Sharif Digital Repository

In many problems, the traditional elasticity cannot predict phenomenon such as nano-scale defects, surface effects, and stress concentration correctly. For example, analysis near the crack tip, dislocation and inhomogeneity shows inconsistent results because in this case values of stress go to infinity. Therefore for solving these kinds of problems, higher order continuum theories were introduced. The appearance of additional constants in the equations of motion can represent the atomic nature of materials. Furthermore, they can be utilized for determining properties of materials vibration with high frequency, granular materials, and polymers.First strain gradient theory introduced by... 

In this thesis an analytical solution is introduced for finding the elastic fields of stress and strain in a confocal elliptic ring at the state of general plane problem. A confocal elliptic ring is a doubly connected region which its external and internal boundaries are ellipses with the same focal points. We used the method of complex variables, the functions of Kolosov-Muskhelishvili potentials, Laurent series expansion for analytical functions, the method of the analytic continuation of Milne-Thomson, elliptic hyperbolic coordinates, and two dimensional conformal mapping to do this study. the importance of this analysis is because we can simulate some problems of the elasticity by... 

Our study is mainly related to speaker verification systems. Given a speech segment and a claimed identity, these systems must decide whether the claimant is admissible or a fraud. Our main focus in on making the speaker verification system robust in case of limited training data. When there is limited training data, the accuracy of speaker verification systems reduces drastically. Our main purpose is to review this problem deeply and to represent methods in order to encounter this challenge. Recently, some methods such as PLDA and distance metric learning have been applied in text-independent speaker verification in order to encounter limited data crisis. One of the important cases in which... 

Nowadays, by adding a small amount 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. In this work, effort is firstly directed at the prediction of the macroscopic shear modulus of composites consisting of nano-/micro-size fibers of elliptic cross-sections via couple stress theory, a... 

This work focuses on developing a theoretical approach for the calculations of the surface elastic constants for (100) planes of fcc crystals. Using this method, the surface elastic constants, as well as the surface residual stress of the (100) planes of Al, Ag, Ni, Pt, and Cu fcc crystals, are evaluated using quantum calculations and VASP code. Surface effects are important in nanostructures and the considered metals are the most applicable ones in nanostructures especially in optic and electronic fields. For verification of the obtained values for surface elastic constants and residual stress, other surface parameters including the equilibrium lattice parameter, the energy per atom of the... 

The elastic field is one of the challenges in optimizing the lifetime and capacity of the lithiumion batteries. Graphite nanoparticles have been widely used in Li-ion batteries, due to their mechanical, thermal and electrical properties. During the lithiation, chemical reactions occurred in the electrolyte, which forms a solid electrolyte interphase(SEI) in the surrounding of nanoparticles as well as stress fields inside the nanoparticles. Therefore, the purpose of this research is to examine the effects of the surface/interface on diffusion induced stresses(DIS) within core-shell nanosphere due to non-uniform distribution of eigenstrain fields. Due to the mechanical behavior of the phases,... 

The elastic field is one of the challenges in optimizing the lifetime and capacity of the lithium-ion batteries. Graphite nanoparticles have been widely used in Li-ion batteries, due to their mechanical, thermal and electrical properties. During the lithiation, chemical reactions occurred in the electrolyte, which forms a solid electrolyte interphase(SEI) in the surrounding of nanoparticles as well as stress fields inside the nanoparticles. Therefore, the purpose of this research is to examine the effects of the surface/interface on diffusion induced stresses(DIS) within core-shell nanosphere due to non-uniform distribution of eigenstrain fields. Due to the mechanical behavior of the phases,... 

In this thesis, concerning Eigenstrain Theory, the micromechanical formulation of dental implants has been derived for the first time in the fields of Mechanics and Medical Science. The proliferation of using dental implants as a prosthesis for the people who lost their teeth because of poor maintenance and smoking cigarette results in scientists think more about the design of these implants and their stress fields inside the mandible. It is crystal clear that these stress fields cause stress shielding, which is a phenomenon that brings about bone loss or decrement in the bone density. Hence, if we know the stress that is produced by the implants inside the mandible, we can optimize the... 

In the past few decades piezoelectric materials have gained extensive applications in electromechanical devices and smart composite materials. Composite piezoelectric materials posses better piezoelectric effects as compared with the homogeneous piezoelectric materials. A special type of composite piezoelectric materials is multiphase spherical ensemble. Consider a set of (N + 1)-phase concentric spherical piezoelectric ensemble consisting of a core region encased by a sequence of nested spherical layers. Each phase is spherically isotropic, the polling direction of it, is radially oriented and it is also functionally graded piezoelectric material (FGPM) in the radial direction. This paper... 

The exact analytical elastic fields within a double-walled silicon nano-tube with a thin layer of SiOx coating associated with surface/ interface effects as well as the classical theory of elasticity due to the presence of an edge dislocation with an arbitrary Burger’s vector and position inside of the silicon is determined via complex potential function method. Stress contours within surface elasticity and classical theory are given, and both theory results are compared. Then, the effects of surface Lamé Constants, magnitude and direction of Burger’s vector, shear modulus, nano-tube size, and position of the edge dislocation on the distribution of stress components are illustrated, and the... 

The aim of this study is to investigate the propagation of anti-plane shear waves in an elastic medium composed of periodic nanolayers (metamaterials) with deformable interfaces.Some of interesting properties of metamaterials are band-gaps and negative refraction angle.In nanolayered mediums the effect of interface becomes significant and classical continuum theory is not sufficient individualy. In this research by introducing 4 interface parameters and adding some equations to classical continuum theory, the possibilty of discontinuity of traction and displacement across the interface is provided and the effect of interface is considered. Then, a functional representing the energy of the... 

It is well-known that classical continuum theory has certain deficiencies in capturing the size effects and predicting the nanoscopic behavior of materials in the vicinity of nano-inhomogeneities and nano-defects with reasonable accuracy. Couple stress theory which is associated with an internal length scale for the medium is one of the higher order continuum theories capable of overcoming such difficulties. Since most reinforcements may not be perfectly bonded to their surrounding matrix, the perfect bonding condition is often inadequate in describing the physical and mechanical behavior of real composite materials. In this work, the problem of a nano-size fiber embedded in an unbounded... 

This work examines the problem of the fully coupled magneto-electro-elastic (MEE) scattering of SH-waves incident upon a heterogeneous MEE scatterer which is embedded in an unbounded medium. The scatterer consists of a circular core and a circular encapsulator with eccentricity. All three regions: the core, encapsulator, and the surrounding matrix have distinct MEE properties and fully coupled constitutive relations. The generated coupled MEE fields coexist simultaneously in all these regions without resort to any simplifying assumptions. The precise description of the multifunctionality involves the solution of three fully coupled partial differential equations in three different regions.... 

The aim of this work is to investigate the surface effects on SH wave propagation in ultra-thin layers with body-centered cubic single-crystal and face-centered cubic single-crystal structures, as well as Love and Rayleigh surface waves propagation in a single crystalline bcc half-space solid.Due to the wide application of wave propagation in science and technology, this issue has attracted the attention of many researchers and engineers. Wave propagation is used in surface science, coustoelectronics, and non-destructive evaluations.In this study, ultra-thin layers have thicknesses between 2 and 6 nm. For such layers, the physical and mechanical effects of surface are not negligible.It is... 

Studying the behavior of electromechanical systems containing nanostructures, because of their widespread applications in the nanoscience and technology is of great interest. For this purpose, this work is devoted to analytical and exact determination of the electroelastic fields associated with periodic and arbitrary distributions of electromechanical nano inclusions and nano inhomogeneities of various shapes within electroelastic mediums of general anisotropy. Since classical continuum Theories are inadequate in accounting for size affects in nanostructures, a first strain gradient - first electric field gradient theory is applied. The present work considers Piezoelectric and Flexoelectric... 

In the current work, the two- and three-dimensional electro-elastic fields of periodically as well as arbitrarily distributed interacting quantum wires (QWRs) and interacting quantum dots (QDs) of arbitrary shapes within a piezoelectric matrix are studied analytically. The lattice mismatch between the QWR/QD and the barrier is accounted through prescribing an initial misfit strain field within the QWR/QD. The distinction between the electro-mechanical properties of the QWR/QD and those of the barrier is treated by introducing a novel electro-mechanical equivalent inclusion method in Fourier space (FEMEIM). Moreover, the theory can readily treat cases where the QWRs/QDs are multi-phase or... 

Nowadays, the excellent technological applications of composites have attracted the attentions of industry and numerous scientists. They are advantageous for their high tensile modulus, strength, and promising electrical and thermal properties. In applying the approach of lamellar inhomogeneity to real composites, the micro-geometries of the reinforcement must be considered such that they can be approximated as limiting case of an ellipsoid. In vapor grown carbon nanofiber, the fiber may have a diameter of about 150nm and length of 10-20 µm [1]. The modulus of carbon nanofiber is normally in the range of 100-600 GPa and sometimes even higher, whereas the modulus of some polymers is usually... 

In this thesis, some new models have been solved via RKPM method, which is one of the meshfree methods family. These models have never been solved via meshfree methods and their analytical solutions do not exist. At first, the RKPM shape functions and their first derivative formulation in 1D and 2D have been presented and then by using FORTRAN program, the shape functions and their first derivative have been obtained. To verifying the code some functions have been reproduced. In the next step by using the governing equations and penalty method whose formulation exists in chapter 2; some famous examples in linear elasticity have been solved via RKPM to verify the FORTRAN code. At last; some... 

By considering the effect of surface/interface stress, classical problems of the interaction between dislocations and inhomogeneities are addressed. Especifically two distinct problems are solved, the first one is consisted of an edge dislocation located near an elliptical nano-inhomogeneity and the second one hasa screw dislocation laid in the core-shell nanowire. The stress field as well as the image force on the dislocation are calculated and discussed in detail. Results show that by decreasing the dimension of the problem to nano-scale, the differences between classical elasticity and surface approachincrease rapidly. By considering the effect of the surface/interface stress, new... 

In the framework of surface elasticity theory, the scattering of in-plane elastic waves by a multicoated nanofiber embedded in an elastic matrix is studied. Atoms near an interface experience a local environment different from it within the bulk. Going from macro to nano dimensions, surface to volume ratio increases significantly. Thus, on this scale it is important to consider the surface/interface properties as well as the bulk properties. In this dissertation, the surface/interface is modeled by a very thin layer in which the traction and displacement are discontinuous. Effects of surface/interface parameters on the dynamic stress concentration factor (DSCF) and scattering cross section...