Sharif Digital Repository

The band gap offset is an effect of coordination numbers (CNs) of atom reduction at the edge of transversal cross-section of Silicon nanowires (SiNWs). In this paper, a hierarchical multi-scale technique is developed to model the edge effect on the band gap shift of SiNWs since the geometric effect is dominant in the energy gap due to the appearance of strain in the self-equilibrium state. The multi-scale model is performed based on the molecular dynamics approach and finite element method for the micro- (atomistic) and macro-scale levels, respectively. The Cauchy–Born (CB) hypothesis is used to relate the atomic positions to the continuum field through the deformation gradient. Finally, the... 

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, a new multi-scale technique is developed for concurrent coupling of atomistic-continuum domains in modeling nano-mechanical behavior of atomic structures. A Lagrange multiplier method is employed over an overlapping domain to coupling the continuum nodal velocities with atomic lattice velocities. The Hamiltonian method is applied to combine the continuum and molecular Hamiltonians with the same weight in the overlapping domain. The mass and stiffness matrices of the continuum domain are obtained using a linear bridging map of the atomic lattice displacement laid underneath the continuum grid to the element displacements. Numerical examples are performed by presenting the... 

The band gap offset is an effect of coordination numbers (CNs) of atom reduction at the edge of transversal cross-section of Silicon nanowires (SiNWs). In this paper, a hierarchical multi-scale technique is developed to model the edge effect on the band gap shift of SiNWs since the geometric effect is dominant in the energy gap due to the appearance of strain in the self-equilibrium state. The multi-scale model is performed based on the molecular dynamics approach and finite element method for the micro- (atomistic) and macro-scale levels, respectively. The Cauchy-Born (CB) hypothesis is used to relate the atomic positions to the continuum field through the deformation gradient. Finally, the... 

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 thorough understanding of determining factors in angiogenesis is a necessary step to control the development of new blood vessels. Extracellular matrix density is known to have a significant influence on cellular behaviors and consequently can regulate vessel formation. The utilization of experimental platforms in combination with numerical models can be a powerful method to explore the mechanisms of new capillary sprout formation. In this study, using an integrative method, the interplay between the matrix density and angiogenesis was investigated. Owing the fact that the extracellular matrix density is a global parameter that can affect other parameters such as pore size, stiffness,... 

This article presents a multi-scale progressive micro-mechanical fatigue model. The model employs fundamental equation of the kinetic theory of fracture to calculate damage parameters of both fiber and matrix during cyclic loading. In order to adapt the equation, required material coefficients of the constituents can be achieved from fatigue test results of longitudinal and transverse unidirectional composites, only. Sharing stress capacities of fiber and matrix are determined using a modified progressive micro-mechanical bridging model in the presence of damage. The damage parameters in the constituents are calculated employing two different equivalent scalars. However, during sinusoidal... 

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... 

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... 

In this paper, a new multi-scale approach is presented based on the modified boundary Cauchy-Born (MBCB) technique to model the surface effects of nano-structures. The salient point of the MBCB model is the definition of radial quadrature used in the surface elements which is an indicator of material behavior. The characteristics of quadrature are derived by interpolating data from atoms laid in a circular support around the quadrature, in a least-square scene. The total-Lagrangian formulation is derived for the equivalent continua by employing the Cauchy-Born hypothesis for calculating the strain energy density function of the continua. The numerical results of the proposed method are... 

The strengthening behavior of particle reinforced metal-matrix composites is primarily attributed to the dislocation strengthening effect and the load transfer effect. To account for these two effects in a unified way, a new multi-scale approach is developed in this paper incorporating the aspect ratio effect into the geometrically necessary dislocation strengthening relationships. By making use of this multi-scale approach, the deformation behavior of metal-matrix composites (MMCs) and metal-matrix nanocomposites (MMNCs) as a function of size, volume fraction, aspect ratio, etc. of the particles has been investigated. Comparison with the previously proposed models and the available... 

In this study, we apply a novel numerical technique for modeling the propagation of mechanical wave in the human arteries using the multiscale method. We define a particle region characterized by molecular dynamics (MD) method which is surrounded by a continuous region characterized by a finite element (FE) method. The interface between the two models are defined so as to minimize spurious reflections at the interface. This is a preliminary work for the modeling of the mechanical stability of atherosclerosis plaques using multiscale method. The model offered has extensive application in cell mechanics  

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.... 

We have used a hierarchical multiscale modeling scheme for the analysis of carbon nanotube reinforced nanocomposites. This scheme consists of definition of two boundary value problems, one for macroscale (the scale in which the material exists homogeneously and we are interested in modeling the material behavior on that scale), and another for microscale (the scale in which the material becomes heterogeneous and microstructural constituents emerge). The coupling between these scales is done by using homogenization techniques. Using the presented scheme, we have studied carbon nanotube (CNT) reinforced composites behavior and the effects of an interphase layer between CNT and matrix material.... 

CNT-reinforced polymer composites have attracted attention due to their exceptional high strength. The high strength can be affected by the presence of defects in the nanotubes used as reinforcements in the practical nanocomposites. In this paper, a Molecular Structural Mechanics / Finite Element (MSM/FE) multiscale modeling is used to study the effect of carbon nanotube geometrical defects on the stability of SWCNT-polymer composites. Here, two types of representative volume elements (RVEs) for these nanocomposites are considered with perfect and defected CNT. These RVEs have the same dimensions. The nanotube is modeled at the atomistic scale using molecular structural mechanics whereas the... 

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...