Elastostatic Fields of an Embedded Circular Rigid Nano/Micro-Fiber with Interfacial Damage in Anti-Plane Couple Stress Elasticity

2015 ◽  
Vol 784 ◽  
pp. 80-85
Author(s):  
Behdad Hashemian ◽  
H.M. Shodja ◽  
Azadeh Goodarzi
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Continuum Theory ◽  
Analytical Determination ◽  
Interfacial Damage ◽  
Stress Theory ◽  
Elastic Fields ◽  
Couple Stress Elasticity ◽  
Continuum Theories

It is well-known that classical continuum theory has certain deficiencies in predicting the nanoscopic behavior of materials in the vicinity of defects. Couple stress theory is one of the higher order continuum theories which can overcome such difficulties by introducing new characteristic length. An accurate analytical determination of the elastic fields of an embedded circular nano/micro-rigid fiber with damaged interface under remote anti-plane loading in the context of couple stress elasticity is of particular interest.

An Embedded Elliptic Nano-Fiber in Anti-Plane Strain Couple Stress Elasticity

2008 ◽  
Author(s):  
Hossein M. Shodja ◽  
Hamed Haftbaradaran
Keyword(s):  
Size Effect ◽  
Isotropic Material ◽  
Couple Stress ◽  
Characteristic Length ◽  
Couple Stress Theory ◽  
Infinite Medium ◽  
Stress Theory ◽  
Couple Stress Elasticity ◽  
Nano Fiber ◽  
Continuum Theories

The application of higher order continuum theories, with size effect considerations, have recently been spread in the micro and nano-scale studies. One famous version of these theories is the couple stress theory. This paper utilizes this theory to study the anti-plane problem of an elliptic nano-fiber, embedded in an infinite medium, both made of centrosymmetric isotropic material. In this framework, a characteristic length appears in the formulation, by which examination of the size effect is possible. This work presents an analytical solution for the proposed problem.

scholarly journals Size-dependent vibration analysis of graphene-PMMA lamina based on non-classical continuum theory

2019 ◽  
Vol 26 (1) ◽  
pp. 491-501 ◽  
Author(s):  
Mehran Karimi Zeverdejani ◽  
Yaghoub Tadi Beni
Keyword(s):  
Natural Frequency ◽  
Couple Stress ◽  
Volume Fraction ◽  
Couple Stress Theory ◽  
Shear Deformation Theory ◽  
Continuum Theory ◽  
Dynamics Simulation ◽  
Physical Parameters ◽  
Stress Theory ◽  
Size Dependent

AbstractThis paper studies the free vibration of polymer nanocomposite reinforced by graphene sheet. In this work, the new size dependent formulation is presented for nanocomposites based on couple stress theory. For this purpose, the first shear deformation theory is applied. The effect of scale parameter is investigated based on anisotropic couple stress theory. Vibration equations of the composite lamina are extracted using Hamilton’s principle. Numerical results are provided for Poly methyl methacrylate/graphene composite.Mechanical properties of the composite are obtained from molecular dynamics simulation. Based on eigenvalue procedure, an analytical solution is obtained for the natural frequency of composite lamina. In the results section, the effect of dimensional and physical parameters are investigated on lamina natural frequency. It is observed that graphene defects caused to diminish the lamina frequency. Furthermore, it is revealed that the increase in graphene volume fraction leads to natural frequency be greater.

Size-dependent two-node axisymmetric shell element for buckling analysis with couple stress theory

2019 ◽  
Vol 233 (13) ◽  
pp. 4729-4741
Author(s):  
Iman Soleimani ◽  
Yaghoub Tadi Beni ◽  
Mohsen Botshekanan Dehkordi
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Continuum Theory ◽  
Shell Element ◽  
Modified Couple Stress Theory ◽  
Element Formulation ◽  
Stress Theory ◽  
Size Dependent ◽  
Axisymmetric Shell ◽  
Modified Couple Stress

In this paper, two-node size-dependent axisymmetric shell element formulation is developed by using thin conical shell model in the place of the beam model, which is used in previous research and using the modified couple stress theory in the place of the classical continuum theory. Since classical continuum theory is unable to correctly compute stiffness and account for size effects in micro/nanostructures, higher order continuum theories such as modified couple stress theory have become quite popular. The mass stiffness matrix and geometric stiffness matrix for axisymmetric shell element are developed in this paper, and by means of size-dependent finite element formulation it is extended to more precisely account for nanotube buckling. The results have indicated using the two-node axisymmetric shell element, where the rigidity of the nano-shell is greater than that in the classical, and the critical axial buckling loads obtained from couple stress theory are greater than that of classical, which is due to the presence of one size parameter in couple stress theory. The findings also indicate that the developed size-dependent axisymmetric shell element is able to analyze the buckling of cylindrical and conical shells and also circular plate, which is reliable for simulating micro/nanostructures and can be used for the analysis of size effect and has desirable convergence characteristic. Besides, in addition to reducing the number of elements required, using axisymmetric shell element also increases convergence speed and accuracy.

A non-classical theory of elastic dielectrics incorporating couple stress and quadrupole effects: part I – reconsideration of curvature-based flexoelectricity theory

2021 ◽  
pp. 108128652110015
Author(s):  
YL Qu ◽  
GY Zhang ◽  
YM Fan ◽  
F Jin
Keyword(s):  
Classical Theory ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Constitutive Relations ◽  
Stress Theory ◽  
Isotropic Materials ◽  
Flexoelectric Effect ◽  
Beam Bending ◽  
Gradient Theories ◽  
Anisotropic And Isotropic Materials

A new non-classical theory of elastic dielectrics is developed using the couple stress and electric field gradient theories that incorporates the couple stress, quadrupole and curvature-based flexoelectric effects. The couple stress theory and an extended Gauss’s law for elastic dielectrics with quadrupole polarization are applied to derive the constitutive relations of this new theory through energy conservation. The governing equations and the complete boundary conditions are simultaneously obtained through a variational formulation based on the Gibbs-type variational principle. The constitutive relations of general anisotropic and isotropic materials with the corresponding independent material constants are also provided, respectively. To illustrate the newly proposed theory and to show the flexoelectric effect in isotropic materials, one pure bending problem of a simply supported beam is analytically solved by directly applying the formulas derived. The analytical results reveal that the flexoelectric effect is present in isotropic materials. In addition, the incorporation of both the couple stress and flexoelectric effects always leads to increased values of the beam bending stiffness.

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