Sharif Digital Repository

In this paper, a novel temperature-dependent multi-scale method is developed to investigate the role of temperature on surface effects in the analysis of nano-scale materials. In order to evaluate the temperature effect in the micro-scale (atomic) level, the temperature related Cauchy–Born hypothesis is implemented by employing the Helmholtz free energy, as the energy density of equivalent continua relating to the inter-atomic potential. The multi-scale technique is applied in atomistic level (nano-scale) to exhibit the temperature related characteristics. The first Piola–Kirchhoff stress and tangential stiffness tensor are computed, as the first and second derivatives of the free energy... 

In this paper the surface effects in 3D complex parts are investigated via classical FEM and the modified boundary Cauchy-Born method, which are continuum based theories, and the results are compared with molecular dynamics simulations. The boundary Cauchy-Born covers the weakness of the surface Cauchy-Born in modeling edge and corner elements, so the results are in better agreement with molecular dynamics simulations. Using super convergent patch recovery method, MBCB shows more precise results in comparison with BCB as it can model acute and obtuse angles which cannot be modeled via BCB. The flexibility of MBCB in modeling 3D complex and non-right angle geometries are utilized to model... 

The Cauchy-Born (CB) hypothesis has been widely used in multi-scale modeling of crystalline nano-structures. The violation of CB hypothesis in stress space and the transition to plasticity, which is equivalent to the violation of CB hypothesis in strain space, are generally confused and it becomes crucial to differentiate between the two distinct phenomena; the violation of the former usually occurs at high values of stress and at regions where the surface effects are manifest while the violation of the latter occurs at low stresses when the material loses its strength to tolerate the applied loading. In this paper, a novel technique is developed to investigate the validity of CB hypothesis... 

We have conducted Molecular Dynamics (MD) simulations with the Environment-Dependent Interatomic Potential (EDIP) to obtain the natural frequency of ultra-thin Silicon Nanowires (SiNWs) with various crystallographic structures, boundary conditions and dimensions. As expected, results show that the mechanical properties of SiNWs are size-/orientation-dependent. The observed phenomena are ascribed to the surface effects which become dominant due to the large surface-to-volume number of atoms at the investigated range of dimensions. Due to their accuracy, atomistic simulations are widely accepted for the investigations of such nano-scaled systems; however, they suffer from high computational... 

The Cauchy–Born (CB) hypothesis has been widely used in multi-scale modeling of crystalline nano-structures. The violation of CB hypothesis in stress space and the transition to plasticity, which is equivalent to the violation of CB hypothesis in strain space, are generally confused and it becomes crucial to differentiate between the two distinct phenomena; the violation of the former usually occurs at high values of stress and at regions where the surface effects are manifest while the violation of the latter occurs at low stresses when the material loses its strength to tolerate the applied loading. In this paper, a novel technique is developed to investigate the validity of CB hypothesis... 

A large amount of research in computational mechanics has biased toward atomistic simulations. This trend, on one hand, is due to the increased demand to perform computations in nanoscale and, on the other hand, is due to the rather simple applications of pairwise potentials in modeling the interactions between atoms of a given crystal. The Cauchy–Born (CB) hypothesis has been used effectively to model the behavior of crystals under different loading conditions, in which the comparison with molecular dynamics simulations presents desirable coincidence between the results. A number of research works have been devoted to the validity of CB hypothesis and its application in post-elastic limit.... 

An important issue in the study of the nanostructures behaviors is the surface effects, which increases with the increase of the surface-to-volume ratio. Continuum theories are capable of modeling structures at micro and larger scales with enough precision and low computational costs. However, these theories are unable to predict the mechanical properties of nanostructures accurately. On the other hand, due to their high precision, atomistic modeling techniques are extensively employed for the study of systems at nanoscale; however, computational costs of these techniques are relatively high. In this research, we aim to study the vibrational behavior of nanobeams made of three FCC metals;... 

We report an unexpected reverse spiral turn in the final stage of the motion of rolling rings. It is well known that spinning disks rotate in the same direction of their initial spin until they stop. While a spinning ring starts its motion with a kinematics similar to disks, i.e., moving along a cycloidal path prograde with the direction of its rigid body rotation, the mean trajectory of its center of mass later develops an inflection point so that the ring makes a spiral turn and revolves in a retrograde direction around a new center. Using high speed imaging and numerical simulations of models featuring a rolling rigid body, we show that the hollow geometry of a ring tunes the rotational... 

In this paper, Mindlin's second strain gradient theory is formulated and presented in an arbitrary orthogonal curvilinear coordinate system. Equilibrium equations, generalized stress-strain constitutive relations, components of the strain tensor and their first and second gradients, and the expressions for three different types of traction boundary conditions are derived in any orthogonal curvilinear coordinate system. Subsequently, for demonstration, Mindlin's second strain gradient theory is represented in the spherical coordinate system as a highly-practical coordinate system in nanomechanics. Second strain gradient elasticity have been developed mainly for its ability to capture the... 

In nano-structures, the influence of surface effects on the properties of material is highly important because the ratio of surface to volume at the nano-scale level is much higher than that of the macro-scale level. In this paper, a novel temperature-dependent multi-scale model is presented based on the modified boundary Cauchy-Born (MBCB) technique to model the surface, edge, and corner effects in nano-scale materials. The Lagrangian finite element formulation is incorporated into the heat transfer analysis to develop the thermo-mechanical finite element model. The temperature-related Cauchy-Born hypothesis is implemented by using the Helmholtz free energy to evaluate the temperature... 

A new method is presented for the extraction of the bulk and surface parameters of a periodic artificial medium which uses the eigenvectors of the generalized transfer matrix of a unit layer. These eigenvectors correspond to the Bloch modes of the periodic structure. The eigenvector related to the propagating Bloch mode directly yields an expression for the effective, intrinsic wave impedance of the medium. Moreover, the interface between the artificial material and a surrounding, conventional (dielectric) region is described by an interface impedance matrix which accounts for the excitation of higher order, nonpropagating Bloch modes at the interface. Although these modes do not propagate...