Green Function for the Problem of a Plane Containing a Circular Hole With Surface Effects

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
S. G. Mogilevskaya ◽  
A. V. Pyatigorets ◽  
S. L. Crouch
Keyword(s):  
Surface Tension ◽  
Green Function ◽  
Circular Hole ◽  
Surface Elasticity ◽  
Continuum Theory ◽  
Surface Effects ◽  
Elastic Plane ◽  
Parametric Studies ◽  
Complex Green Function ◽  
Hoop Stresses

This paper presents the complex Green function for the plane-strain problem of an infinite, isotropic elastic plane containing a circular hole with surface effects and subjected to a force applied at a point outside of the hole. The analysis is based on the Gurtin and Murdoch [1975, “A Continuum Theory of Elastic Material Surfaces,” Arch. Ration. Mech. Anal., 57, pp. 291–323; 1978, “Surface Stress in Solids,” Int. J. Solids Struct., 14, pp. 431–440] model, in which the surface of the hole possesses its own mechanical properties and surface tension. Systematic parametric studies are performed to investigate the effects of both surface elasticity and surface tension on the distribution of hoop stresses on the boundary of the hole and on a line that connects the point of the applied force and the center of the hole.

Surface Effects on the Mechanical Behavior of Buckled Thin Film

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
Yong Wang ◽  
Xue Feng ◽  
Bingwei Lu ◽  
Gangfeng Wang
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Surface Tension ◽  
Mechanical Behavior ◽  
Flexible Electronics ◽  
Geometric Nonlinearity ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Design Strategy ◽  
Piezoelectric Effects

The buckling of thin films with natural nonlinearity can provide a useful tool in many applications. In the present paper, the mechanical properties of controllable buckling of thin films are investigated by accounting for both geometric nonlinearity and surface effects at nanoscale. The effects of surface elasticity and residual surface tension on both static and dynamic behaviors of buckled thin films are discussed based on the surface-layer-based model. The dynamic design strategy for buckled thin films as interconnects in flexible electronics is proposed to avoid resonance in a given noise environment based on the above analysis. Further discussion shows that the thermal and piezoelectric effects on mechanical behavior of buckled thin film are equivalent to that of residual surface tension.

Effect of the Casimir Force on Buckling of a Double-Nanowire System with Surface Effects

2018 ◽  
Vol 18 (10) ◽  
pp. 1850118 ◽  
Author(s):  
J. Zou ◽  
X.-F. Li
Keyword(s):  
Surface Tension ◽  
Carrying Capacity ◽  
Critical Loads ◽  
Casimir Force ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Load Carrying Capacity ◽  
Governing Equations ◽  
Simply Supported ◽  
Load Carrying

Structural stability of a double-nanowire system with surface effects subjected to axial compressive forces is analyzed. Taking into account the Casimir force between the two nanowires, two coupled governing equations for buckling of a double-nanowire system are derived. For four typical end supports including simply-supported, clamped, cantilevered, and clamped-pinned double-nanowire systems, the characteristic equations are derived and the critical loads are determined for the out-of-phase in-plane buckling. Numerical results indicate that positive surface elasticity enhances the load-carrying capacity of the nanowires, and the reverse is also true. The Casimir force and residual surface tension always increase the critical loads.

Analysis of Residual Stresses on the Vibration of a Circular Sensor Diaphragm with Surface Effects

2016 ◽  
Vol 33 (3) ◽  
pp. 323-329 ◽  
Author(s):  
S.-S. Zhou ◽  
S.-J. Zhou ◽  
A.-Q. Li ◽  
B.-L. Wang
Keyword(s):  
Residual Stresses ◽  
Natural Frequency ◽  
Flexural Rigidity ◽  
Plate Theory ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Transition Range ◽  
Biochemical Sensors ◽  
Tension Parameter ◽  
Wide Range

AbstractResonant micro-biochemical sensors play important roles in a wide range of emerging applications to detect biochemical molecules. As the resonators of micro-biochemical sensors, the vibration characteristics of circular sensor diaphragms are important for the design of diaphragm-based resonant micro-biochemical sensors. In this paper, the influence of residual stresses on the vibration of a circular sensor diaphragm with surface effects is analyzed. Based on the Kirchhoff's plate theory and surface elasticity theory, the governing equation is presented. The material characteristic lengths for different surface effects are obtained. The influences of residual stresses on the effective flexural rigidity and natural frequency of the diaphragm with surface effects are discussed. Results show that the influence of residual stresses on the effective flexural rigidity becomes obvious with the increasing of residual stresses. The first order natural frequency increases rapidly when the tension parameter is larger than 30 for the stiffened surfaces, while for the softened surfaces the value is 10. Moreover, surface effects can influence the transition range of diaphragm from the plate behavior to membrane behavior in terms of the tension parameter. The transition range can be enlarged by the stiffened surface and be shortened by the softened surface. The analysis and results are helpful for the design of sensor diaphragm-based resonant micro-biochemical sensors and some related researches.

Asymmetric Bifurcation of Initially Curved Nanobeam

2015 ◽  
Vol 82 (9) ◽  
Author(s):  
X. Chen ◽  
S. A. Meguid
Keyword(s):  
Symmetry Breaking ◽  
Degrees Of Freedom ◽  
Surface Elasticity ◽  
Beam Theory ◽  
Surface Effects ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Reduced Order ◽  
Euler Bernoulli Beam ◽  
Bifurcation Behavior

In this paper, we investigate the asymmetric bifurcation behavior of an initially curved nanobeam accounting for Lorentz and electrostatic forces. The beam model was developed in the framework of Euler–Bernoulli beam theory, and the surface effects at the nanoscale were taken into account in the model by including the surface elasticity and the residual surface tension. Based on the Galerkin decomposition method, the model was simplified as two degrees of freedom reduced order model, from which the symmetry breaking criterion was derived. The results of our work reveal the significant surface effects on the symmetry breaking criterion for the considered nanobeam.

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.

Nanoindentation hardness of a Steigmann–Ogden surface bounding an elastic half-space

2018 ◽  
Vol 24 (9) ◽  
pp. 2754-2766 ◽  
Author(s):  
Xiaobao Li ◽  
Changwen Mi
Keyword(s):  
Surface Tension ◽  
Half Space ◽  
Surface Elasticity ◽  
Elastic Half Space ◽  
Indentation Hardness ◽  
Bending Rigidity ◽  
Size Dependent ◽  
Significant Difference ◽  
Nanoindentation Hardness ◽  
Membrane Stiffness

Previous studies demonstrate that, for nanostructures under transverse bending, the effective Young modulus is appreciably greater (in magnitude) than that of the same elements under axial loads. Therefore, in addition to the conventional residual surface tension and membrane stiffness, the curvature dependence of surface energy is desired for inhomogeneously strained nanostructures. In this paper, we aim to reevaluate the size-dependent nanoindentation hardness of an elastic half-space subjected to nanosized frictionless traction, through the use of both the curvature-independent Gurtin–Murdoch and the curvature-dependent Steigmann–Ogden models of surface elasticity. The nanoindentation problem is solved by the integration of Boussinesq’s method of displacement potentials and Hankel integral transforms. As examples, the effects of residual surface tension, membrane stiffness, and bending rigidity of the half-space boundary are parametrically analyzed in detail for a uniform circular pressure and a concentrated normal force. The observations in semianalytical calculations suggest a significant difference in the nanoindentation hardnesses predicted from the two popular models of surface mechanics. In most cases, the inclusion of bending rigidity results in smaller displacements and stresses, and therefore higher indentation hardness. Based on physically interpretable numerical values of surface material properties, we show that a curvature-dependent model of surface elasticity is required in order to characterize the size-dependent feature of nanoindentation problems correctly.

Axisymmetric Boussinesq problem of a transversely isotropic half space with surface effects

2018 ◽  
Vol 24 (5) ◽  
pp. 1425-1437 ◽  
Author(s):  
Jing Jin Shen
Keyword(s):  
Half Space ◽  
Mixed Boundary ◽  
Contact Stiffness ◽  
Surface Elasticity ◽  
Transversely Isotropic ◽  
Surface Effects ◽  
Building Blocks ◽  
Material Anisotropy ◽  
Residual Surface Stress ◽  
Special Cases

A transversely isotropic half space with surface effects subjected to axisymmetric loadings is investigated in terms of the Lekhnitskii formulism. Surface effects including residual surface stress and surface elasticity are introduced by using the Gurtin–Murdoch continuum model. With the aid of the Hankel transforms, solutions corresponding to several different axisymmetic loadings are derived and used to determine the influence of surface effects on contact stiffness in nanoindentations. Numerical results are provided to show the influence of surface effects and material anisotropy on the material behaviours. Meanwhile, the obtained analytical Green’s functions for two special cases can be used as building blocks for further mixed boundary value problems.

The Neumann problem in plane deformations of a micropolar elastic solid with micropolar surface effects

2020 ◽  
Vol 26 (1) ◽  
pp. 30-44
Author(s):  
Alireza Gharahi ◽  
Peter Schiavone
Keyword(s):  
Neumann Problem ◽  
Existence Theorems ◽  
Surface Elasticity ◽  
Elastic Solid ◽  
Singular Integral Equations ◽  
Surface Effects ◽  
Integral Representations ◽  
Matrix Functions ◽  
Micropolar Elasticity ◽  
The Neumann Problem

We consider the Neumann problem in a theory of plane micropolar elasticity incorporating micropolar surface effects. The incorporation of surface elasticity utilizes the Eremeyev–Lebedev–Altenbach shell model, leading to a set of second-order boundary conditions describing the separate micropolar elasticity of the surface. The Neumann problem is of particular interest, since the question of solvability is complicated by the fact that the corresponding systems of homogeneous singular integral equations admit nontrivial solutions that affect the solvability of both the interior and exterior Neumann boundary value problems. We overcome this difficulty by constructing integral representations of the solutions based on specifically constructed auxiliary matrix functions leading to uniqueness and existence theorems in appropriate classes of smooth matrix functions.

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.

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