Sharif Digital Repository

In the present paper, some new and compact basis-free expressions are derived for representing stresses conjugate to the Lagrangean Hill's strain measures. Solving a tensor equation in the form of AX + XA = C, a rather simple general expression is obtained for the conjugate stresses in the case of distinct principal stretches. The result decomposes the conjugate stresses additively into two parts, such that one part is coaxial with the right stretch tensor while another part is orthogonal to it. An expression for the case of double-coalescent principal stretches is also obtained. As an example of the general results, simple expressions are obtained for the stress conjugate to the logarithmic... 

In this paper basis-free expressions are derived for the stresses conjugate to the Jaumann rate of the general Eulerian strain measures. The component-form of the expressions is also presented. The basis-free results are compact and also valid for all different cases of distinct and coalescent principal stretches. As an example, the compact basis-free expressions for the stress conjugate to the Jaumann rate of logarithmic strain lnV are determined. © Springer-Verlag Wien 2007  

To investigate the effect of 3D and 2D deformations on flattened wires, the effective strain fields of flat rolled and sidepressed wires are predicted using the combined finite and slab element method (FSEM) and two-dimensional finite element method (TDFEM), respectively. The validity of the calculated strain fields are verified using the Vickers microhardness test. Utilizing the calculated strain fields, the strain inhomogeneity of the flat rolled and sidepressed wires are investigated. To assess the effects of height to width ratio and frictional condition on the strain inhomogeneity, an inhomogeneity factor (IF) is defined. The results show that for both the flat rolled and sidepressed... 

In this research, deformation of material during equal channel angular extrusion (ECAE) is analyzed using an upper bound model. The model considers the effect of die angle and friction between the sample and the die walls on the geometry of dead metal zone and total strain. The relationship between the friction coefficient, the extent of dead metal zone and total strain is derived. It is found that strain decreases with increasing die angle and friction coefficient. Moreover, a critical value for friction coefficient is determined that when the friction coefficient is more than the critical, deformation zone and therefore, the dead metal zone forms which consequently total strain decreases.... 

The present study is concerned with introducing a new configuration of equal channel angular extrusion (ECAE) process nominated as multi-stage ECAE. This die configuration is not a real processing die and is just used to calculate strain in ECAE dies with outer curved corner. A solution is presented for evaluating total strain in those dies consisting of two or more ECAE sub-dies. The solution is extended for calculating strain in frictionless ECAE dies with outer curved corner. A complete agreement is found between calculated and previously published results by other authors. © 2006 Elsevier B.V. All rights reserved  

In this study, a new plasticity-based constitutive model is proposed for the behavior of soil-structure interfaces under monotonic and cyclic loadings. The features of the interface including the strain-softening behavior, phase transformation, steady-state, and dilatancy behavior were described by the proposed model with satisfactory accuracy. The proposed model does not require additional concepts such as damage or disturbance, and the model parameters can be obtained easily using straight-forward analyses of the results obtained from constant normal stress tests. Moreover, the results of the proposed model showed its capability in predicting the experimental results obtained from various... 

Displacement and strain fields of a screw dislocation in a nanowire are considered within the theory of gradient elasticity. The gradient solution of the corresponding boundary value problem is derived and discussed in detail. It is shown that the dislocation fields do not contain classical jumps and singularities at the dislocation line. The maximum values of the dislocation displacement and elastic strain strongly depend on both the dislocation position and nanowire radius, thus demonstrating a nonclassical size effect. © 2008 Acta Materialia Inc  

In this paper, with introducing and based on a new configuration of equal channel angular extrusion (ECAE) process, nominated as multi-stage equal channel angular extrusion, two relationships are derived to calculate the effective strain based on shear and principal strains. First, a solution is presented for evaluating the effective strain in multi-stage ECAE dies consisting of two or more ECAE sub-dies. Then, the solution is extended to calculate the effective strains in ECAE dies with outer curved corner. The effective strain based on shear strains shows an exact agreement with previously published results. The derived relationships were compared with each other, with the relationships... 

In this paper dynamic property of Cement-Admixed clay under a wide range of strains were studied considering the effect of different mixing ratio and the change of confining pressures through dynamic triaxial test. Triaxial tests were conducted on untreated and cement treated soils and the results were then analyzed to study the variations in dynamic elastic modulus (Ed) and the damping ratio (D) of soil specimens at different cement ratio. Increasing cement ratio has a significant effect on Ed of the treated soils, and increases it. In contrast, increasing cement ratio decreases D; however, the rate of decreasing D with increasing cement ratio is not considerable. The feed-forward... 

In this paper, a general class of Eshelby-like or weighted stress tensors based on the right stretch tensor is defined as the product of a general type of Lagrangian stress tensor and a class of stretch measure. In addition, basis free relations for conjugate strains of Eshelby-like stress tensors are investigated, which are based on Hill's definition of energy conjugacy. The equations for strain tensors conjugate to Eshelby-like stress tensors are generally determined, but the case in which the conjugate strains are coaxial with the right stretch tensor is mostly investigated. © 2006 Elsevier Ltd. All rights reserved  

If the double contraction of a stress tensor such as T and rate of a Lagrangean strain tensor such as E, i.e. T : Ė produces the stress power then these stress and strain tensors are called a conjugate pair. The applications of the conjugate stress and strain measures are in the development of the basic relations in nonlinear continuum mechanics analysis such as modeling of constitutive equations of elastic-plastic materials. In this paper relations for stress tensors conjugate to an arbitrary Lagrangean strain measure of Hill's class are obtained. The results of this paper are more compact and simpler in compare with those available in the literature. The results are valid for the three... 

In this paper, vibration suppression of micro-or nano-scale beams subjected to nonlinear distributed electrostatic force is studied. For the sake of precision, we use the beam model derived from strain gradient elasticity theory aimed at prediction of size effect. In addition, the electrostatic force is considered with first order fringing field correction. The continuous model of the strain gradient beam is truncated by using Kantorovich method as a semi-analytical finite element method. A boundary control feedback law is proposed to suppress forced vibrations of the beam. Both measurements and actuations are taken place in the boundary to avoid spillover instabilities. Simulation results... 

In this paper, the mechanical behavior of micro-rotating disks is investigated utilizing the strain gradient theory. The governing equation and boundary conditions are derived utilizing the variational method. The analytical solution for the derived equation is also presented. As a case study, some numerical results are presented to emphasize the importance of utilization of non-classical theories such as the strain gradient elasticity instead of the classical continuum theory in dealing with micro-rotating disks  

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... 

Solids usually show complex material behavior. If deformation is finite, the description of the kinematics makes the mechanical model complicated. In fact, one of the basic questions in the formulation and analysis procedures of finite deformation thermoelasticity is: "How can the finite deformation thermoelasticity response be best accounted for in the kinematic formulation?" A rather attractive way to proceed is to use the approach of small strain analysis, and decompose the total strain into a mechanical part and a thermal part. In this paper, based on the multiplicative decomposition of the deformation gradient, the mechanical and thermal strains are defined in the power and exponential... 

In this paper, a deformation measure is introduced which leads to a class of strain measures in the Lagrangian and Eulerian descriptions. In order to develop a constitutive equation, a second-order constitutive relation based on these strain measures is considered for modeling the mechanical behavior of solids at finite deformation. For this purpose and performance evaluation of the proposed strains, a Hookean-type constitutive equation is considered and the uniaxial loading as well as simple shear and pure shear tests are examined. It is shown that the constitutive modeling based on the proposed strains give results which are in good agreement with the experimental data  

We study the thermal properties of ultra-narrow silicon nanowires (NW) with diameters from 3 nm to 12 nm. We use the modified valence-force-field method for computation of phononic dispersion and the Boltzmann transport equation for calculation of phonon transport. Phonon dispersion in ultra-narrow 1D structures differs from dispersion in the bulk and dispersion in thicker NWs, which leads to different thermal properties. We show that as the diameter of the NW is reduced the density of long-wavelength phonons per cross section area increases, which increases their relative importance in carrying heat compared with the rest of the phonon spectrum. This effect, together with the fact that... 

In this paper, a size-dependent formulation is presented for vibration analysis of micro-end mill tool. The formulation is developed based on the strain gradient elasticity theory in order to enhance the modeling capability of micro-size structures. Due to stubby geometry of micro-tool, the shear deformation and rotary inertia effects are considered in the derivation of equations. Hence, based on the strain gradient Timoshenko beam theory, the extended Hamilton's principle is used to formulate a detailed dynamical model of the rotating micro-tool. The dynamical model includes a set of partial differential equations with gyroscopic coupling produced due to the spindle rotation. The governing... 

Study of the plastic deformation in polymeric honeycombs can pave the way for understanding the deformation localization in more complex cellular structures, which have received progressive attention in the past few years. This study compares the strain localization in deforming honeycombs made by two cost-effective 3D-printing technologies. Hexagonal honeycombs and their unit cell models were 3D-printed by both PolyJet™, using a photo-crosslinkable polymer, and fused deposition modeling (FDM) using a thermoplastic material. The state of the art digital image correlation (DIC) technique was employed as the experimental route in order to calculate the strain field during the deformation of...