Sharif Digital Repository

In this paper, the scattering of anti-plane shear waves in an infinite matrix containing a multi-coated nanofiber/nanotube is studied. Based on the fact that the surface to volume ratio for nano-size objects increases, the usual classical theories which generally neglect the surface/interface effects fail to provide reasonable results. Therefore, to analyze the problem the wave-function expansion method is coupled with the surface/interface elasticity theory. In order to provide some quantitative results through consideration of several examples, the knowledge of the relevant surface and/or interface properties of the corresponding constituent materials are required. For this reason, part of... 

Eshelby's theories on the nature of the disturbance strains due to polynomial eigenstrains inside an isotropic ellipsoidal inclusion, and the form of homogenizing eigenstrains corresponding to remote polynomial loadings in the equivalent inclusion method (EIM) are not valid for spherically anisotropic inclusions and inhomogeneities. Materials with spherically anisotropic behavior are frequently encountered in nature, for example, some graphite particles or polyethylene spherulites. Moreover, multi-inclusions/inhomogeneities/ inhomogeneous inclusions have abundant engineering and scientific applications and their exact theoretical treatment would be of great value. The present work is devoted... 

The usual continuum theories are inadequate in predicting the mechanical behavior of solids in the presence of small defects and stress concentrators; it is well known that such continuum methods are unable to detect the change of the size of the inhomogeneities and defects. For these reasons various augmented continuum theories and strain gradient theories have been proposed in the literature. The major difficulty in implication of these theories lies in the lack of information about the additional material constants which appear in such theories. For fcc metals, for the calculation of the associated characteristic lengths which arise in first strain gradient theory, an atomistic approach... 

It is well-known that classical continuum theory has certain deficiencies in predicting material's behavior at the micro- and nanoscales, where the size effect is not negligible. Higher order continuum theories introduce new material constants into the formulation, making the interpretation of the size effect possible. One famous version of these theories is the couple stress theory, invoked to study the anti-plane problems of the elliptic inhomogeneities and inclusions in the present work. The formulation in elliptic coordinates leads to an exact series solution involving Mathieu functions. Subsequently, the elastic fields of a single inhomogeneity in conjunction with the Mori-Tanaka theory... 

Due to inadequacy of the classical continuum theories at the nano-scale when dealing with defects, stress concentrators, and relevant deformation phenomena in solids, a refined approach that can capture the discrete atomic features of solids is essential. The inability to detect the size effect, giving unrealistically high values for some components of the stress field right on the edge of the stress concentrators, and infirmity to address the complex interaction between small inhomogeneities, cracks and as such when they are only a few nanometers apart, are among some of the drawbacks of the classical approach. An atomistic study which employs atomic finite element method in conjunction... 

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. Copyright © 2008 by ASME  

Nowadays, by adding a small amount (about 0.5–5% by weight) of a desired nanomaterial to a matrix having certain properties one may design a multifunctional nanocomposites with a remarkably improved macroscopic properties of interest. The capability of conventional continuum theories in treating the problems of embedded ultra-small inhomogeneity with any of its dimensions comparable to the characteristic lengths of the involved constituent phases is questioned, mainly, on the grounds of the accuracy and the size effect. The micromechanical framework based on the Eshelby's ellipsoidal inclusion theory [1] which has been widely used to estimate the overall behavior of composites falls under... 

To date, the examination of surface energy and surface layer relaxation has been the subject of several experimental and simulation works, whereas evaluation of surface residual stresses and surface elastic constants has received very little attention. In addition to the fundamental importance of these properties in the understanding of such phenomena as crystal equilibrium shape, surface roughening and segregation, they are also crucial for use in the theoretical studies based on continuum theory of elastic material surfaces. This work focuses on developing a theoretical approach for the calculations of the surface residual stress and surface elastic constants for (100) planes of fcc... 

Propagation of the torsional surface waves in a medium consisting of a functionally graded (FG) substrate bonded to a thin piezoelectric over-layer has been analytically formulated in the mathematical framework of surface/interface elasticity theory. In the cases where the wavelength and/or the thickness of the over-layer are comparable to the surface/interface characteristic length, then the surface/interface effects are not negligible. It is assumed that the over-layer is made of hexagonal 622 crystals with a single axis of rotational symmetry coinciding with the axis of polarization. The half-space is made of an FG transversely isotropic material in which the elasticity tensor and the... 

An elliptic micro-/nano-obstacle bonded to an infinite body incident upon by SH-waves, where both domains are couple stress media with micro-inertia, is of major concern. The formulation of this problem in the mathematical framework of couple stress elasticity with micro-inertia leads to angular and radial Mathieu differential equations which are solved analytically. These equations carry two characteristic lengths which are peculiar to the discrete nature of each domain enabling the capture of size effect, dispersion phenomenon, as well as the enhancement of the accuracy of the results. For verification, the ratio of the semi-axis of the elliptic obstacle is set equal to 1, and the result... 

To date, the examination of surface energy and surface layer relaxation has been the subject of several experimental and simulation works, whereas evaluation of surface residual stresses and surface elastic constants has received very little attention. In addition to the fundamental importance of these properties in the understanding of such phenomena as crystal equilibrium shape, surface roughening and segregation, they are also crucial for use in the theoretical studies based on continuum theory of elastic material surfaces. This work focuses on developing a theoretical approach for the calculations of the surface residual stress and surface elastic constants for (100) planes of fcc... 

In this work, after formulating the weakly nonlocal micromorphic equations of motion for non-Bravais crystals with general anisotropy, specialization to diamond structures is made. A critical dilemma is the determination of the elastic moduli tensor appearing in the equations of motion. From the equivalency of these equations with the pertinent equations obtained in the context of lattice dynamics, the expressions of the components of the elastic moduli tensors in terms of the atomic force constants are derived analytically. Subsequently, the atomic force constants are calculated via ab initio density functional perturbation theory (DFPT) with high precision. As a benchmark for the accuracy... 

The examination of the effect of couple stresses on anti-plane electro-mechanical behaviour of piezoelectric media is of interest. The constitutive equations of piezoelectricity for a transversely isotropic piezoelectric medium of crystal class C6 v = 6   mm are derived in the context of couple stress elasticity. In this framework, a characteristic length appears in the formulation of anti-plane problems, by which examination of the size effect is possible. Also stemming from this approach is a new elasticity constant defined as the ratio of couple stress to the curvature, which based on the assumption of positive definiteness of the internal energy density, must be positive. For... 

Consider a lamellar inhomogeneity embedded in an unbounded isotropic elastic medium. When the elastic moduli of the lamellar inhomogeneity are zero it is a crack, if its elastic moduli are infinite it is an anticrack, and when its elastic moduli are finite it is called a quasicrack. Based on the Eshelby's equivalent inclusion method (EIM), the present paper develops a unified approach for determination of the exact closed-form expressions for modes I, II, and III stress intensity factors (SIFs) at the tips of lamellar inhomogeneities under a remote applied polynomial loading. © 2006 Elsevier Ltd. All rights reserved  

By virtue of a method of displacement potentials, an analytical treatment of the response of a transversely isotropic substrate-coating system subjected to axisymmetric time-harmonic excitations is presented. In determination of the corresponding elastic fields, infinite line integrals with singular complex kernels are encountered. Branch points, cuts, and poles along the path of integration are accounted for exactly, and the physical phenomena pertinent to wave propagation in the medium are also highlighted. For evaluation of the integrals at the singular points, an accurate analytical residual theory is presented. Comparisons with the existing numerical solutions for a two-layered... 

A new meshless method called gradient reproducing kernel particle method (GRKPM) is proposed for numerical solutions of one-dimensional Burgers' equation with various values of viscosity and different initial and boundary conditions. Discretization is first done in the space via GRKPM, and subsequently, the reduced system of nonlinear ordinary differential equations is discretized in time by the Gear's method. Comparison with the exact solutions, which are only available for restricted initial conditions and values of viscosity, approves the efficacy of the proposed method. For challenging cases involving small viscosities, comparison with the results obtained using other numerical schemes... 

A major disadvantage of conventional meshless methods as compared to finite element method (FEM) is their weak performance in dealing with constraints. To overcome this difficulty, the penalty and Lagrange multiplier methods have been proposed in the literature. In the penalty method, constraints cannot be enforced exactly. On the other hand, the method of Lagrange multiplier leads to an ill-conditioned matrix which is not positive definite. The aim of this paper is to boost the effectiveness of the conventional reproducing kernel particle method (RKPM) in handling those types of constraints which specify the field variable and its gradient(s) conveniently. Insertion of the gradient term(s),... 

Gradient reproducing kernel particle method (GRKPM) is a meshless technique which incorporates the first gradients of the function into the reproducing equation of RKPM. Therefore, in two-dimensional space GRKPM introduces three types of shape functions rather than one. The robustness of GRKPM's shape functions is established by reconstruction of a third-order polynomial. To enforce the essential boundary conditions (EBCs), GRKPM's shape functions are modified by transformation technique. By utilizing the modified shape functions, the weak form of the nonlinear evolutionary Buckley-Leverett (BL) equation is discretized in space, rendering a system of nonlinear ordinary differential equations... 

A thin coating made of linear elastic functionally graded material (FGM) perfectly bonded to an elastic substrate is considered. This work which is of particular interest to tribological community is devoted to the determination of the thermal and mechanical stresses due to mixed normal and tangential Hertzian surface pressure. The thermomechanical properties of the FGM coating are assumed to vary exponentially through the thickness. Solutions for temperature rise and stresses are obtained by use of Fourier transform technique. The influences of coating thickness, Peclet number and friction coefficient on temperature rise and stresses in the FGM coating are investigated. Comparative studies... 

The stress intensity factors (SIFs) for an arbitrarily oriented plane crack in the vicinity of a coated circular fiber is being sought. The method of solution is based on Shodja and Sarvestani’s [1] equivalent inclusion method (EIM) for multi-inhomogeneity systems, which is an extension of Eshelby’s [2] theory for a single ellipsoidal inhomogeneity. The proposed approach is very robust in the sense that it can effectively and systematically be applied to wide variety of fundamental problems, which are essential for micromechanical studies of composite materials, for example, see, Shodja et al. [3], Shodja and Roumi [4],[5]