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 >

G. Fitzgerald¹, G. Goldbeck-Wood², P. Kung¹, M. Petersen¹, L. Subramanian¹, J. Wescott²

CMES-Computer Modeling in Engineering & Sciences, Vol.24, No.2&3, pp. 169-184, 2008, DOI:10.3970/cmes.2008.024.169

Abstract Molecular modeling has established itself as an important component of applied research in areas such as drug discovery, catalysis, and polymers. Algorithmic improvements to these methods coupled with the increasing speed of computational hardware are making it possible to perform predictive modeling on ever larger systems. Methods are now available that are capable of modeling hundreds of thousands of atoms, and the results can have a significant impact on real-world engineering problems. The article reviews some of the modeling methods currently in use; provides illustrative examples of applications to challenges in sensors, fuel cells, and nanocomposites; and finally discusses prospects… 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 >

J. Ma¹, H. Lu¹, B. Wang¹, S. Roy¹, R. Hornung², A. Wissink², R. Komanduri^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.2, pp. 135-152, 2005, DOI:10.3970/cmes.2005.008.135

Abstract In the simulation of a wide range of mechanics problems including impact/contact/penetration and fracture, the material point method (MPM), Sulsky, Zhou and Shreyer (1995), demonstrated its computational capabilities. To resolve alternating stress sign and instability problems associated with conventional MPM, Bardenhagen and Kober (2004) introduced recently the generalized interpolation material point (GIMP) method and implemented for one-dimensional simulations. In this paper we have extended GIMP to 2D and applied to simulate simple tension and indentation problems. For simulations spanning multiple length scales, based on the continuum mechanics approach, we present a parallel GIMP computational method using the Structured Adaptive Mesh… More >

Y. Tomita ¹, M. Uchida ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.3, pp. 239-248, 2005, DOI:10.3970/cmes.2005.010.239

Abstract In this study, we clarified the micro- to mesoscopic deformation behavior of a semicrystalline polymer by employing a large-deformation finite element homogenization method. The crystalline plasticity theory with a penalty method for the inextensibility of the chain direction and the nonaffine molecular chain network theory were applied for the representation of the deformation behavior of the crystalline and amorphous phases, respectively, in the composite microstructure of the semicrystalline polymer. The 3D structure of lamellae in the spherulite of high-density polyethylene was modeled, and the tensile and compressive deformation behaviors were investigated. A series of computational simulations clarified the difference in… More >

Paul R. Dawson¹, Donald E. Boyce², Ronald Rogge³

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.2, pp. 123-142, 2005, DOI:10.3970/cmes.2005.010.123

Abstract Computational mechanics provides a powerful environment for modeling the evolution of material structure during deformation processes and for associating that evolution with changes to the mechanical properties. In this paper, we illustrate a two-scale formulation that links the mechanical loading applied at the scale of a component (the continuum scale) to the responses of the material at the scale of the crystals that comprise it (the crystal scale). Employing the capabilities offered by computational mechanics, we can better understand how heterogeneity of deformation arising at both the continuum and crystal scales influences the behaviors observed experimentally. Such an understanding is… More >

V.K. Tewary², D.T. Read²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.4, pp. 359-372, 2004, DOI:10.3970/cmes.2004.006.359

Abstract An integrated Green's function and molecular dynamics technique is developed for multiscale modeling of a nanostructure in a semi-infinite crystal lattice. The equilibrium configuration of the atoms inside and around the nanostructure is calculated by using molecular dynamics that accounts for nonlinear interatomic forces. The molecular dynamics is coupled with the lattice statics Green's function for a large crystallite containing a million or more atoms. This gives a fully atomistic description of a nanostructure in a large crystallite that includes the effect of nonlinear forces. The lattice statics Green's function is then related to the anisotropic continuum Green's function that… 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 >

Nasr M. Ghoniem¹, Kyeongjae Cho²

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.2, pp. 147-174, 2002, DOI:10.3970/cmes.2002.003.147

Abstract As a result of surging interest in finding fundamental descriptions for the strength and failure properties of materials, and the exciting prospects of designing materials from their atomic level, an international symposium on Multiscale Modeling was convened at ICES'2K in Los Angeles during August 23 - 25, 2000. In this symposium, 23 speakers with research interests spanning fields as diverse as traditional mechanics, physics, chemistry and materials science have given talks at this symposium. The topics of discussion were focused on sub-continuum modeling of the mechanics of materials, taking into account the atomic structure of solid materials. The main motivation… More >

A.Z. Lorbiecka¹, R.Vertnik², H.Gjerkeš¹, G. Manojlovič², B.Senčič², J. Cesar², B.Šarler^1,3

CMC-Computers, Materials & Continua, Vol.8, No.3, pp. 195-208, 2008, DOI:10.3970/cmc.2008.008.195

Abstract A numerical model is developed for the simulation of solidification grain structure formation (equiaxed to columnar and columnar to equiaxed transitions) during the continuous casting process of steel billets. The cellular automata microstructure model is combined with the macroscopic heat transfer model. The cellular automata method is based on the Nastac's definition of neighborhood, Gaussian nucleation rule, and KGT growth model. The heat transfer model is solved by the meshless technique by using local collocation with radial basis functions. The microscopic model parameters have been adjusted with respect to the experimental data for steel 51CrMoV4. Simulations have been carried out… More >