Begell House
International Journal for Multiscale Computational Engineering
International Journal for Multiscale Computational Engineering
1543-1649
14
6
2016
REITERATED MULTISCALE MODEL REDUCTION USING THE GENERALIZED MULTISCALE FINITE ELEMENT METHOD
Numerical homogenization and multiscale finite element methods construct effective properties on a coarse grid by solving local problems and extracting the average effective properties from these local solutions. In some cases, the
solutions of local problems can be expensive to compute due to scale disparity. In this setting, one can basically apply a homogenization or multiscale method reiteratively to solve for the local problems. This process is known as reiterated homogenization and has many variations in the numerical context. Though the process seems to be a straightforward extension of two-level process, it requires some careful implementation and the concept development for problems without scale separation and high contrast. In this paper, we consider the generalized multiscale finite element method (GMsFEM) and apply it iteratively to construct its multiscale basis functions. The main idea of the GMsFEM is to construct snapshot functions and then extract multiscale basis functions (called offline space) using local spectral decompositions in the snapshot spaces. The extension of this construction to several levels uses snapshots and offline spaces interchangeably to achieve this goal. At each coarse-grid scale, we assume that the offline space is a good approximation of the solution and use all possible offline functions or randomization as boundary conditions and solve the local problems in the offline space at the previous (finer) level, to construct snapshot space. We present an adaptivity strategy and show numerical results for flows in heterogeneous media and in perforated domains.
Eric T.
Chung
Department of Mathematics, The Chinese University of Hong Kong (CUHK), Hong Kong SAR; Department of Mathematics & Institute for Scientific Computation (ISC), Texas A&M
University, College Station, Texas 77843-3368, USA
Yalchin
Efendiev
Center for Numerical Porous Media (NumPor), King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia; Department of Mathematics and Institute for Scientific Computation (ISC), Texas A&M University, College Station, Texas 77843-3368, USA
Wing Tat
Leung
Department of Mathematics and Institute for Scientific Computation (ISC), Texas A&M University, College Station, Texas 77843-3368, USA
Maria
Vasilyeva
Department of Mathematics & Institute for Scientific Computation (ISC), Texas A&M University, College Station, Texas 77843-3368, USA; Department of Computational Technologies, Institute of Mathematics and Informatics,
North-Eastern Federal University, Yakutsk, 677980, Republic of Sakha (Yakutia), Russia
535-554
GRAPHENE/CARBON NANOTUBE REINFORCED METALLIC GLASS COMPOSITES: A MOLECULAR DYNAMICS STUDY
Single-layer graphene sheets and carbon nanotubes (CNTs) have resulted in the development of new materials for a variety of applications. Though there are a large number of experimental and numerical studies related to these nanofillers, still there is a lack of understanding of the effect of geometrical characteristics of these nanofillers on their mechanical properties. In this study, molecular dynamics (MD) simulation has been used to study the effect of CNT and graphene reinforcements on the mechanical properties of amorphous metallic glass (MG). Materials Studio 7.0 has been used as a tool for finding the tensile modulus, yield strength, and yield strain of anocomposites. Both short and long CNT and graphene reinforced MG composites have been studied. The effect of nanofiller volume fraction (Vf) on the mechanical properties has also been studied. Results showed that with increase in Vf the Young's modulus of long graphene/MG composites increased at a faster rate than that for long CNT/MG composites. For the same Vf, the Young's modulus of long graphene/MG composite was higher than long CNT/MG composite, thus showing that graphene is a better reinforcement than CNT for MG based composites. MG with short nanoreinforcements showed very small improvement in mechanical properties.
Sumit
Sharma
Materials Engineering, Department of Mechanical Engineering, Lovely
Professional University, Phagwara 144411, Punjab, India
Pramod
Kumar
Department of Mechanical Engineering, Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, India
Rakesh
Chandra
Department of Mechanical Engineering, Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, India
555-584
POSTBUCKLING OF NANOCOMPOSITE PLATE REINFORCED WITH RANDOMLY ORIENTED AND DISPERSED CNTS MODELED THROUGH RSA TECHNIQUE
The aim of the present paper is to study the buckling and postbuckling behavior of carbon nanotube (CNT)-reinforced magnesium (Mg) nanocomposite plates. A Boolean-based random sequential adsorption (RSA) technique is employed to model a representative volume element (RVE) with randomly oriented and positioned CNTs using uniform and normal distributions. The elastic properties of the resulting nanocomposite are evaluated using that RVE. Further, the evaluated stiffness properties of CNT-Mg nanocomposite are utilized to investigate the effects of CNT reinforcement on buckling and postbuckling behavior of the nanocomposite plate. Buckling and postbuckling studies of the nanocomposite plate are carried out using nonlinear finite element methods formulation based on the first-order shear deformation theory and von Karman's assumptions. The arc-length method is utilized to solve the resulting nonlinear finite-element algebraic equations. It is concluded that CNT reinforcement leads to substantial increase in the stiffness properties of soft matrix materials as compared to the stiff matrix materials, and hence percentage enhancements in buckling load and postbuckling strength of CNT-reinforced soft matrix materials are found to be more pronounced than those of CNT-reinforced stiff matrix materials.
Ashish
Srivastava
Mechanical Engineering Department, Malaviya National Institute of Technology, Jaipur, India
Dinesh
Kumar
Mechanical Engineering Department, Malaviya National Institute of Technology, Jaipur, India
585-606
MULTISCALE SEAMLESS-DOMAIN METHOD BASED ON DEPENDENT VARIABLE AND DEPENDENT-VARIABLE GRADIENTS
Previous work presented the multiscale seamless-domain method (SDM) for heterogeneous structures. The method consists of two analyses. In the macroscopic analysis, we need not model the constituents separately and the structure has only coarse-grained points (i.e., meshless). A dependent-variable value at a point is expressed as a weighted average of the variables at surrounding points. This equation determines the relation among the neighboring points. The variables at all points are determined by formulating and solving the equations for all the points. The weighting coefficients are constructed from results of the microscopic analysis of a local model, which is extracted from the whole structure. To enhance analytical accuracy and C1 continuity, this study presents a new formulation for the SDM. The proposed formulation computes the variable at a coarse-grained point referring to the variable gradients as well as the variable values. Numerical experiments related to heat conduction compare the previous and proposed SDMs.
Yoshiro
Suzuki
Tokyo Institute of Technology, Department of Mechanical Sciences and Engineering, Tokyo 1528552, Japan
Masato
Takahashi
Tokyo Institute of Technology, Department of Mechanical Sciences and Engineering, Tokyo 1528552, Japan
607-630
INDEX, VOLUME 14, 2016
631-636