Sharif Digital Repository

Incorporation of the first gradient of strain, in addition to the strain itself, into the strain energy density of an elastic solid leads to Mindlin's first strain gradient theory, which is useful for examination of size effect as well as other mechanical phenomena at the nano-scale. For isotropic elastic solids, the first strain gradient theory, in addition to the two independent Lamé constants, gives rise to five new material constants which in turn reduce to two material parameters, ℓ1 and ℓ2 with dimension of length. The evaluation of these parameters, however, has posed serious challenges, both experimentally and theoretically. In this work ab initio method is used to compute the... 

An elliptic micro-/nano-obstacle bonded to an infinite body incident upon by SH-waves, where both domains are couple stress media with micro-inertia, is of major concern. The formulation of this problem in the mathematical framework of couple stress elasticity with micro-inertia leads to angular and radial Mathieu differential equations which are solved analytically. These equations carry two characteristic lengths which are peculiar to the discrete nature of each domain enabling the capture of size effect, dispersion phenomenon, as well as the enhancement of the accuracy of the results. For verification, the ratio of the semi-axis of the elliptic obstacle is set equal to 1, and the result... 

Mesoscopic hydrodynamic equations are solved to investigate the dynamics of nanodroplets positioned near a topographic step of the supporting substrate. Our results show that the dynamics depends on the characteristic length scales of the system given by the height of the step and the size of the nanodroplets as well as on the constituting substances of both the nanodroplets and the substrate. The lateral motion of nanodroplets far from the step can be described well in terms of a power law of the distance from the step. In general the direction of motion depends on the details of the effective laterally varying intermolecular forces. But for nanodroplets positioned far from the step it is... 

The application of higher order continuum theories, with size effect considerations, have recently been spread in the micro and nano-scale studies. One famous version of these theories is the couple stress theory. This paper utilizes this theory to study the anti-plane problem of an elliptic nano-fiber, embedded in an infinite medium, both made of centrosymmetric isotropic material. In this framework, a characteristic length appears in the formulation, by which examination of the size effect is possible. This work presents an analytical solution for the proposed problem. Copyright © 2008 by ASME  

Nanoscopic elastic behavior of the field quantities in the vicinities of nanosize defects and nano-inhomogeneities cannot be properly described within the size independent classical theory. As a remedy to this type of dilemmas and enhancement of the accuracy of the solution, polar or gradient continuum theories may be utilized. The current work is concerned with composites consisting of micropolar matrix and micropolar ellipsoidal particles with periodic distribution throughout the three dimensional space. In particular, the analytical determinations of the effective micropolar elastic moduli tensor, effective micropolar couple stress moduli tensor, and effective micropolar characteristic... 

Nanoscopic elastic behavior of the field quantities in the vicinities of nanosize defects and nano-inhomogeneities cannot be properly described within the size independent classical theory. As a remedy to this type of dilemmas and enhancement of the accuracy of the solution, polar or gradient continuum theories may be utilized. The current work is concerned with composites consisting of micropolar matrix and micropolar ellipsoidal particles with periodic distribution throughout the three dimensional space. In particular, the analytical determinations of the effective micropolar elastic moduli tensor, effective micropolar couple stress moduli tensor, and effective micropolar characteristic... 

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

Since the efficiency of non-classical continuum theories is strongly dependent on the recognition of the suitable values of small length scale parameters and there is still uncertainty about them, a novel approach, equivalent lattice stiffness method is developed here. This approach without the characteristic length scale parameter which arises in non-classical continuum theories, such as nonlocal theory and strain gradient theory, is capable to capture size effect more easily and accurately. This method is proposed based on the concept of lattice dynamics but a Taylor series expansion is involved to approximate the displacements of the continuous domain; accordingly, this approach is in... 

Since the efficiency of non-classical continuum theories is strongly dependent on the recognition of the suitable values of small length scale parameters and there is still uncertainty about them, a novel approach, equivalent lattice stiffness method is developed here. This approach without the characteristic length scale parameter which arises in non-classical continuum theories, such as nonlocal theory and strain gradient theory, is capable to capture size effect more easily and accurately. This method is proposed based on the concept of lattice dynamics but a Taylor series expansion is involved to approximate the displacements of the continuous domain; accordingly, this approach is in... 

This paper presents and discusses the effect of maximum size of coarse aggregate on fracture characteristics and brittleness of self-compacting concrete (SCC). Based on an experimental program, a series of three point bending tests were carried out on 86 notched beams, as recommended by RILEM. For all mixes, the parameters were analyzed by the work-of-fracture method (WFM) and by the size effect method (SEM) and consequently a correlation between these methods was obtained which is used to calibrate cracking numerical models. Test results showed that with increase of size of coarse aggregate, (a): fracture energies of GF in WFM and Gf in SEM increase which may be explained by the change in... 

This paper presents the effect of volume of coarse aggregate on fracture characteristics of self- compacting concrete (SCC). Based on an experimental programme, a series of three point bending tests were carried out on 58 notched beams. SCC was prepared with coarse aggregate in varying percentages of 30%, 40%, 50% and 60% (as the percentage of the total aggregate volume). For all mixes, the fracture parameters were analyzed by the work-of- fracture method (WFM) and by the size effect method (SEM) to obtain a suitable correlation between these methods which is used to calibrate fracture numerical models. The results showed that with decrease of volume of coarse aggregate from 60% to 30% in... 

The elastic behavior of an edge dislocation placed in the shell of a free-standing core-shell nanowire is considered within the theory of surface/interface elasticity. Using the method of complex potential functions the expressions for the stress field of the dislocation, image forces on the dislocation, and the dislocation strain energy are derived and studied in detail. A special attention is paid to non-classical effects revealed within the surface/interface elasticity approach where a characteristic length parameter referred to as surface/interface modulus is introduced. These effects are (i) the stress oscillations along the shell surface and core-shell interface for negative values of... 

The paper describes an experimental research on fracture characteristics of self-compacting concrete (SCC). Three point bending tests conducted on 154 notched beams with different water to cement (w/c) ratios. The specimens were made from mixes with various w/c ratios from 0.7 to 0.35. For all mixes, common fracture parameters were determined using two different methods, the work-of-fracture method (WFM) and the size effect method (SEM). Test results showed that with decrease of w/c ratio from 0.7 to 0.35 in SCC: (a) the fracture toughness increases linearly: (b) the brittleness number is approximately doubled: (c) the effective size of the process zone cf in SEM and the characteristic... 

Propagation of the torsional surface waves in a medium consisting of a functionally graded (FG) substrate bonded to a thin piezoelectric over-layer has been analytically formulated in the mathematical framework of surface/interface elasticity theory. In the cases where the wavelength and/or the thickness of the over-layer are comparable to the surface/interface characteristic length, then the surface/interface effects are not negligible. It is assumed that the over-layer is made of hexagonal 622 crystals with a single axis of rotational symmetry coinciding with the axis of polarization. The half-space is made of an FG transversely isotropic material in which the elasticity tensor and the... 

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 fee metals are given in terms of the parameters of Sutton-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... 

In this paper, strain gradient elasticity formulation for analysis of FG (functionally graded) micro-cylinders is presented. The material properties are assumed to obey a power law in radial direction. The governing differential equation is derived as a fourth order ODE. A power series solution for stresses and displacements in FG micro-cylinders subjected to internal and external pressures is obtained. Numerical examples are presented to study the effect of the characteristic length parameter and FG power index on the displacement field and stress distribution in FG cylinders. It is observed that the characteristic length parameter has a considerable effect on the stress distribution of FG... 

This paper deals with investigation of fracture behavior of steel fiber reinforced high strength concrete (SFRHSC) and compare it to plain high strength concrete (HSC). Based on an experimental program, a series of three point bending tests were carried out on 54 notched beams, as recommended by RILEM. The fracture parameters were measured by two methods: work of fracture method (WFM) and size effect method (SEM). Then the fracture parameters obtained from these two methods were compared. The results showed that with increase of steel fibers, fracture energy of GF in WFM and Gf in SEM increase but this increase in work of fracture method is more significant. The effective size of the process... 

Accurate estimation of the in-plane shear modulus of solids reinforced by nano-/micro-size elliptical multi-coated fibers is the focus of this paper. It is well-known that at the scales comparable to the nanoscopic length scales of the material, traditional theory of elasticity ceases to hold and, moreover, due to lack of consideration of such length scales has an innate weakness of sensing the size effect. Therefore, it is proposed to formulate and calculate the effective shear modulus of the nano-/micro-composite within micropolar theory which introduces two material characteristic lengths into the field equations. For this purpose, Mori-Tanaka theory is extended to treat nested... 

It is well-known that classical continuum theory has certain deficiencies in predicting material's behavior at the micro- and nanoscales, where the size effect is not negligible. Higher order continuum theories introduce new material constants into the formulation, making the interpretation of the size effect possible. One famous version of these theories is the couple stress theory, invoked to study the anti-plane problems of the elliptic inhomogeneities and inclusions in the present work. The formulation in elliptic coordinates leads to an exact series solution involving Mathieu functions. Subsequently, the elastic fields of a single inhomogeneity in conjunction with the Mori-Tanaka theory...