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    Concurrent Multi-Scale Approach for Modeling Mechanical Behavior of Crystalline Nano-Structures

    , M.Sc. Thesis Sharif University of Technology Aramoon, Amin (Author) ; Khoei, Amir Reza (Supervisor)
    Abstract
    Mindboggling advances in nanotechnology have urged researchers to develop state-of-the-art numerical methods to enable them to simulate and to interpret phenomena at this scale. Unfortunately, Classical models have numerous shortcomings which hinder their applications in new contexts. For instance, classical Continuum Mechanics fails to appropriately depict material behavior at small scales, and, on the other hand, Molecular Dynamics simulations are computationally prohibitive. As a consequence, researchers have devised multi-scale methods during the past decade to overcome these obstacles. In fact, in multi-scale methods information is passed from one mathematical description to the other.... 

    Investigation of Wear Properties of Nanocrystalline through Multiscale Modeling of Nanoindentation and Nanoscratch Test

    , Ph.D. Dissertation Sharif University of Technology Chamani, Mohammad (Author) ; Farrahi, Gholamhossein (Supervisor) ; Movahhedy, Mohammad Reza (Supervisor)
    Abstract
    Nanocrystalline materials have received increasing attention during the last decades. Polycrystalline structures with grain sizes less than 100 nm are referred as nanocrystalline (NC). Their mechanical properties differ significantly from polycrystalline structures. As an example, hardness and wear resistance of nanocrystalline structures are higher than those of polycrystalline structures. With the reduction of grain size, hardness increases based on the Hall–Petch relation. However, at the very small grain sizes the Hall–Petch relation breaks down and a fundamental shift takes place in hardening mechanism. Molecular dynamics (MD) simulation offers a powerful method for the investigation of... 

    A Concurrent Multiscale Modelling of Crack Propagation with the Use of Extended Finite Element Method

    , M.Sc. Thesis Sharif University of Technology Alizadeh, Omid (Author) ; khoei, Amir Reza (Supervisor)
    Abstract
    Crack propagation problem is one of the most important problems that are being investigated for a long time. Plenty of various approaches have been utilized to simulate the crack propagation phenomenon. Continuum based methods like Finite element (FE), Extended Finite element (XFEM), have been successfully applied, and the obtained results are valid in macro scale. However, the stress filed near crack tip in FEM modeling of crack, is not exquisite enough due to inability of continuum based approaches in revealing atomistic aspects of the material.
    In order to gather efficiency of the continuum based domain and the accuracy of the atomistic based domain, Multiscale methods are employed.... 

    A Concurrent Multi-Scale Modeling of Heterogeneous Nano-Structures

    , M.Sc. Thesis Sharif University of Technology Jahanbakhshi, Farzaneh (Author) ; Khoei, Amir Reza (Supervisor)
    Abstract
    In line with the high computational cost of Molecular Dynamics resulting in restrictions in time and domain, and incompetency of Finite Element method to deal with problems like those consisting of inhomogeneities, where no distinctive constitutive law may be considered, the multi scale methods have extensively settled as an alternative in recent decades. In continuation of preceding studies in the presented research, a concurrent multi scale procedure is employed for coupling MD-FE methods applying Lagrange multiplier approach in order for energy to resemble in transient zone and calculating the stiffness matrix of FE mesh employing the atomic grid laid beneath in order to investigate 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 Khoei, A. R. (Amir Reza) ; 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 Khoei, A. R. (Amir Reza) ; 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 Khoei, A. R ; 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 concurrent multi-scale modeling for dynamic behavior of nano-crystalline structures

    , Article Computational Materials Science ; Volume 79 , 2013 , Pages 841-856 ; 09270256 (ISSN) Khoei, A. R ; Aramoon, A ; Jahanbakhshi, F ; Dormohammadi, H ; Sharif University of Technology
    2013
    Abstract
    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... 

    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) Khoei, A. R ; 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... 

    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) Khoei, A. R ; 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... 

    Temperature-dependent multi-scale modeling of surface effects on nano-materials

    , Article Mechanics of Materials ; Volume 46 , 2012 , Pages 94-112 ; 01676636 (ISSN) Khoei, A. R ; 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 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) Qomi, M. J. A ; 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... 

    A concurrent multi-scale technique in modeling heterogeneous FCC nano-crystalline structures

    , Article Mechanics of Materials ; Volume 83 , April , 2015 , Pages 40-65 ; 01676636 (ISSN) Khoei, A. R ; Jahanbakhshi, F ; Aramoon, A ; Sharif University of Technology
    Elsevier  2015
    Abstract
    In this paper, a multi-scale molecular dynamics-finite element coupling is presented to study the mechanical behavior of heterogeneous nano-crystalline structures. The stiffness and mass matrices of the continuum sub-domain are generated by applying a linear transformation on the matrices obtained via the atomic structure underlying the FE mesh. A Lagrange multiplier method is employed to the transition zone imposing velocity resemblance of the coupling regions. The constraint equations of motion are solved by the multi-time-step decomposition thus giving the opportunity to ascribe different time steps to each individual zone. The molecular dynamics is performed by employing the... 

    Investigation of the interphase effects on the mechanical behavior of carbon nanotube polymer composites by multiscale modeling

    , Article Journal of Applied Polymer Science ; Volume 117, Issue 1 , March , 2010 , Pages 361-367 ; 00218995 (ISSN) Montazeri, A ; Naghdabadi, R ; Sharif University of Technology
    2010
    Abstract
    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... 

    Incorporating aspect ratio in a new modeling approach for strengthening of MMCs and its extension from micro to nano scale

    , Article Advanced Composite Materials ; Volume 19, Issue 4 , Apr , 2010 , Pages 299-316 ; 09243046 (ISSN) Zehtab Yazdi, A ; Bagheri, R ; Zebarjad, S. M ; Razavi Hesabi, Z ; Sharif University of Technology
    2010
    Abstract
    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... 

    Validity of cauchy-born hypothesis in multi-scale modeling of plastic deformations

    , Article International Journal of Solids and Structures ; 2017 ; 00207683 (ISSN) Khoei, A. R ; 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... 

    Toward multiscale modeling of wave propagation in arteries

    , Article Journal of Mechanics in Medicine and Biology ; Volume 16, Issue 3 , 2016 ; 02195194 (ISSN) Raustin, R ; Mohammadi, H ; Sharif University of Technology
    World Scientific Publishing Co. Pte Ltd 
    Abstract
    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 comparative study of collagen matrix density effect on endothelial sprout formation using experimental and computational approaches

    , Article Annals of Biomedical Engineering ; Volume 44, Issue 4 , 2016 , Pages 929-941 ; 00906964 (ISSN) Shamloo, A ; Mohammadaliha, N ; Heilshorn, S. C ; Bauer, A. L ; Sharif University of Technology
    Abstract
    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,... 

    A progressive multi-scale fatigue model for life prediction of laminated composites

    , Article Journal of Composite Materials ; Volume 51, Issue 20 , 2017 , Pages 2949-2960 ; 00219983 (ISSN) Hosseini Kordkheili, S.A ; Toozandehjani, H ; Soltani, Z ; Sharif University of Technology
    SAGE Publications Ltd  2017
    Abstract
    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... 

    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) Khoei, A. R ; 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...