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#### Analysis of a Lamellar Inhomogeneity Via Repordusing Kernel Particle Method

, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

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...

#### Propagation of SH Wave in Elastic Media with Cylindrical Inhomogeneity at Micro and Nano Scales by Couple Stress Theory

, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

It is well known that the classical continuum theory does not consider size effect in predicting material’s behavior, however at the micro and nano scales, this effect is not negligible and the classical theory has deficiencies at these scales. To take into account the size effect, higher order continuum theories introduce new material constants into the formulation. One famous version of these theories is couple stress which is applied in this research. This theory considers size effect of inhomogeneity by employing Characteristic length of materials. Quasi-static couple stress and classical dynamic approaches do not include explicitly the size of the material unit cell in the formulation...

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Elastoplastic Analysis of Planar Cracks Under Tension Using RKPM

,
M.Sc. Thesis
Sharif University of Technology
;
Mohammadi Shodja, Hossein
(Supervisor)
Abstract

During recent years, many researches on meshfree methods to solve differential equations and crack problem have been accomplished, and acceptable results have been obtained. One of these methods which is widely used in fracture mechanics specially in problems including crack is RKPM (reproducing kernel particle method). RKPM is one of the modern numerical methods in solving differential equations that has been lately introduced and developed. In this method, the genuine response of the system is replaced with a good approximation of the real response called ‘Reproduced Function’. The formulation of this method obviates the need for discretizing the domain by meshing with elements. In this...

#### Calculation of the Additional Constants for Fcc Materials in Second Strain Gradient Elasticity: Behavior of a Nano-Size Bernouli--Euler Beam with Surface Effects

, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

In addition to enhancement of the results near the point of application of a concentrated load in the vicinity of nano-size defects, capturing surface effects in small structures, in the framework of second strain gradient elasticity is of particular interest. In this framework sixteen additional material constants are revealed, incorporating the role of atomic structures of the elastic solid. In this work, the analytical formulations of these constants corresponding to fcc metals are given in terms of the parameters of Sutten-Chen interatomic potential function. The constants for ten fcc metals are computed and tabulized. Moreover, the exact closed-form solution of the bending of a...

#### Studying Edge Dislocations and Wedge Disclinations in Core-Shell Nanowires by Incorporating Surface Effect

, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

By considering the effect of surface/interface stresses, classical problems of the interaction between dislocations/disclinations and nanowires are addressed. In particular, two distinct problems are solved: the first one consists of an edge dislocation seated inside the shell of a core-shell nanowire and the second one investigates a wedge disclination (dipole) located inside the shell of a core-shell nanowire. The stress field of the nanowire, strain energy per unit length and the image forces acting on the defects are calculated and discussed in detail. Moreover, the results are compared with their classical counterparts. These results show that by considering the effect of...

#### Surface/Interface Effect on the Interaction of an Embedded Core-Shell Nanowire and Edge Dislocation and Generation of Misfit Dislocations in a Core-Shell Nanowire

, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

Within the surface/interface elasticity, two following problem are solved: First the elastic behavior of an edge dislocation located inside the core of a core-shell nanowire which is embedded in an infinite matrix is studied within the surface/interface elasticity theory. The corresponding boundary value problem is solved exactly by using complex potential functions. The stress field of the dislocation, image force acting on the dislocation, and the dislocation strain energy is calculated by considering the interface effect. Second, the surface/interface elasticity approach is applied to the case of a misfit core-shell nanowire system in which the misfit strain is adjusted through the...

#### Determination of Elastic Surface Constants for fcc Materials and their Applications in Nanostructures

, Ph.D. Dissertation Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

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...

####
Determination of the Two-Dimensional Plastic Zone Size and SIF at the Crack Tip Using RKPM

,
M.Sc. Thesis
Sharif University of Technology
;
Mohammadi Shodja, Hossein
(Supervisor)
Abstract

It is proposed to obtain the mode I plastic zone size and shape at the crack-tip in a work-hardening material using reproducing kernel particle method (RKPM). RKPM is a meshless technology which has proven very useful for solving problems of fracture mechanics. Ramberg-Osgood stress-strain relation is assumed. In this project the crack-tip stress intensity factor (SIF) before and after formation of the plastic zone will be examined. To impose the essential boundary conditions, penalty method is used. To construct the shape functions in the vicinity of the crack and crack-tip, both the diffraction and visibility methods are employed. The effects of different dilation parameters on SIF under...

#### First Principles Studies of Mechanical, Physical, and Electronic Properties of a-Si - also, Diffusion of a Self-interstitial Atom in an Ultra-thin fcc Film Via Lattice Statics

, Ph.D. Dissertation Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

By employing first principles density functional theory-based (DFT) molecular dynamics (MD), the influences of dangling and floating bonds as well as distorted tetrahedral bonds are studied on the mechanical, physical, and electronic properties of amorphous Si (a-Si). For further examination of the effects of these geometrical defects, two distinct amorphous samples, namely as-quenched and annealed are generated and examined. To verify the validity of the representative cells, the obtained radial distribution function, pair correlation function, and cohesive energy are compared with those corresponding results presented in the literature. Moreover, the surface energy is calculated at final...

####
Studying the Interaction Between Dislocation Sandin Homogeneities in Nano-Scale, by Incorporating Surface Effect

,
M.Sc. Thesis
Sharif University of Technology
;
Mohammadi Shodja, Hossein
(Supervisor)
Abstract

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...

#### Elastic Fields of a Confocal Elliptic Ring at the States of Plane Strain and Plane Stress

, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

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...

#### Innovative Theories of Micro and Nano Ellipsoidal Inclusion and Inhomogeneity in Magneto-electro-elastic Media with General Anisotropy

, Ph.D. Dissertation Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

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...

#### Calculation of the Energy Release Rate of Nano-Cracks in FCC Materials Via the Many Body Atomic Scale FEM

, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

Since the classical continuum theory fails to deal with the problems associated with defects, stress concentrators, and relevant deformation phenomena in solids, alternative approaches that can detect the atomistic nature of materials' fracture are required. The deficiency of the capture the size effect which yields delusively high values for some components of the stress field right on the edge of the stress concentrators, and its weakness in describing the complex interaction between small inhomogeneities, cracks and the like when they are only a few nanometers apart, are among some of the disadvantages of the classical approach. In recent years, however, atomistic methods are emerging to...

#### Mixed Boundary Value Problems in Transversely Isotropic Materials

, Ph.D. Dissertation Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

By virtue of a robust and efficient method, the solution of triple and quadruple integral equations which are the keys of various mixed boundary value problems corresponding to half-space and full-space media is addressed. These multiple integral equations are reduced to a well-known Fredholm integral equation of the second kind. In order to write the governing integral equations of the problem, Green’s functions play an important role. Therefore, Green’s functions of homogeneous and non-homogeneous transversely isotropic media in the form of line integrals including Bessel functions are obtained. Three interesting mixed boundary value problems in transversely isotropic materials are...

#### A Nanoscopic Approach to the Determination of the Elastic Constants of Cubic Crystals in first Strain Gradient Theory

, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

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...

#### Modeling Material Discontinuities Via An Augmented RKPM and Performance of GRKPM in Fracture Mechanics

, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

During the past decade, element free methods have achieved great successes. One of these methods is the so called RKPM which has a suitable structure for use in fracture mechanics problems. Despite all characteristic abilities of element free methods; these methods due to their higher order continuous differentiable approximations fail to model discontinuous material properties of the subjected domains. In this study by improving the collocation method in RKPM treatment of such conditions have been achieved. Also in this study performance of a new meshfree method in fracture mechanics problems has been analyzed. GRKPM is one of these methods which its suitable accuracy and convergence has...

#### Effective Shear Modulus of Elastic Solids Reinforced by Coated Elliptic Nanofibers in the Context of Couple Stress and Micropolar Theories

, Ph.D. Dissertation Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

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...

#### GRKPM: Theory and Applications in Laminated Composite Plates and Nonlinear Evolutionary Partial Differential Equations With Large Gradients

, Ph.D. Dissertation Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

Reproducing kernel particle method (RKPM) is a meshfree method for solving various differential equations. RKPM is based on pure mathematics; therefore, it is in the center of attention of many scientists. One major problem in RKPM is satisfying the essential boundary conditions (EBCs) involving the derivative of the field function. This problem is considered herein and its solution is proposed. To this end, two actions should be undertaken. First, the concept of Hermitian interpolation is employed to add the derivative term to the reproducing equation of RKPM and a new meshless method called gradient RKPM (GRKPM) is introduced. Second, the corrected collocation method is modified so...

#### Elastic Field of an Anticrack Via Reproducing Kernel Particle Method

, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

Meshless Methods using kernel approximation like Reproducing Kernel Particle Method (RKPM) are methods for solving partial differential equations that require only nodal data and a description of the geometry without requiring element connectivity data and mesh producing. An innovative method of nonplanar material partitioning method (NMPM) with implementation of RKPM is employed to calculate the stress intensity factor (SIF) at the tip of an anticrack sited in an isotropic plate under a remote applied loading. Numerical examples in comparison with the exact closed form expressions show that accurate SIF for mode I can be obtained.

#### Surface/Interface Effects on The Scattering of In-Plane Elastic Waves by a Multi-Coated Nanofiber

, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

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...