Sharif Digital Repository

In this paper, the method of additive plasticity at finite deformations is generalized to the micropolar continuous media. It is shown that the non-symmetric rate of deformation tensor and gradient of gyration vector could be decomposed into elastic and plastic parts. For the finite elastic deformation, themicropolar hypo-elastic constitutive equations for isotropicmicropolar materials are considered.Concerning the additive decomposition and the micropolar hypo-elasticity as the basic tools, an elastic-plastic formulation consisting of an arbitrary number of internal variables and arbitrary form of plastic flow rule is derived. The localization conditions for the micropolar material obeying... 

Permutation and scaling ambiguities are relevant issues in tensor decomposition and source separation algorithms. Although these ambiguities are inevitable when working on real data sets, it is preferred to eliminate these uncertainties for evaluating algorithms on synthetic data sets. As shown in the paper, the existing performance indices for this purpose are either greedy and unreliable or computationally costly. In this paper, we propose a new performance index, called CorrIndex, whose reliability can be proved theoretically. Moreover, compared to previous performance indices, it has a low computational cost. Theoretical results and computer experiments demonstrate these advantages of... 

The experimental 13C NMR chemical shift components of uracil in the solid state are reported for the first time (to our knowledge), as well as newer data for the 15N nuclei. These experimental values are supported by extensive calculated data of the 13C, 15N and 17O chemical shielding and 17O and 14N electric field gradient (EFG) tensors. In the crystal, uracil forms a number of strong and weak hydrogen bonds, and the effect of these on the 13C and 15N chemical shift tensors is studied. This powerful combination of the structural methods and theoretical calculations gives a very detailed view of the strong and weak hydrogen bond formation by this molecule. Good calculated results for the... 

By examination of the exerted electromagnetic (EM) force on boundary of an object in a few examples, we look into the compatibility of the stress tensors corresponding to different formulas of the EM force density with special relativity. Ampere-Lorentz's formula of the EM force density is physically justifiable in that the electric field and the magnetic flux density act on the densities of the total charges and the total currents, unlike Minkowski's formula which completely excludes the densities of the bounded charges and the bounded currents inside homogeneous media. Abraham's formula is fanciful and devoid of physical meaning. Einstein-Laub's formula seems to include the densities of... 

In this paper, some basis-free expressions for the material time derivative of Lagrangian stress tensors are presented which are generally valid in all cases of coalescent principal stretches. The material is assumed to be elastic and isotropic  

The effective constitutive parameters of a three-dimensional periodic structure are calculated using its Bloch modes. These modes and their propagation constants are obtained from eigenvectors and eigenvalues of the generalized transfer matrix of a unit layer of the structure. Effective bulk permittivity and permeability tensors of the medium are obtained when two of the Bloch modes are dominant, i.e., propagate without significant decay inside the medium. The effect of the strongly decaying Bloch modes, which are excited at the interface with a conventional medium, are included by means of surface impedance matrices. The results are in excellent agreement with full-wave electromagnetic... 

The effective constitutive parameters of a three-dimensional periodic structure are calculated using its Bloch modes. These modes and their propagation constants are obtained from eigenvectors and eigenvalues of the generalized transfer matrix of a unit layer of the structure. Effective bulk permittivity and permeability tensors of the medium are obtained when two of the Bloch modes are dominant, i.e., propagate without significant decay inside the medium. The effect of the strongly decaying Bloch modes, which are excited at the interface with a conventional medium, are included by means of surface impedance matrices. The results are in excellent agreement with full-wave electromagnetic... 

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... 

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... 

In this paper a finite deformation constitutive model for rigid plastic hardening materials based on the logarithmic strain tensor is introduced. The flow rule of this constitutive model relates the corotational rate of the logarithmic strain tensor to the difference of the deviatoric Cauchy stress and the back stress tensors. The evolution equation for the kinematic hardening of this model relates the corotational rate of the back stress tensor to the corotational rate of the logarithmic strain tensor. Using Jaumann, Green-Naghdi, Eulerian and logarithmic corotational rates in the proposed constitutive model, stress-strain responses and subsequent yield surfaces are determined for rigid... 

MOG as a modified gravity theory is designed to be replaced with dark matter. In this theory, in addition to the metric tensor, a massive vector is a gravity field where each particle has a charge proportional to the inertial mass and couples to the vector field through the four-velocity of a particle. In this work, we present the Hamiltonian formalism for the dynamics of particles in this theory. The advantage of Hamiltonian formalism is a better understanding and analysing the dynamics of massive and massless particles. The massive particles deviate from the geodesics of space-time and photons follow the geodesics. We also study the dynamics of particles in the Newtonian and post-Newtonian...