Sharif Digital Repository

Traditional continuum theory of elasticity becomes remarkably inaccurate in the vicinity of singularities, and when the size eect is of concern. For example in the study of ultra-small objects and ultra-thin lms, near defects, near point of application of a concentrated load and as such, the classical solutions are not reliable. This work focuses on determination of the elastic elds of an edge dislocation near the grain boundary of two perfectly bonded nano-size crystals. It is proposed to study this problem in the context of surface/interface elasticity, and incorporate the eect of the grain boundary on the elastic elds. In contrast to the surface/interface elasticity theory, traditional... 

The  usual  continuum  theories  are  inadequate  in  predicting  the  mechanical  behavior of solids in 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.  For  fcc  metals,  for  calculation of the associated characteristic lengths which arise in first strain gradient  theory,  an ... 

Classical continuum mechanics fails to give an accurate solution near the crack tip, moreover, it implies that a solid is able to sustain an infinite stress at the Griffith-Inglis crack tips. Among other critical issues is the inability of classical approach to sense the size effect. For these reasons, for more in-depth understanding and accurate behavioral predictions, it is essential to develop some atomistic methods which properly accounts, not only for the structure but also the long and short range atomic interactions effectively. In this work the interaction of coated inhomogeneity and crack under polynomial loading is simulated by using the many body Rafii-Tabar and Sutton potential... 

In this project the goal is to study where, when and how the cracks in the steel connection plate between beam and column initiate and how far would the crack grow before failure and how to detect crack initiation by utilizing piezoelectric sensors. In this analysis piezoelectric is placed in line of crack propagation for sensing strain and changing it to voltage. A thin plate with edge notch which is an ideal model of typical beam to column connection is assumed. The plate is subjected to a uniaxial uniform load. With the aid of ANSYS software, the plate is analyzed in both elastic and plastic stages. The strain-stress curve with kinematic hardening part is considered and modeled with... 

In this thesis one of the mesh-free methods called RKPM is employed to solve the differential equations of strain-gradient elasticity. To this end the corresponding weak form is laid down. Subsequently the relevant stiffness-matrix is obtained by discretization of the weak form. To be sure about the accuracy of the relations, the problem of a plate weakened by a hole under uniform far-field tension, for which the exact solution is available in the literature, is solved. The obtained numerical result is in good agreement with the solution of Eshel and Rosenfeld. Afterwards, a plate containing a crack of finite length subjected to uniform far-field tension (mode I) is considered. This problem... 

The so-called moving least square reproducing kernel method (MLSRKM), which is a meshfree Galerkin method, has two special properties in comparison with its prior version, say moving least square method (MLSM): (i) stability in preserving completeness conditions to the desired order for a discrete reproducing formula due to implementation of shifted and scaled basis, (ii) use of more accurate quadrature weights in a discrete reproducing form, especially along boundaries. However, because of employing shifted basis in MLSRKM, some of enrichment techniques, specifically in the context of linear elastic fracture mechanics (LEFM) problems, cannot be applied to this method. Therefore, we are... 

Determination of the elastic fields associated with a spherical multiply-coated inhomogeneous inclusion is a problem of great interest among researchers. In this work a set consisting of N+1 concentric spherical domains is considered. Each domain is either isotropic or spherically isotropic and is functionally graded (FG) in the radial direction. The outermost spherical surface is subjected to nonuniform loading and the constituent phases are subjected to some prescribed nonuniform body force and eigenstrain fields. When the outermost domain is an unbounded medium with zero eigenstrain and body force fields then an N-phase multi-inhomogeneous inclusion problem is realized for which the... 

In this research, a new Kirchhoff plate model based on the modified couple stress theory has been utilized to derive the corresponding closed-form expression for the buckling load. Moreover, a numerical mesh-less method, Reproducing Kernel Particle Method (RKPM), in combination with Corrected Collocation Method (CCM) has been employed to model the nano-plate and calculate its buckling load in the framework of the modified couple stress theory. To this end, two kinds of nano-plates have been modeled, the square nano-plates with all edges simply supported 1) in the presence of the nano-void and 2) without the nano-void. It should be noted that the analytical and numerical solutions for the... 

The broad range of applicability of nano devices particularly in electronics, optoelectronics, and micro/ nano-electro- mechanical systems has drawn the attentions of the industrial and scientific communities of various disciplines. This work is devoted to study the effect of surface and interface elasticity in the analysis of the mechanical behavior of ultra-thin objects in the presence of some statical or dynamical loadings. Based on the fact that the surface-volume ratio increases in nano-scale, description of the behavior of such a small structure via usual classical theories, which generally neglect the surface/interface effect, ceases to hold. In the present study, first, a... 

Based on Hamilton’s principle, a three-dimensional semi-analytical method for the analysis of free vibration of a nano-composite plate within the couple stress theory is developed. Computation of dynamic behavior as well as natural frequencies and mode shapes is interested. In this method, the mechanical displacement functions, in each layer, are defined as product of a base function and a three-dimensional polynomial with unknown coefficients. The base functions are defined with respect to the kinematical boundary condition and the domain geometry. The mode shapes will be obtained and the accuracy of the present approach is demonstrated by comparison it in both classical elasticity and... 

An accurate numerical methodology for capturing the field quantities a center lamellar inhomogeneity within the interface of two different phases of a bimaterial rectangular plate subjected to non-uniform tensile stress, in the context of reproducing kernel particle method (RKPM), is of particular interest. For this purpose the innovative numerical technique, so-called extended augmented corrected collocation method is introduced; this technique is an extension of the augmented corrected collocation method used for imposing continuity condition of the displacement at the interface. The robustness of this methodology is shown by solving problems of material discontinuities, namely plates... 

In this study, an analytical solution is presented for anti-plane scattering of Love waves by a surface-breaking crack normal to the free surface of an ultra-thin layer bonded to a semi-infinte medium within the surface/interface elasticity theory. The Fourier transform techniques are used to formulate the corresponding mixed-boundary value problem as a singular integral equation of the Cauchy type which is solved numerically. Mode III dynamic stress intensity factor at the crack tip, crack face and crack mouth opening displacements, the reflection coefficient at large distances from the crack face, and the stress field on the interface are computed and plotted for different valued of... 

The investigation of interface residual stress and interface elastic moduli tensors plays a crucial role in enhancing the conventional theory of elasticity. These considerations allow us to account for size effects and eliminate nonphysical singularities near defects. The primary objective of this study is to comprehensively calculate interface energy, residual stress components, and interface elastic moduli tensors for various interfaces between non-magnetic fcc metals using density functional theory (DFT). We achieve this by performing ab initio DFT calculations to determine the interface energies for different coherent interfaces among these metals. Subsequently, these energies are... 

Studying the behavior of piezoelectric materials containing self-assembled quantum wires and quantum dots is of great interest. This work is devoted to analytical and exact determination of the electro-elastic fields associated to quantum wires and quantum dots in piezoelectric mediums. The present work accounts for: (1) different shapes and orientations of quantum wires and quantum dots, (2) different types of anisotropy, and (3) high concentrations of quantum wires and quantum dots, that is, the corresponding interaction is considered properly. The presented solution is valid for general anisotropy and different shapes of quantum wires and quantum dots. In this work, periodic and... 

The principle of micromechanics has been used to determine the maximum allowable press-fit for the hip stem during total hip arthroplasty. A 2D parametric solution has been presented. Bone and stem cross sections are modeled parametrically with respect to their geometry and mechanical properties. Surrounding soft tissue is also modeled and all the participating materials are considered as linear isotropic. Drucker-Prager fracture criterion is used to interpret the fracture phenomenon which is considered as both strain- and stress-state fracture. Considering presence of a thin layer of cancellous bone in the model caused a significant increase in results in comparison with previous numerical... 

Vibration is one of the most important factors in design, operation and lifetime of drill strings. There for, investigation of vibrations in drill string, like every other rotary machine, is very important. The main goal of this research is developing a nonlinear model for a drill string system dynamics in an inclined well. Effects of drilling mud flow rate, weight on bit, angular velocity along with viscous damping, on the stability and vibration of a drill string are studied. Dynamic equation of the model is developed considering axial displacement and lateral bending geometric nonlinear coupling. The effect of drilling mud flow is modeled using Paidoussis formulations. Equation of motion... 

Viability and proliferation of cells in cell culture mainly depends on i) cell culture medium, ii) cell-cell interaction, and iii) the supporting scaffold. Among these factors, and within recent years, surface and mechanical properties of the supporting ECM has attracted many researchers. Experiment results show that the animal cell adhesion is accelerated on stiffer scaffolds. Electrical charge of the scaffold is also a determinant term in the kinetics of adhesion and on a relatively charged scaffold, one can expect an increment in kinetics of adhesion front movement. This is due to the natural negative charges of the cell wall membrane. In this thesis, an analytical model is proposed to... 

Nowadays, multifunctional two-dimensional (2D) nanostructured materials due to their important role in biomedical and nanotechnological developments have gained the attention of many engineers and scientists with a wide spectrum of disciplines. The present work aims to provide an accurate description of the tensile behavior (from the initial unloaded state through axial strain of about 0.25) of the planar as well as low-buckled stanene and to capture their ideal strength in armchair- and zigzag-directions. Stanene is 2D hexagonal lattice which belongs to D6 hcrystal class having a six-fold rotational symmetry. For an accurate description of anisotropic response of such hyperelastic materials... 

This project presents an outline of the crack tip stress fields in the presence of a plastic enclave around a growing fatigue crack using RKPM and Drucker-Prager criterion for pressure sensitive materials such as concrete and rock. Two distinguished features of RKPM are the arbitrarily high order smoothness and the interpolation property of the shape function which has kronecker delta property at the associated nodes. This method has proved to handle extreme material deformation and moving discontinuities. For the frictional materials such as rock in geotechnical engineering, a non-associated or associated Drucker- Prager plasticity model is appropriate for modeling its constitutive...