Sharif Digital Repository

Capture of the discrete nature of crystalline solids for the purpose of the determination of their mechanical behavior with high precision is of interest. To achieve this objective, two fundamental contributing factors are on top of the list: (1) formulation in the mathematical framework of an appropriate higher order continuum theory rather than using classical treatment, and (2) incorporation of the true anisotropy of the media. The present work revisits Toupin–Mindlin first strain gradient theory for media with general anisotropy, and then specialize it to cubic crystals of hexoctahedral class. This formulation in addition to 3 classical material constants encountered in classical theory... 

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  

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]  

The elastica is referred to the shape of the curve into which the centreline of a flexible lamina is bent. Hence, single-walled carbon nanotubes (SWCNTs) are treated as the elastica obtained from bending of graphene. The corresponding large deformation accompanies both the material and geometrical non-linearities. The morphology of the free-standing SWCNTs such as the natural angle of twist, bond lengths, tube radius and wall thickness are determined. Moreover, it is shown that the induced self-equilibriated strain field has a remarkable impact on the mechanical behaviour of the nanotube. Utilization of an appropriate non-linear continuum constitutive relation for graphene leads to exact... 

The present work aims to provide an accurate description of the tensile behavior of the planar as well as low-buckled stanene and to capture their ideal strength in armchair (AC)- and zigzag (ZZ)-directions. For an accurate description of anisotropic response of such hyperelastic materials as stanene, consideration of a highly nonlinear constitutive model in which up to the fourth power of strains is incorporated is inevitable. By utilizing first principles calculations based on density functional theory (DFT), the second, third, fourth, and fifth order elastic moduli tensors corresponding to both planar and low-buckled states are obtained. Moreover, the morphology of the free-standing... 

Examination of the role of strain on the quantum spin hall (QSH) effect and band inversion for the monolayer of tin, stanene, is of interest. To this end, several uniaxial and biaxial strain loadings along the armchair (AC)- and zigzag (ZZ)-directions are applied using first principles calculations based on density functional theory (DFT). We observe QSH insulator as well as semi-metallic property associated with the strained stanene. © 2017 Elsevier B.V