Nonlinear Analysis for Bending, Buckling and Post-buckling of Nano-Beams with Nonlocal and Surface Energy Effects

2019 ◽  
Vol 19 (11) ◽  
pp. 1950130 ◽  
Author(s):  
Thai Binh Nguyen ◽  
J. N. Reddy ◽  
Jaroon Rungamornrat ◽  
Jintara Lawongkerd ◽  
Teerapong Senjuntichai ◽  
...  
Keyword(s):  
Surface Energy ◽  
Elasticity Theory ◽  
Mechanical Response ◽  
Bulk Material ◽  
Surface Elasticity ◽  
Closed Form Solution ◽  
Buckling Load ◽  
Material Surface ◽  
Material Layer ◽  
Post Buckling

The modeling and analysis for mechanical response of nano-scale beams undergoing large displacements and rotations are presented. The beam element is modeled as a composite consisting of the bulk material and the surface material layer. Both Eringen nonlocal elasticity theory and Gurtin–Murdoch surface elasticity theory are adopted to formulate the moment–curvature relationship of the beam. In the formulation, the pre-existing residual stress within the bulk material, induced by the residual surface tension in the material layer, is also taken into account. The resulting moment-curvature relationship is then utilized together with Euler–Bernoulli beam theory and the elliptic integral technique to establish a set of exact algebraic equations governing the displacements and rotations at the ends of the beam. The linearized version of those equations is also established and used in the derivation of a closed-form solution of the buckling load of nano-beams under various end conditions. A discretization-free solution procedure based mainly upon Newton iterative scheme and a selected numerical quadrature is developed to solve a system of fully coupled nonlinear equations. It is demonstrated that the proposed technique yields highly accurate results comparable to the benchmark analytical solutions. In addition, the nonlocal and surface energy effects play a significant role on the predicted buckling load, post-buckling and bending responses of the nano-beam. In particular, the presence of those effects remarkably alters the overall stiffness of the beam and predicted solutions exhibit strong size-dependence when the characteristic length of the beam is comparable to the intrinsic length scale of the material surface.

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.

Stress Field Near a Nanosized Spheroidal Cavity under Bi-Axial Tension Perpendicular to the Revolution Axis

2008 ◽  
Vol 33-37 ◽  
pp. 1005-1010
Author(s):  
Zhi Ying Ou ◽  
Gang Feng Wang ◽  
Tie Jun Wang
Keyword(s):  
Surface Energy ◽  
Stress Field ◽  
Elasticity Theory ◽  
Surface Elasticity ◽  
Elastic Field ◽  
Classical Elasticity ◽  
Axial Tension ◽  
Spheroidal Cavity ◽  
Shape And Size ◽  
The Revolution

The elastic field around a nanosized spheroidal cavity is derived on the basis of surface elasticity theory. The effects of surface energy, shape and size of the cavity are discussed. It is seen that the stress field near the nanosized cavity depends on the shape and the size of the cavity as well as the properties of the surface. These new characteristics are different from those predicted by the classical elasticity and may illuminate some new mechanisms at nanoscale.

A new isogeometric Timoshenko beam model incorporating microstructures and surface energy effects

2020 ◽  
Vol 25 (10) ◽  
pp. 2005-2022 ◽  
Author(s):  
Shuohui Yin ◽  
Yang Deng ◽  
Gongye Zhang ◽  
Tiantang Yu ◽  
Shuitao Gu
Keyword(s):  
Surface Energy ◽  
Elasticity Theory ◽  
Timoshenko Beam ◽  
Couple Stress Theory ◽  
Surface Elasticity ◽  
Numerical Results ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Order Continuity ◽  
Microstructure Effect

A new isogeometric Timoshenko beam model is developed using a modified couple stress theory (MCST) and a surface elasticity theory. The MCST is wildly used to capture microstructure effects that includes only one material length scale parameter, while the Gurtin–Murdoch surface elasticity theory containing three surface elasticity constants is employed to approximate the nature of surface energy effects. A new effective computational approach is presented for the current nonclassical Timoshenko beam model based on isogeometric analysis with high-order continuity basis functions of non-uniform rational B-splines, which effectively fulfills the higher continuity requirements in MCST. To validate the new approach and quantitatively illustrate both the microstructure and surface energy effects, the numerical results obtained from the developed approach for static deflection and natural frequencies of beams are compared with the analytical results available in the literature. Numerical results reveal that both the microstructure effect and surface energy effect should be considered in very thin beams, which also explains the size-dependent behavior.

Numerical Analysis of Frictionless Nano-Contact Problems Based on Surface Elasticity

2015 ◽  
Vol 07 (02) ◽  
pp. 1550022 ◽  
Author(s):  
Mohamed A. Attia ◽  
Ahmed G. El-Shafei ◽  
Fatin F. Mahmoud
Keyword(s):  
Finite Element ◽  
Surface Energy ◽  
Finite Element Model ◽  
Bulk Material ◽  
Surface Elasticity ◽  
Contact Problems ◽  
Element Model ◽  
Contact Forces ◽  
Nonlinear Finite Element Model ◽  
Effect Of Surface

A nonlinear finite element model is developed to predict the response of frictionless contact of isotropic, elastic nano-bodies incorporating the effect of surface energy. The boundary value problem is formulated based on the classical theory of linear elasticity of the bulk material, while the complete Gurtin–Murdoch constitutive relation is adopted to accommodate the effect of surface energy. The Lagrange multiplier approach is employed to enforce inequality contact constraints without any need of an appropriate value for the penalty parameter, where the contact forces are treated as independent variables. The proposed finite element model accounts for both advancing and receding contact problems. The output results are compared favorably with those published analytical solutions. The influence of surface energy and its size-dependency on the behavior of conformal and nonconformal conformal/nonconformal nano-contact systems is demonstrated by carrying out by analyzing three different contact problems.

High Strength Autoclaved Mortars

1984 ◽  
Vol 42 ◽  
Author(s):  
R. Baggott ◽  
A. Sarandily
Keyword(s):  
Surface Energy ◽  
Modulus Of Elasticity ◽  
Preparation Method ◽  
High Strength ◽  
Dominant Factor ◽  
Material Surface ◽  
Specific Material

AbstractAutoclaved cement-silica mortars having flexural strengths of up to 57 MPa were prepared by pressing and casting methods of fabrication. It was found that the Griffith dependence of strength upon the size of the largest flaw, the modulus of elasticity and the surface energy was applicable. The relative contributions of these three parameters were evaluated and it was established that although the maximum flaw was the dominant factor in a specific material, surface energy changes were responsible for major strength differences associated with water-solid ratios or variations in the preparation method. Preliminary studies identified the various microstructural features that operated as Griffith's flaws.

Pull-In Instability of Functionally Graded Cantilever Nanoactuators Incorporating Effects of Microstructure, Surface Energy and Intermolecular Forces

2018 ◽  
Vol 10 (08) ◽  
pp. 1850091 ◽  
Author(s):  
Mohamed A. Attia ◽  
Salwa A. Mohamed
Keyword(s):  
Residual Stress ◽  
Surface Energy ◽  
Boundary Conditions ◽  
Van Der Waals ◽  
Surface Elasticity ◽  
Van Der Waals Forces ◽  
Functionally Graded ◽  
Surface Residual Stress ◽  
Electrically Actuated ◽  
Classical Boundary

In this paper, an integrated non-classical continuum model is developed to investigate the pull-in instability of electrostatically actuated functionally graded nanocantilevers. The model accounts for the simultaneous effects of local-microstructure, surface elasticity and surface residual in the presence of fringing field as well as Casimir and van der Waals forces. The modified couple stress and Gurtin–Murdoch surface elasticity theories are employed to conduct the scaling effects of microstructure and surface energy, respectively, in the context of Euler–Bernoulli beam hypothesis. Bulk and surface material properties are varied according to the power-law distribution through the beam thickness. The physical neutral axis position for mentioned FG nanobeams is considered. Hamilton principle is employed to derive the nonlinear size-dependent governing equations and the non-classical boundary conditions. The resulting nonlinear differential equations are solved utilizing the generalized differential quadrature method (GDQM). In addition, the non-classical boundary conditions of nanocantilever beams due to surface residual stress are exactly implemented. After validation of the obtained results by previously available data in the literature, the influences of different geometrical and material parameters on the pull-in instability of the FG nanocantilevers are examined in detail. It is concluded that the pull-in behavior of electrically actuated FG micro/nanocantilevers is significantly influenced by the material distribution, material length scale parameter, surface elasticity constant, surface residual stress, initial gap, slenderness ratio, Casimir, and van der Waals forces. The obtained results can be considered for modeling and analysis of electrically actuated FG nanocantilevers.

Buckling and Post Buckling Behavior of a Transversely Stiffened Ship Hull Model

1964 ◽  
Vol 8 (04) ◽  
pp. 7-21
Author(s):  
H.G. Schultz
Keyword(s):  
Reasonable Agreement ◽  
Ship Hull ◽  
Buckling Load ◽  
Experimental Results ◽  
Postbuckling Behavior ◽  
Pure Bending ◽  
Box Girder ◽  
Buckling Behavior ◽  
Theoretical Investigations ◽  
Post Buckling

In the paper presented the behavior of a transversely formed box-girder model subjected to pure bending is discussed, where the deck plating of the model is loaded above the buckling load. The experimental results obtained are in reasonable agreement with theoretical investigations and show the influence of fabrication initiated plate deflections on the buckling and postbuckling behavior of the deck plating clearly. A method is suggested for determining the buckling load of plates having large initial deformations.

scholarly journals Electrospinning of PCL-Based Blends: Processing Optimization for Their Scalable Production

Materials ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 3853
Author(s):  
Marina P. Arrieta ◽  
Adrián Leonés Gil ◽  
Maysa Yusef ◽  
José M. Kenny ◽  
Laura Peponi
Keyword(s):  
Thermal Stability ◽  
Mechanical Response ◽  
Bulk Material ◽  
Processing Parameters ◽  
Industrial Sector ◽  
Industrial Applications ◽  
Elongation At Break ◽  
Processing Optimization ◽  
Scalable Production

In this work poly(ε-caprolactone) (PCL) based electrospun mats were prepared by blending PCL with microcrystalline cellulose (MCC) and poly(3-hydroxybutyrate) (PHB). The electrospinning processing parameters were firstly optimized with the aim to obtain scalable PCL-based electrospun mats to be used in the industrial sector. Neat PCL as well as PCL-MCC and PCL-PHB based mats in different proportions (99:1; 95:5; 90:10) were prepared. A complete morphological, thermal and mechanical characterization of the developed materials was carried out. Scanning electron microscopy (SEM) observations showed that the addition of PHB to the PCL matrix considerably reduced the formation of beads. Both the addition of MCC and PHB reduced the thermal stability of PCL, but obtained materials with enough thermal stability for the intended use. The electrospun PCL fibers show greatly reduced flexibility with respect to the PCL bulk material, however when PCL is blended with PHB their stretchability is increased, changing their elongation at break from 35% to 70% when 10 wt% of PHB is blended with PCL. However, the mechanical response of the different blends increases with respect to the neat electrospun PCL, offering the possibility to modulate their properties according to the required industrial applications.

scholarly journals Microstructural and Mechanical Response of NiTi Lattice 3D Structure Produced by Selective Laser Melting

Metals ◽  
2020 ◽  
Vol 10 (6) ◽  
pp. 814 ◽  
Author(s):  
Carlo Alberto Biffi ◽  
Paola Bassani ◽  
Jacopo Fiocchi ◽  
Ausonio Tuissi
Keyword(s):  
Martensitic Transformation ◽  
Selective Laser Melting ◽  
Mechanical Response ◽  
Electron Backscatter Diffraction ◽  
Bulk Material ◽  
Niti Alloy ◽  
3D Structure ◽  
Lattice Structures ◽  
Laser Melting ◽  
Scanning Calorimetry

Nowadays, additive manufacturing (AM) permits to realize complex metallic structural parts, and the use of NiTi alloy, known as Nitinol, allows the integration of specific functions to the AM products. One of the most promising designs for AM is concerning the use of lattice structures that show lightweight, higher than bulk material deformability, improved damping properties, high exchange surface. Moreover, lattice structures can be realized with struts, having dimensions below 1 mm—this is very attractive for the realization of Nitinol components for biomedical devices. In this light, the present work regarded the experimental characterization of lattice structures, produced by selective laser melting (SLM), by using Ni-rich NiTi alloy. Differential scanning calorimetry (DSC), electron backscatter diffraction (EBSD), and compression testing were carried out for analyzing microstructure, martensitic transformation (MT) evolution, and superelasticity response of the SLMed lattice samples. The lattice microstructures were compared with those of the SLMed bulk material for highlighting differences. Localized martensite was detected in the nodes zones, where the rapid solidification tends to accumulate solidification stresses. An increase of martensitic transformation temperatures was also observed in lattice NiTi.

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