizing the significance of surface energy. One is the critical length of nanostructures for self-buckling; the other reflects the competition between residual surface stress and surface elasticity, indicating that the surface effect does not always strengthen the stiffness of nanostructures. These results are conducive to shed light on the importance of the residual surface stress and the initial stress in the bulk solids.

Surface Energy Effects on the Nonlinear Free Vibration of Functionally Graded Timoshenko Nanobeams Based on Modified Couple Stress Theory

2019 ◽  
Vol 19 (11) ◽  
pp. 1950127 ◽  
Author(s):  
Mohamed A. Attia ◽  
Rabab A. Shanab ◽  
Salwa A. Mohamed ◽  
Norhan A. Mohamed
Keyword(s):  
Surface Energy ◽  
Boundary Conditions ◽  
Nonlinear Vibration ◽  
Surface Stress ◽  
Couple Stress ◽  
Surface Elasticity ◽  
Functionally Graded ◽  
Residual Surface Stress ◽  
Stress Surface ◽  
Modified Couple Stress

An integrated nonlinear couple stress-surface energy continuum model is developed to study the nonlinear vibration characteristics of size-dependent functionally graded nanobeams for the first time. The nanobeam theory is formulated based on the Timoshenko kinematics, augmented by von Kármán’s geometric nonlinearity. The modified couple stress and Gurtin–Murdoch surface elasticity theories are incorporated to capture the long-range interaction and surface energy, respectively. Unlike existing Timoshenko nanobeam models, the effects of surface elasticity, residual surface stress, surface mass density and Poisson’s ratio, in addition to bending and axial deformations, are incorporated in the newly developed model. A power law function is used to model the material distribution through the thickness of the beam, considering the gradation of bulk and surface material parameters. A variational formulation of the nonlinear nonclassical governing equations and associated nonclassical boundary conditions is established by employing Hamilton’s principle. The generalized differential quadrature method is exploited in conjunction with either the Pseudo-arclength continuation or Runge–Kutta method to solve the problem with an exact implementation of the nonclassical boundary conditions. The formulation and solution procedure presented are verified by comparing the obtained results with available ones. Based on the parametric study, it is concluded that the nonclassical boundary conditions, material length scale parameter, residual surface stress, surface elasticity, bulk elasticity modulus, gradient index, nonlinear amplitude and thickness have important influences on the linear and nonlinear vibration responses of functionally graded Timoshenko nanobeams.

Transverse Vibrations of Mixed-Mode Cracked Nanobeams With Surface Effect

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Kai-Ming Hu ◽  
Wen-Ming Zhang ◽  
Zhi-Ke Peng ◽  
Guang Meng
Keyword(s):  
Surface Energy ◽  
Surface Stress ◽  
Mixed Mode ◽  
Natural Frequencies ◽  
Surface Effect ◽  
Crack Depth ◽  
Crack Tip ◽  
Residual Surface Stress ◽  
Transverse Vibrations ◽  
Local Flexibility

Slant edge cracked effect considering the inherent relation between surface energy and mixed-mode crack propagations on the free transverse vibrations of nanobeams with surface effect is investigated. First, the slant edge cracked effect, which considers residual surface stress effect on the crack tip fields of a mode-I and mode-II surface edge crack, is developed and the corresponding stress intensity factors (SIFs) and local flexibility coefficients are derived. Moreover, a refined continuum model of slant cracked nanobeams is established by considering both slant edge cracked effect and surface effect. The effects of fracture angles, crack depth, surface elasticity, surface stress, and surface density on the local flexibility and free transverse vibration characteristics of cracked nanobeams are, respectively, analyzed. The results show that the flexibility coefficients distribute symmetrically about residual surface stress. Fracture angles have a profound influence on both the symmetries of the mode shapes and the natural frequencies of nanobeams, and the influence becomes more pronounced as crack depth ratios increase. Furthermore, the natural frequencies will first decrease and then increase with fracture angles when the slant edge cracked effect is considered. The results demonstrate that the inherent relation between surface energy and crack propagations should be considered for both the stress distributions at the crack tip and the dynamic behavior of cracked nanobeams.

Revisiting Bangham's law of adsorption-induced deformation: changes of surface energy and surface stress

2016 ◽  
Vol 18 (14) ◽  
pp. 9788-9798 ◽  
Author(s):  
Gennady Y. Gor ◽  
Noam Bernstein
Keyword(s):  
Surface Energy ◽  
Surface Stress ◽  
P Adsorption

Adsorption-induced deformation has to be described in terms of the change of the surface stress Δfand not the surface energy Δγ. The former explains both expansion and contraction.

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