C. J. Wu¹, C. Y. Chou¹, C. N. Han¹, K. N. Chiang²

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.1, pp. 49-68, 2009, DOI:10.3970/cmes.2009.041.049

Abstract In this paper, the atomistic-continuum mechanics method (ACM) is applied for carbon nanotube modeling. The atomistic-continuum mechanics is based on the transformation of chemical bonds between atoms in molecular mechanics into appropriate elements in finite element method and continuum mechanics. Spring elements are treated as chemical bonds between carbon atoms in carbon nanotube, whose force-displacement function is determined by the Reactive Empirical Bond Order (REBO) potential model. The advantages and unique feature of ACM method is same analytical model can be used for both tensile and vibration analyses, and most importantly, there are no prior inputs such as Young's Modulus,… More >

Shardool U. Chirputkar¹, Dong Qian²

CMES-Computer Modeling in Engineering & Sciences, Vol.24, No.2&3, pp. 185-202, 2008, DOI:10.3970/cmes.2008.024.185

Abstract A multiscale method based on the extended space-time finite element method is developed for the coupled atomistic/continuum simulation of nanoscale material systems. Existing single scale approach such as the finite element method has limited capability of representing the fine scale physics in both the spatial and temporal domains. This is a major disadvantage for directly incorporating FEM in coupled atomistic/continuum simulations as it results in errors such as spurious wave reflections at the atomistic/continuum interface. While numerous efforts have been devoted to eliminating the interfacial mismatch effects, less attention has been paid to developing fine scale, atomistic level representations within… More >

Jong Youn Park¹, Young-Sam Cho², Sung Youb Kim¹, Sukky Jun³, Seyoung Im¹

CMES-Computer Modeling in Engineering & Sciences, Vol.11, No.2, pp. 61-72, 2006, DOI:10.3970/cmes.2006.011.061

Abstract We present a coarse-graining computation for deformations of CNTs (carbon nanotubes) via QC (quasicontinuum), particularly targeting analysis of multi-walled carbon nanotubes. Higher order triangular elements are utilized for proper interpolation of atom positions of the CNT on the basis of QC approach. The computing scheme enables one to differentiate between the fully atomistic zone and the coarse-grained zone in the framework of the multiscale computing. Several numerical examples demonstrate the effectiveness and accuracy of the present methodology. More >

K. Garikipati¹

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.2, pp. 175-184, 2002, DOI:10.3970/cmes.2002.003.175

Abstract The embedding of micromechanical models in the macromechanical formulation of continuum solid mechanics can be treated by a variational multiscale method. A scale separation is introduced on the displacement field into coarse and fine scale components. The fine scale displacement is governed by the desired micromechanical model. Working within the variational framework, the fine scale displacement field is eliminated by expressing it in terms of the coarse scale displacement and the remaining fields in the problem. The resulting macromechanical formulation is posed solely in terms of the coarse scale displacements, but is influenced by the fine scale; thereby it has… More >

Yu.A. Melnikov, M.Yu. Melnikov¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 291-306, 2001, DOI:10.3970/cmes.2001.002.291

Abstract The use of potential (integral) representations is studied when computing Green's functions for boundary value problems stated for Laplace and biharmonic equations over regions of complex configuration in two dimensions. The emphasis is on the non-traditional potentials, whose observation and source points occupy different sets. Such potentials reduce the original boundary value problems to functional (integral) equations with smooth kernels. Special integral representations are studied, the ones whose kernels are built not of the fundamental solutions of governing differential equations but of the Green's functions for simply shaped regions, which are associated with boundary value problems under consideration. Such integral… More >

Zhentao Wang^1,*, Kai Dong, Shuiqing Zhan

FDMP-Fluid Dynamics & Materials Processing, Vol.13, No.4, pp. 221-234, 2017, DOI:10.3970/fdmp.2017.013.221

Abstract We have investigated the unsteady internal flow occurring in an evaporating droplet interacting with a high-temperature atmospheric environment. The Navier-Stokes equations for both the liquid and the gas phases have been solved numerically in the framework of a Volume of Fluid (VOF) method relying on the so-called Continuum Surface Force (CSF) model. A specific kernel able to account for evaporation and related phase change has been incorporated directly in the VOF approach. The temperature distributions within the droplet has been found to be relatively uniform by virtue of the Marangoni flow. The transient evolution of the flow pattern and related… More >

Cosmina S. Hogea¹, Bruce T. Murray¹, James A. Sethian^2,3

FDMP-Fluid Dynamics & Materials Processing, Vol.1, No.2, pp. 109-130, 2005, DOI:10.3970/fdmp.2005.001.109

Abstract A computational framework for simulating growth and transport in biological materials based on continuum models is proposed. The advantages of the finite difference methodology employed are generality and relative simplicity of implementation. The Cartesian mesh/level set method developed here provides a computational tool for the investigation of a host of transport-based tissue/tumor growth models, that are posed as free or moving boundary problems and may exhibit complicated boundary evolution including topological changes. The methodology is tested here on a widely studied "incompressible flow" type tumor growth model with a numerical implementation in two dimensions; comparisons with results obtained from a… More >

Łukasz Kaczmarczyk¹

CMC-Computers, Materials & Continua, Vol.4, No.2, pp. 55-62, 2006, DOI:10.3970/cmc.2006.004.055

Abstract In recent years the multiscale computational homogenisation has been extensively developed. Such micro-macro modelling does not require any constitutive assumptions at the macro-level. The multi-scale computational homogenisation has also been extended for the second order continuum at the macro level Kouznetsova V.G., Geers M.G.D., and Brekelmans V.A.M (2004). The second-order framework is based on incorporation of the gradient of macroscopic deformation in micro to macro multiscale transition. The introduction of the secondorder continuum at macro-scale takes into account the size effect and gives more accurate results in case of insufficient scale separation. The general framework of computational homogenisation has been… More >

Puneet Kumar^1,*, J. Srinivas²

CMC-Computers, Materials & Continua, Vol.54, No.1, pp. 1-20, 2018, DOI:10.3970/cmc.2018.054.001

Abstract Evolution of computational modeling and simulation has given more emphasis on the research activities related to carbon nanotube (CNT) reinforced polymer composites recently. This paper presents the composite cylinder assemblage (CCA) approach based on continuum mechanics for investigating the elastic properties of a polymer resin reinforced by multi-walled carbon nanotubes (MWCNTs). A three-phase cylindrical representative volume element (RVE) model is employed based on CCA technique to elucidate the effects of inter layers, chirality, interspacing, volume fraction of MWCNT, interphase properties and temperature conditions on the elastic modulus of the composite. The interface region between CNT and polymer matrix is modeled… More >

Anna Y. Matveeva¹, Helmut J. Böhm², Grygoriy Kravchenko², Ferrie W. J. van Hattum¹

CMC-Computers, Materials & Continua, Vol.42, No.1, pp. 1-23, 2014, DOI:10.3970/cmc.2014.042.001

Abstract This paper presents a comparison of different finite element approaches to modelling polymers reinforced with wavy, hollow fibres with the aim of predicting the effective elastic stiffness tensors of the composites. The waviness of the tubes is described by sinusoidal models with different amplitude-to-wavelength parameters. These volume elements are discretized by structured volume meshes onto which fibres in the form of independently meshed beam, shell or volume elements are superimposed. An embedded element technique is used to link the two sets of meshes. Reference solutions are obtained from conventional three-dimensional volume models of the same phase arrangements. Periodicity boundary conditions… More >