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Validity and size-dependency of cauchy–born hypothesis with Tersoff potential in silicon nano-structures
, Article Computational Materials Science ; Volume 63 , October , 2012 , PP. 168–177 ; Dormohammadi, H. (Hossein) ; Sharif University of Technology
Abstract
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...
A temperature-related boundary Cauchy-Born method for multi-scale modeling of silicon nano-structures
, Article Physics Letters, Section A: General, Atomic and Solid State Physics ; Vol. 378, issue. 5-6 , 2014 , pp. 551-560 ; ISSN: 03759601 ; Dormohammadi, H ; Aramoon, A ; Sharif University of Technology
Abstract
The surface, edge and corner effects have significant influences in the electrical and optical properties of silicon nano-structures. In this paper, a novel hierarchical temperature-related multi-scale model is presented based on the boundary Cauchy-Born method to investigate not only the surface but also the edge and corner effects in thermal properties of diamond-like structures such as silicon nano-structures at finite temperature. A combined finite element method and molecular dynamics are respectively employed in macro- and micro-scale levels. The temperature-related Cauchy-Born rule is applied using the Helmholtz free energy, as the energy density of equivalent continua relating to the...
Multi-scale modeling of edge effect on band gap offset in polygonal cross-section silicon nanowires
, Article Computational Materials Science ; Volume 79 , November , 2013 , PP. 262–275 ; DorMohammadi, H ; Aramoon, A ; Sharif University of Technology
Abstract
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...
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...
Investigation of surface stress effect in 3D complex nano parts using FEM and modified boundary Cauchy-Born method
, Article Journal of Computational Science ; Volume 10 , 2015 , Pages 1-12 ; 18777503 (ISSN) ; Alipour, K ; Solgi, S ; Irani, S ; Haddadpour, H ; Sharif University of Technology
Abstract
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...
A multi-scale modeling of surface effect via the modified boundary Cauchy-Born model
, Article Materials Science and Engineering C ; Volume 32, Issue 7 , 2012 , Pages 1993-2000 ; 09284931 (ISSN) ; Aramoon, A ; Sharif University of Technology
Elsevier
2012
Abstract
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...
Stability and size-dependency of temperature-related Cauchy-Born hypothesis
, Article Computational Materials Science ; Volume 50, Issue 5 , March , 2011 , Pages 1731-1743 ; 09270256 (ISSN) ; Ghahremani, P ; Abdolhosseini Qomi, M. J ; Banihashemi, P ; Sharif University of Technology
2011
Abstract
In continuum mechanics, the constitutive models are usually based on the Cauchy-Born (CB) hypothesis which seeks the intrinsic characteristics of the material via the atomistic information and it is valid in small deformation. The main purpose of this paper is to investigate the temperature effect on the stability and size-dependency of Cauchy-Born hypothesis. Three-dimensional temperature-related Cauchy-Born formulations are developed for crystalline structure and the stability and size-dependency of temperature-related Cauchy-Born hypothesis are investigated by means of direct comparison between atomistic and continuous mediums. In order to control the temperature effect, the Nose-Hoover...
Multi-scale modeling of surface effect via the boundary Cauchy-Born method
, Article International Journal for Numerical Methods in Engineering ; Volume 85, Issue 7 , August , 2011 , Pages 827-846 ; 00295981 (ISSN) ; Aghaei, A ; Khoei, A. R ; Sharif University of Technology
2011
Abstract
In this paper, a novel multi-scale approach is developed for modeling of the surface effect in crystalline nano-structures. The technique is based on the Cauchy-Born hypothesis in which the strain energy density of the equivalent continua is calculated by means of inter-atomic potentials. The notion of introducing the surface effect in the finite element method is based on the intrinsic function of quadratures, called as an indicator of material behavior. The information of quadratures is derived by interpolating the data from probable representative atoms in their proximity. The technique is implemented by the definition of reference boundary CB elements, which enable to capture not only...
Multi-scale modeling of edge effect on band gap offset in polygonal cross-section Silicon nanowires
, Article Computational Materials Science ; Volume 79 , 2013 , Pages 262-275 ; 09270256 (ISSN) ; Dormohammadi, H ; Aramoon, A ; Sharif University of Technology
2013
Abstract
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...
Validity and size-dependency of Cauchy-Born hypothesis with Tersoff potential in silicon nano-structures
, Article Computational Materials Science ; Volume 63 , 2012 , Pages 168-177 ; 09270256 (ISSN) ; Dormohammadi, H ; Sharif University of Technology
Elsevier
2012
Abstract
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...
Validity of cauchy-born hypothesis in multi-scale modeling of plastic deformations
, Article International Journal of Solids and Structures ; 2017 ; 00207683 (ISSN) ; Jahanshahi, M ; Toloui, G ; Sharif University of Technology
Elsevier Ltd
2017
Abstract
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...
Validity of cauchy–born hypothesis in multi-scale modeling of plastic deformations
, Article International Journal of Solids and Structures ; Volume 115-116 , 2017 , Pages 224-247 ; 00207683 (ISSN) ; Jahanshahi, M ; Toloui, G ; Sharif University of Technology
Elsevier Ltd
2017
Abstract
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...
Multi-scale modeling of plastic deformations in nano-scale materials; transition to plastic limit
, Article International Journal for Numerical Methods in Engineering ; Volume 109, Issue 8 , 2017 , Pages 1180-1216 ; 00295981 (ISSN) ; Jahanshahi, M ; Sharif University of Technology
Abstract
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....
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...
Multi-scale modeling of surface effects in nano-materials with temperature-related Cauchy-Born hypothesis via the modified boundary cauchy-born model
, Article International Journal for Numerical Methods in Engineering ; Vol. 97, issue. 2 , 2014 , pp. 79-110 ; ISSN: 00295981 ; Ghahremani, P ; Dormohammadi, H ; Sharif University of Technology
Abstract
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 novel nonlinear constitutive relation for graphene and its consequence for developing closed-form expressions for Young's modulus and critical buckling strain of single-walled carbon nanotubes
, Article Acta Mechanica ; Volume 222, Issue 1-2 , 2011 , Pages 91-101 ; 00015970 (ISSN) ; Delfani, M. R ; Sharif University of Technology
2011
Abstract
Carbon nanotubes (CNTs) are viewed as rolled graphene. Thus, an appropriate formulation describing the behavior of CNTs must contain the key information about both their initial configuration as graphene and final configuration as CNT.On this note, to date, somemodels, in particular based on the Cauchy- Born rule, for the description of CNTs behavior exist. A simplifying assumption in some of these models is that the length and perimeter of the CNT equal the corresponding dimensions of the unrolled initial configuration, thus neglecting the induced hoop and longitudinal strains. On the other hand, the present work offers a purely nonlinear continuum model suitable for the description of the...
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...
An investigation on the validity of Cauchy-Born hypothesis using Sutton-Chen many-body potential
, Article Computational Materials Science ; Volume 44, Issue 3 , January , 2009 , Pages 999-1006 ; 09270256 (ISSN) ; Abdolhosseini Qomi, M. J ; Kazemi, M. T ; Aghaei, A ; Sharif University of Technology
2009
Abstract
The Cauchy-Born hypothesis has been used to concurrently bridge atomistic information to continuum model. It has been a prevalent assumption in computational nano-mechanics during the past decade. This kinematic assumption relates the deformation of the continuum to the deformation of its underlying crystalline structure. The main objective of this paper is to investigate the validity of this hypothesis by means of direct atomistic simulations and the continuum mechanic calculations. In fact, we intend to determine under which strain or stress state the crystalline structure undergoes inhomogeneous deformation due to a small perturbation of the homogeneously deformed system. Two failure...
Stability and size-dependency of cauchy-born hypothesis in three-dimensional applications
, Article International Journal of Solids and Structures ; Volume 46, Issue 9 , 2009 , Pages 1925-1936 ; 00207683 (ISSN) ; Abdolhosseini Qomi, M. J ; Kazemi, M. T ; Khoei, A. R ; Sharif University of Technology
2009
Abstract
The Cauchy-Born hypothesis (CB) provides a hierarchical approach in the molecular theory of crystal elasticity to relate the continuum and atomic deformations. This kinematic theory has been extensively used as the constitutive law of continuum regions in multi-scale models. In these models, the fine scale is proposed to describe the real behavior of crystalline structure wherever the continuum description fails. The main objective of this article is to investigate the stability and size-dependency of CB hypothesis in three-dimensional applications by direct comparison of information between atomistic and continuous description of a medium. The Sutton-Chen many-body potential is used for the...