Sharif Digital Repository

When applying the equivalent inclusion method (EIM) to a composite material with non-dilute distribution of reinforcement particles, due to the complex interaction between the particles, the homogenizing eigenstrain field will in general be highly nonlinear. The interaction becomes more complex, when the reinforcements are multi-phase particles, i.e., the core inhomogeneity is surrounded by many layers of coatings. In this paper, a treatment for an accurate determination of the distribution of homogenizing eigenstrain fields corresponding to composites with non-dilute periodic distribution of multi-phase reinforcement particles is given. The proposed method is applicable to problems, where... 

Carbon nanotubes (CNTs) are viewed as rolled graphene. Thus, an appropriate formulation describing the behavior of CNTs must contain the key information about both their initial configuration as graphene and final configuration as CNT.On this note, to date, somemodels, in particular based on the Cauchy- Born rule, for the description of CNTs behavior exist. A simplifying assumption in some of these models is that the length and perimeter of the CNT equal the corresponding dimensions of the unrolled initial configuration, thus neglecting the induced hoop and longitudinal strains. On the other hand, the present work offers a purely nonlinear continuum model suitable for the description of the... 

Based on wave-function expansion, the time harmonic wave scattered by a circular and spherical inhomogeneity has been studied by numerous investigators. This method has also been employed to axisymmetrically coated circular and spherical inhomogeneities by some authors. When the geometry of the obstacle is not axisymmetric, the wave-function expansion is no longer applicable. In this paper, it is proposed to employ the dynamic equivalent inclusion method (DEIM) which is more general than the methods presented in the literature. It will be seen that DEIM may be used to treat a wide range of situations in a unified manner and is not bound to certain symmetries. The DEIM was first proposed by... 

The scattering of in-plane P- and SV-waves by a multi-coated circular nanofiber with deformable interfaces is of interest. To this end, in the present work, after introducing two kinds of interface momenta defined as the derivative of the interface excess kinetic energy with respect to the average and relative velocities at the interface, we extend the elastostatic theory of Gurtin et al. (1998) on deformable interfaces to the elastodynamic theory and derive the interface equations of motion using Hamilton principle. The effects of the generalized interface properties including the interface inertial parameters and interface stiffness towards stretch and slip on the dynamic stress... 

By considering a single-walled carbon nanotube (SWCNT) as a two-dimensional elastica obtained from the roll-up of a graphene sheet into a circular tube, the present paper develops a precise well-posed continuum theory for describing the entire torsional behavior of SWCNTs from an initial unloaded state through their ultimate levels of loading. In addition, the proposed approach can capture the dual ideal shear strengths as well as the asymmetrical behavior of chiral tubes with respect to the direction of the applied torsional loading. The theory incorporates a highly nonlinear constitutive equation which provides information about the nanoscopic morphological parameters of the tubes. As it... 

The stress fields of cylindrical and spherical multi-phase inhomogeneity systems with perfect or imperfect interfaces under uniform thermal and far-field mechanical loading conditions are investigated by use of the Boussinesq displacement potentials. The radius of the core inhomogeneity and the thickness of its surrounding coatings are arbitrary. The discontinuities in the tangential and normal components of the displacement at the imperfect interfaces are assumed to be proportional to the associated tractions. In this work, for the problems where the phases of the inhomogeneity system are homogeneous, the exact closed-form thermo-elastic solutions are presented. These solutions along with a... 

When a tensor-valued function σ(x) is continuous in regions ∑0 and ∑1, but has a finite jump across the interface Γ01 between ∑0 and ∑1, then Γ01 is referred to as singular surface relative to the field σ (x). In this paper, it is intended to give a general treatment of three-dimensional static and free vibration analysis of bodies composed of multi-phase elastic and/or piezoelectric bodies with electro-mechanical singular surfaces. The geometry of the medium, boundary conditions, and the geometry of the singular surfaces may be arbitrary. The displacement field and the electric potential in each region are expressed in terms of functions composed of 3-D series and special 3-D functions. The... 

In association with multi-inhomogeneity problems, a special class of eigenstrains is discovered to give rise to disturbance stresses of interesting nature. Some previously unnoticed properties of Eshelby's tensors prove useful in this accomplishment. Consider the set of nested similar ellipsoidal domains {Ω1, Ω2,⋯,ΩN+1}, which are embedded in an infinite isotropic medium. Suppose that Ωt= {x|x ∈ ℝ3, ∑p=13 x p2/ap2 ≤ ξt 2}, which 0 ≤ ξ1 < ξ2 < ⋯ < ξN+1 and ξ t a p , p=1,2,3 are the principal half axes of Ω t . Suppose, the distribution of eigenstrain, ε ij *(x) over the regions Γ t =Ω t+1-Ω t , t=1,2,⋯,N can be expressed as εij*(x)={f ijkl⋯mt(∑p=13 x p2/ap2)xkx l⋯xm, x∈ Γ, 0, x ∈ Ω1∪(ℝ3 -... 

Stress-induced anisotropy appears during the course of deformation in response to the applied stresses. The distribution of contact normals may be a dominant source of stress-induced anisotropy in granular assemblies. In the present study, stress-induced anisotropy in the fabric of granular materials is investigated through implication of several strain-controlled biaxial compression simulations on random assemblies of oval cross-sectional particles with mixed sizes. Based on a new formulation for distinct element method (DEM), which is referred to as static DEM (SDEM), an efficient computer program is developed to observe the evolution of the fabric in assemblies of oval granules under... 

The dilemma with the deficiencies of the nonlocal kernel functions as the building blocks of the Eringen’s nonlocal theory has been of concern. The aim of the current work is to provide a remedy for the calculation of the components of the nonlocal moduli tensor pertinent to face center cubic (fcc) crystals accounting for their true symmetry group. To this end, three new distinct nonlocal kernel functions which are the discrete atomistic Green’s functions in the stress space are obtained through the nonlocal dispersion relations associated with the longitudinal and shear waves in fcc crystals combined with the corresponding ones calculated via ab initio based on density functional... 

The evolution of the microstructure of an assembly of cohesionless granular materials with associated pores, which carry the overall applied stresses through frictional contacts is a complex phenomenon. The macroscopic flow of such materials take place by the virtue of the relative rolling and sliding of the grains on the micro-scale. A new discrete element method for biaxial compression simulations of random assemblies of oval particles with mixed sizes is introduced. During the course of deformation, the new positions of the grains are determined by employing the static equilibrium equations. A key aspect of the method is that, it is formulated for ellipse cross-sectional particles, hence... 

In this paper, an accurate series solution in conjunction with an energy formulation for the treatment of piezocomposite plates with arbitrary geometry and aspect ratio, under both electrical and mechanical loadings are proposed. A remedy for dealing with nonhomogeneous boundary conditions is also presented. Through introduction of amending polynomials of order pk for the kth layer, the accuracy and convergence rate are dramatically improved. These polynomials ensure continuity of the generalized displacement fields across the interfaces, while their derivatives can have the required discontinuities up to a desired order. Moreover, depending on the nature of the physical problem under... 

Consider a double-inhomogeneity system whose microstructural configuration is composed of an ellipsoidal inhomogeneity of arbitrary elastic constants, size, and orientation encapsulated in another ellipsoidal inhomogeneity, which in turn is surrounded by an infinite medium. Each of these three constituents in general possesses elastic constants different from one another. The double-inhomogeneity system under consideration is subjected to far-field strain (stress). Using the equivalent inclusion method (EIM), the double inhomogeneity is replaced by an equivalent double-inclusion (EDI) problem with proper polynomial eigenstrains. The double inclusion is subsequently broken down to... 

The dynamic equivalent inclusion method (DEIM) which was first proposed by Fu and Mura (1983), in its original context has some shortcomings, which were pointed out and remedied by Shodja and Delfani (2009) who introduced the new consistency conditions along with the related micromechanically substantiated notion of eigenstress and eigenbody-force fields. However, these theories are bound to elastic media with isotropic phases. The present work extends the idea of the above-mentioned new DEIM to the dynamic electro-mechanical equivalent inclusion method (DEMEIM) for the treatment of the scattering of SH-waves by a two-phase circular piezoelectric obstacle bonded to a third phase... 

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... 

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... 

One of the most crucial factors affecting the service life of reinforced concrete (RC) structures attacked by aggressive ions is reinforcement corrosion. As the steel corrosion progresses, crack propagation in concrete medium endangers the serviceability and the strength of RC structural members. In this study, a nonlinear mathematical model for determining the displacement and stress fields in RC structures subjected to reinforcement corrosion is introduced. For corrosion products, a nonlinear stress-strain relation which has been previously confirmed by experimental data is incorporated in the present analysis. In formulation of the governing equations for steel-rust-concrete composite,...