Sharif Digital Repository

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... 

Direct/inverse scattering of high frequency SH-waves by a circular micro-/nano-fiberembedded in an infinite elastic isotropic medium is addressed in the framework of couple stresstheory with micro inertia. The inadequacy of classical theory of elasticity in the problems dealingwith propagation of high frequency waves as well as the problems concerning the elastic fields inthe vicinity of micro-/nano-size defects in which the wavelengths and the size of the defects arecomparable to intrinsic length of the material is well-known. These dilemmas can be remedied byemploying the more accurate higher order continuum theories. So, in the context of couple stresstheory with micro inertia, the... 

This thesis presents an analytical solution for determination of the
electro-elastic media subjected to an anti plane shear harmonic wave containing a multi-phase cylindrical fiber whose electro-elastic properties differ from those of the matrix. Both the matrix and the coated-fiber system are transversely isotropic piezoelectric materials with symmetry and poling axes parallel to the fiber axis. The coating can have variable thickness. The dynamic electro-mechanical equivalent inclusion method (DEMEIM) is presented and employed as an extension of dynamic equivalent inclusion method (DEIM) in order to take into account the electro-mechanical coupling. Accordingly, the coating-fiber... 

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... 

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... 

It is the main idea of present thesis to provide a micromechanical method as a general treatment for several fundamental problems of the piezoelectric inhomogeneities. For initial demonstration of pertinent methodology, a single piezoelectric inhomogeneity of ellipsoidal geometry, under non-uniform far-field loading is considered. Accordingly, it is taken equivalent to elastic and dielectric inclusion problems connected by proper eigenstrain-electric field. This approach is named the electro-mechanical equivalent inclusion method (EMEIM) and requires that the electroelastic fields of the inhomogeneity to be equal to fields of the equivalent inclusions. Afterwards, the complex problem of... 

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... 

With the progress of engineering science, the development of underground spaces and buried tunnels has witnessed remarkable expansion. Considering the frequency of hazardous events such as earthquakes and unforeseen consequences arising from underground activities and geology in underground engineering, the determination of the Dynamic Stress Concentration Factor (DSCF) has been widely recognized as a crucial factor in the study and design of tunnels and underground structures. It is also extensively considered in evaluating their damage. The investigation of wave dispersion and determination of the stress concentration factor was first proposed by Sezawa (1927). In this study, the... 

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... 

The electro-elastic fields of nano-sized piezoelectric structures are considered based on the non-classical continuum theory. Nowadays because of increasing the application of piezoelectric materials in nano technology and exclusive properties of this kind of materials, they can use as the ingredients of electromechanical systems. Therefore, the determination of induced electro-mechanical fields is important. In this study the constitutive equations based on non-classical continuum theory and general anisotropy for the elastic, piezoelectric and dielectric tensors are considered, and the electromechanical fields are determined using the micromechanical method. Furthermore, the size effects... 

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... 

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... 

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... 

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... 

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... 

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... 

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... 

For half a century, the problem of extracting the components of the nonlocal moduli tensor of anisotropic materials has been remained unsolved. In the present work, for the first time, the solution of this problem is proposed and the components of nonlocal moduli tensor are obtained for close-packed crystals, i.e. face center cubic or hexagonal closed packed. To this end, new distinct nonlocal kernel functions which have the characteristics of discrete atomistic Green’s functions in the stress space are obtained through consideration of the nonlocal dispersion relations. Each of dispersion relations are associated with certain directions and are combined with ab initio Density Functional... 

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,...