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Temperature-dependent multi-scale modeling of surface effects on nano-materials
, Article Mechanics of Materials ; Volume 46 , March , 2012 , PP. 94–112 ; Ghahremani, P ; Sharif University of Technology
Abstract
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...
A continuum-atomistic multi-scale technique for nonlinear behavior of nano-materials
, Article International Journal of Mechanical Sciences ; Volume 148 , 2018 , Pages 191-208 ; 00207403 (ISSN) ; Sameti, A. R ; Kazerooni, Y. N ; Sharif University of Technology
Elsevier Ltd
2018
Abstract
In this paper, a hierarchical RVE-based continuum-atomistic multi-scale procedure is developed to model the nonlinear behavior of nano-materials. The atomistic RVE is accomplished in consonance with the underlying atomistic structure, and the inter-scale consistency principals, i.e. kinematic and energetic consistency principals, are exploited. To ensure the kinematic compatibility between the fine- and coarse-scales, the implementation of periodic boundary conditions is elucidated for the fully atomistic method. The material properties of coarse-scale are modeled with the nonlinear finite element method, in which the stress tensor and tangent modulus are computed using the Hill-Mandel...
Modeling the interphase layer between CNT and matrix in nanocomposites using nonlinear large deformation hierarchical multiscale
, Article 4th International Conference on Multiscale Materials Modeling, MMM 2008, 27 October 2008 through 31 October 2008 ; 2008 , Pages 239-242 ; 9780615247816 (ISBN) ; Naghdabadi, R ; Sharif University of Technology
Department of Scientific Computing, Florida State University
2008
Abstract
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....
A computational model for atomistic-based higher-order continua using the FEM technique
, Article Finite Elements in Analysis and Design ; Volume 137 , 2017 , Pages 26-39 ; 0168874X (ISSN) ; Rezaei Sameti, A ; Sharif University of Technology
Abstract
In this paper, an atomistic-based higher-order continuum model is developed in the framework of nonlinear finite element method to present the geometrically nonlinear behavior of nano-structures. In order to model the inhomogeneous deformation within the Cauchy-Born hypothesis, the higher-order CB hypothesis is presented based on a hierarchical multi-scale technique, in which the constitutive model of higher-order continuum is obtained using the derivatives of strain energy density. In order to avoid the use of C1–continuity element, as an alternative procedure, the mixed-type element is utilized employing the nodal deformation gradient as additional degrees of freedom. The relation between...
Temperature-dependent multi-scale modeling of surface effects on nano-materials
, Article Mechanics of Materials ; Volume 46 , 2012 , Pages 94-112 ; 01676636 (ISSN) ; Ghahremani, P ; Sharif University of Technology
Abstract
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...