Sharif Digital Repository

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 present effort is the development of a multiscale modeling, simulation methodology for investigating complex phenomena arising from flowing fiber suspensions. Specific consideration was given to dynamic simulations of viscoelastic fibers in which the fluid flow is predicted by a method that is a hybrid between Direct Numerical Simulations (DNS) and Large Eddy Simulation techniques (LES), and fluid fibrous structure interactions (FSI) will be taken into account. Numerical results are presented for which focus is on fiber floc deformation by hydrodynamic forces in turbulent flows. Dynamics of simple fiber networks in a shearing flow of water in a channel flow illustrate that the... 

In this paper, a multiscale finite element framework is developed based on the first-order homogenization method for fully coupled saturated porous media using an extension of the Hill-Mandel theory in the presence of microdynamic effects. The multiscale method is employed for the consolidation problem of a 2-dimensional saturated soil medium generated from the periodic arrangement of circular particles embedded in a square matrix, which is compared with the direct numerical simulation method. The effects of various issues, including the boundary conditions, size effects, particle arrangements, and the integral domain constraints for the microscale boundary value problem, are numerically... 

A finite element-based hierarchical multiscale modeling scheme is presented and used for the analysis of nanotube-reinforced polymer composites. The scheme presented here consists of micro- and macroscale boundary value problems linked together using a computational homogenization scheme. Using the presented hierarchical multiscale scheme, we have studied nanotube-reinforced polymer composites, and the elastic properties are determined. Using different representative volume elements (RVEs) representing different volume fractions of aligned nanotubes, the effect of the nanotube volume fraction and the existence of an interphase layer on the effective elastic modulus of the nanocomposite are... 

Background: Understanding cancer development crossing several spatial-temporal scales is of great practical significance to better understand and treat cancers. It is difficult to tackle this challenge with pure biological means. Moreover, hybrid modeling techniques have been proposed that combine the advantages of the continuum and the discrete methods to model multiscale problems. Methods: In light of these problems, we have proposed a new hybrid vascular model to facilitate the multiscale modeling and simulation of cancer development with respect to the agent-based, cellular automata and machine learning methods. The purpose of this simulation is to create a dataset that can be used for... 

Carbon nanotube (CNT)-reinforced polymer composites have attracted great attention due to their exceptionally high strength. Their high strength can be affected by the presence of defects in the nanotubes used as reinforcements in practical nanocomposites. In this article, a new three-phase molecular structural mechanics/finite element (MSM/FE) multiscale model is used to study the effect of CNT vacancy defects on the stability of single-wall (SW) CNT-polymer composites. The nanotube is modeled at the atomistic scale using MSM, whereas the interphase layer and polymer matrix are analyzed by the FE method. The nanotube and polymer matrix are assumed to be bonded by van der Waals interactions... 

In this article, a multiscale modeling procedure is implemented to study the effect of interphase on the Young's modulus of CNT/polymer composites. For this purpose, a three-phase RVE is introduced which consists of three components, i.e., a carbon nanotube, an interphase layer, and an outer polymer matrix. The nanotube is modeled at the atomistic scale using molecular structural mechanics. Moreover, three-dimensional elements are employed to model the interphase layer and polymer matrix. The nanotube and polymer matrix are assumed to be bonded by van der Waals interactions based on the Lennard-Jones potential at the interface. Using this Molecular Structural Mechanics/Finite Element... 

Research on the characteristics of composites material has received enormous interest in recent years. The multi-scale nature of composite material leads to employing advanced techniques. Moreover, the presence of a wave with the high-frequency source adds complexity to the analysis. In this paper, a novel multi-scale elasticity model was developed to predict the wave dispersion property of particulate composites. The methodology was based on the simultaneous participation of translational and rotational degrees of freedom in motion equations. The method scheme of gaining motion equations was accomplished by using Taylor's expansion as a continualization method. The framework of the motion... 

This paper presents a numerical multiscale formulation for analysis of the transient heat and fluid flow in deformable heterogeneous porous media. Due to the heterogeneity of the media, the direct numerical simulation of the micro-structures leads to high computational costs. Hence, the multi-scale method can provide an efficient computational procedure. To this end, the first-order computational homogenization is adopted for two-scale simulation of THM problems. The governing equations of the problem contain a stress equilibrium equation, a mass continuity equation and an advection–diffusion equation in a fully coupled manner. Accordingly, the proper virtual power relations are defined as a... 

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... 

A mathematically rigorous, multiscale modeling methodology capable of coupling behaviors from the Kolmogorov turbulence scale through the full scale system in which a fiber suspension is flowing is presented. Here the key aspect is adaptive hierarchical modeling. Numerical results are presented focus of which are on fiber floe formation and destruction by hydrodynamic forces in turbulent flows. Specific consideration was given to molecular-dynamics simulations of viscoelastic fibers in which the fluid flow is predicted by a method which is a hybrid between direct numerical simulations and large eddy simulation techniques, and fluid fibrous structure interactions were taken into account. The... 

A combination of molecular dynamics (MD), continuum elasticity and FEM is used to predict the effect of CNT orientation on the shear modulus of SWCNT-polymer nanocomposites. We first develop a transverse-isotropic elastic model of SWCNTs based on the continuum elasticity and MD to compute the transverse-isotropic elastic constants of SWCNTs. These constants are then used in an FEM-based simulation to investigate the effect of SWCNT alignment on the shear modulus of nanocomposites. Furthermore, shear stress distributions along the nanotube axis and over its cross-sectional area are investigated to study the effect of CNT orientation on the shear load transfer  

Continuum-based modeling of nanostructures is an efficient and suitable method to study the behavior of these structures when the deformation can be considered homogeneous. This paper is concerned about multiscale nonlinear tensorial constitutive modeling of carbon nanostructures based on the interatomic potentials. The proposed constitutive model is a tensorial equation relating the second Piola-Kirchhoff stress tensor to Green-Lagrange strain tensor. For carbon nanotubes, some modifications are made on the planar representative volume element (RVE) to account for the curved atomic structure resulting a non-planar RVE. Using the proposed constitutive model, the elastic behavior of the... 

Hybrid FVM-LBM schemes are developed in the past few years to use capabilities of both Navier-Stokes based finite volume method (FVM) and lattice Boltzmann method (LBM) to solve macro-meso multiscale problems. In this scheme, the major task is to develop some lifting relations that reconstruct distribution functions in LBM sub-domain from macroscopic variables and their derivatives. The macroscopic variables are computed using Navier-Stokes based FVM in macroscale sub-domain, while distribution functions are computed using LBM in mesoscale sub-domain. The pioneer works in this area used the single relaxation time (SRT) version of LBM. However, it is known that the numerical stability and... 

We have used a hierarchical multiscale modeling scheme for the analysis of cortical bone considering it as a nanocomposite. This scheme consists of definition of two boundary value problems, one for macroscale, and another for microscale. The coupling between these scales is done by using the homogenization technique. At every material point in which the constitutive model is needed, a microscale boundary value problem is defined using a macroscopic kinematical quantity and solved. Using the described scheme, we have studied elastic properties of cortical bone considering its nanoscale microstructural constituents with various mineral volume fractions. Since the microstructure of bone... 

Polymer-layered silicate nanocomposites have been observed to demonstrate enhanced mechanical properties particularly at low weight fractions of silicate. Experimental and theoretical investigations reveal that numerous structural parameters strongly influence the modulus of such nanocomposites. A multiscale micromechanical model is developed which considers a wide range of different affecting parameters including the particle aspect ratio, the number of silicate layers per stack, the d-spacing ratio between the layers, the penetration of polymer chains along silicate sheets, the intercalation feature, and the particle volume fraction. The developed model illustrates the accuracy and... 

Airflow simulation of the whole respiratory system is still unfeasible due to the geometrical complexity of the lung airways and the diversity of the length scales involved in the problem. Even the new CT imaging system is not capable of providing accurate 3D geometries for smaller tubes, and a complete 3D simulation is impeded by the limited computational resources available. The aim of this study is to develop a fully coupled 3D-1D model to make accurate prediction of airflow and particle deposition in the whole respiratory track, with reasonable computational cost and efficiency. In the new proposed method, the respiratory tree is divided into three parts to be dealt with using different... 

In this article, a Molecular Structural Mechanics/Finite Element (MSM/FE) multiscale modeling of carbon nanotube/polymer composites with viscoelastic (VE) polymer matrix is introduced. The nanotube is modeled at the atomistic scale using structural molecular mechanics. The matrix deformation is analyzed by nonlinear finite element method considering VE behavior. The nanotube and matrix are assumed to be bonded by van der Waals interactions based on the Lennard-Jones potential at the interface. Using the MSM/FE multiscale model, we investigate the effect of carbon nanotube (CNT) on the improvement of mechanical stability of the nanocomposite. Also, the buckling behavior of these... 

One of the most popular constitutive rules that correlate the continuum and atomic properties in multi-scale models is the Cauchy-Born (CB) hypothesis. Based on this constitutive law of continuum media, it assumes that all atoms follow the deformation subjected to the boundary of crystal. In this paper, the validity and failure of CB hypothesis are investigated for the silicon nano-structure by comparison of the continuum and atomic properties. In the atomistic level, the stresses and position of atoms are calculated using the molecular dynamics (MD) simulation based on the Tersoff inter-atomic potential. The stresses and strains are compared between the atomistic and continuous media to...