nach oben

International Journal of Mechanics and Materials in Design

Erschienen in:

01.01.2009

Coupling atomistics and continuum in solids: status, prospects, and challenges

verfasst von: J. M. Wernik, S. A. Meguid

Erschienen in: International Journal of Mechanics and Materials in Design | Ausgabe 1/2009

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

The recent focus of the scientific community on multiscale computer modeling techniques of nano-engineered materials stems from the desire to develop more realistic methodologies that are capable of accurately describing the varied time and length scales associated with this class of materials. Of importance is the ability to model the atomistic region using the appropriate techniques such as quantum mechanics/molecular dynamics, and the continuum region using homogenized properties. The continuity of atomistic and continuum regions in a solid necessitates a seamless coupling between these two regions. This is carried out using a transition region. In view of the large discrepancy between length and time scales in atomistic and continuum regions, the development of the transition region has been the main concern of the research community. It is the purpose of this review to critically discuss the issues concerning the transition region and the efforts made by the scientific community in treating them. In particular, this review addresses issues concerning the coupling of molecular dynamics to finite element modeling techniques. Three aspects of this review are accordingly considered. The first is concerned with the current state of atomistic–continuum coupling techniques in computational mechanics. The second is concerned with present the research conducted in the Engineering Mechanics and Design Laboratory at the University of Toronto in the field of nano-reinforced interfaces. Finally, we present the limitations of the current techniques and suggestions for improvements.

Vorheriger Artikel Theoretical and experimental sensitivity analysis of extra insensitive input shapers applied to open loop control of flexible arm

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Abraham, F.F.: Madly spanning the length scales in dynamic fracture. Comp. Model. Eng. Sci. 1(4), 63–69 (2000)MathSciNet

Abraham, F.F., Broughton, J.Q.: Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture. Europhys. Lett. 44(6), 783–787 (1998). doi:10.1209/epl/i1998-00536-9 CrossRef

Abraham, F.F., Walkup, R., Gao, H., Duchaineau, M., De la Rubia, T.D., Seager, M.: Simulating materials failure by using up to one billion atoms and the world’s fastest computer: brittle fracture. Proc. Natl. Acad. Sci. USA 99(9), 5777–5782 (2002). doi:10.1073/pnas.062012699 CrossRef

Adelzadeh, M., Shodja, H.M., Rafii-Tabar, H.: Computational modeling of the interaction of two edge cracks, and two edge cracks interacting with a nanovoid, via an atomistic finite element method. Comput. Mater. Sci. 42, 186–193 (2008). doi:10.1016/j.commatsci.2007.07.012 CrossRef

Allen, M.P., Tildesley, D.J.: Computer Simulation of Liquids. Claredon Press, Oxford (1987)MATH

Almeida, T.S., Coutinho, K., Cabral, B.J.C., Canuto, S.: Electronic properties of liquid ammonia: a sequential molecular dynamics/quantum mechanics approach. J. Chem. Phys. 128, 014506 (2008)

An, W., Wu, X., Yang, J.L., Zeng, X.C.: Adsorption and surface reactivity on single-walled boron nitride nanotubes containing stone-wales defects. J. Phys. Chem. C 111, 14105–14112 (2007). doi:10.1021/jp072443w

Aoyagi, T., et al.: A general-purpose coarse-grained molecular dynamics program. Comput. Phys. Commun. 145, 267–279 (2002). doi:10.1016/S0010-4655(02)00271-0 MATHCrossRef

Baker, A., Dutton, S., Kelly, D.: Composite Materials for Aircraft Structures, 2nd edn. American Institute of Aeronautics and Astronautics, USA (2004)

Bockenheimer, C., Valeske, B., Possart, W.: Network structure in epoxy aluminium bonds after mechanical treatment. Int. J. Adhes. Adhes. 22, 349–356 (2002). doi:10.1016/S0143-7496(02)00014-3 CrossRef

Broughton, J., Abraham, F.: Concurrent coupling of length scales methodology and application. Phys. Rev. B 60, 4 (1999). doi:10.1103/PhysRevB.60.2391

Buehler, M., Kong, Y., Gao, H.: Deformation mechanisms of very long single-wall carbon nanotubes subject to compressive loading. J. Eng. Mater. Technol. 126, 245–249 (2004)

Cao, G., Chen, X.: Buckling behavior of single-walled carbon nanotubes and a targeted molecular mechanics approach. Phys. Rev. B, 74, 10pp (2006a)

Cao, G., Chen, X.: Buckling of single-walled carbon nanotubes upon bending: molecular dynamics simulations and the finite element method. Phys. Rev. B. 73, 11pp (2006b)

Cao, G., Chen, X.: The effects of chirality and boundary conditions on the mechanical properties of single-walled carbon nanotubes. Int. J. Solids Struct. 44, 5447–5465 (2007). doi:10.1016/j.ijsolstr.2007.01.005 MATHCrossRef

Carlsson, A.: Beyond pair potentials in elemental transition metals and semiconductors. Solid. State. Phys. 43, 1–91 (1990). doi:10.1016/S0081-1947(08)60323-9 CrossRef

Cavallotti, C., Di Stanislao, M., Moscatelli, D., Veneroni, A.: Materials computation towards technological impact: the multiscale approach to thin films deposition. Electrochim. Acta 50, 4566–4575 (2005). doi:10.1016/j.electacta.2004.10.092 CrossRef

Chandraseker, K.I., Mukherjee, S.: Atomistic-continuum and ab initio estimation of the elastic moduli of single-walled carbon nanotubes. Comput. Mater. Sci. 40, 147–158 (2007). doi:10.1016/j.commatsci.2006.11.014 CrossRef

Clementi, E.: Global scientific and engineering simulations on scalar, vector and parallel LCAP-type supercomputers. Philos. Trans. R. Soc. Lond. A 326, 445–470 (1988). doi:10.1098/rsta.1988.0097 MATHCrossRef

Curtin, W., Miller, R.: Atomistic/continuum coupling in computational materials science. Model Simul. Mater. Sci. Eng. 11, R33–R68 (2003). doi:10.1088/0965-0393/11/3/201 CrossRef

Daw, M., Baskes, M.: Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B. 29, 12 (1984). doi:10.1103/PhysRevB.29.6443 CrossRef

Ding, F.: Theoretical study of the stability of defects in single-walled carbon nanotubes as a function of their distance from the nanotube end. Phys. Rev. B. 72, 245–409 (2005)

Dupuy L., Tadmor, E., Miller, R., Phillips, R.: Finite-temperature quasicontinuum: molecular dynamics without all the atoms. PRL 95 (2005)

Endo, M., Hayashi, T., Kim, Y.A., Terrones, M., Dresselhaus, M.S.: Applications of carbon nanotubes in the twenty-first century. Philos. Trans. R. Soc. Lond. A 362, 2223–2238 (2004). doi:10.1098/rsta.2004.1437 CrossRef

Ercolessi, F.: A Molecular Dynamics Primer. Spring College in Computational Physics, Trieste (1997)

Esfarjani, K., Gorjizadeh, N., Nasrollahi, Z.: Molecular dynamics of single wall carbon nanotube growth on nickel surface. Comput. Mater. Sci. 36, 117–120 (2006). doi:10.1016/j.commatsci.2005.02.022 CrossRef

Fiedler, B., Gojny, F.H., Wichmann, M.H.G., Nolte, M.C.M., Schulte, K.: Fundamental aspects of nano-reinforced composites. Compos. Sci. Technol. 66, 3115–3125 (2006). doi:10.1016/j.compscitech.2005.01.014 CrossRef

Fish, J., Nuggehally, M.A., Shepard, M.S., Picu, C.R., Badia, S., Parks, M.L., et al.: Concurrent AtC coupling based on a blend of the continuum stress and the atomistic force. Comput. Methods Appl. Mech. Eng. 196, 4548–4560 (2007). doi:10.1016/j.cma.2007.05.020 CrossRef

Frankland, S.J.V., Caglar, A., Brenner, D.W., Griebel, M.: Molecular simulation of the influence of chemical cross-links on the shear strength of carbon nanotube-polymer interfaces. J. Phys. Chem. B. 106, 12 (2002). doi:10.1021/jp015591+ CrossRef

Galano, A., Francisco-Marquez, M.: Reactivity of silicon and germanium doped CNTs toward aromatic sulfur compounds: a theoretical approach. Chem. Phys. 345, 87–94 (2008). doi:10.1016/j.chemphys.2008.01.040 CrossRef

Gao, X.L., Li, K.: A shear-lag model for carbon nanotube-reinforced polymer composites. Int. J. Solids Struct. 42, 1649–1667 (2005). doi:10.1016/j.ijsolstr.2004.08.020 MATHCrossRef

Gates, T.S., Odegard, G.M., Frankland, S.J.V., Clancy, T.C.: Computational materials: multi-scale modeling and simulation of nanostructured materials. Compos. Sci. Technol. 65, 2416–2434 (2005). doi:10.1016/j.compscitech.2005.06.009 CrossRef

Ghoniem, N., Busso, E., Kioussis, N., Huang, H.: Multiscale modeling of nanomechanics and micromechanics an overview. Philos. Mag. V83(31–34), 3475–3528 (2003). doi:10.1080/14786430310001607388 CrossRef

Gong, S.X., Meguid, S.A.: On the elastic fields of an elliptical inhomogeneity under plane deformation. Proc. R. Soc. Lond. A. 443(1919), 457–471 (1993)

Gong, N., Liang, Y., Yao, Y., Liu, B.: Static and dynamic analysis of carbon nanotube cantilever based on molecular dynamics simulation. Key Eng. Mater. 375–376, 631–635 (2008)CrossRef

Gumbsch, P.: An atomistic study of brittle fracture: toward explicit failure criteria from atomistic modeling. J. Mater. Res. 10(11), 2897–2907 (1995). doi:10.1557/JMR.1995.2897 CrossRef

Gumbsch, P., Beltz, G.: On the continuum versus atomistic descriptions of dislocation nucleation and cleavage in nickel. Model. Simul. Mater. Sci. Eng. 3, 597–613 (1995). doi:10.1088/0965-0393/3/5/002 CrossRef

Guo, Z., Yang, W.: MPM/MD handshaking method for multiscale simulation and its application to high energy cluster impacts. Int. J. Mech. Sci. 48, 145–159 (2006). doi:10.1016/j.ijmecsci.2005.08.007 MATHCrossRef

Guo, X., Leung, A.Y.T., Jiang, H., He, X.Q., Huang, Y.: Critical strain of carbon nanotubes: an atomic-scale finite element study. J. Appl. Mech. 74, 347–351 (2007)

Hao, S., Moran, B., Liu, W., Olson, G.: A hierarchical multi-physics model for design of high toughness steels. J. Comput. Aided Mater. Des. 10, 99–142 (2003). doi:10.1023/B:JCAD.0000036813.66891.41 CrossRef

Haslam, A.J., Moldovan, D., Phillpot, S.R., Wolf, D., Gleiter, H.: Combined atomistic and mesoscale simulation of grain growth in nanocrystalline thin films. Comput. Mater. Sci. 23, 15–32 (2002). doi:10.1016/S0927-0256(01)00218-X CrossRef

Hockney, R.W.: The potential calculation and some applications. Methods Comput. Phys. 9, 135–211 (1970)

Hu, N., Fukunaga, H., Lu, C., Kameyama, M., Yan, B.: Prediction of elastic properties of carbon nanotube reinforced composites. Proc. R. Soc. 461, 1685–1710 (2005). doi:10.1098/rspa.2004.1422 CrossRef

Hughes, T.R.: The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Englewood Cliffs, NJ Prentice-Hall (1987)MATH

Izvekov, S., Voth, G.: A multiscale coarse-graining method for biomolecular systems. Phys. Chem. B. 109, 2469–2473 (2005)

Jones, J.: On the determination of molecular fields: II from the equation of state of a gas. Proc. R. Soc. A106, 463–477 (1924). doi:10.1098/rspa.1924.0082 CrossRef

Karpov, E., Wagner, G., Liu, W.: A green’s function approach to deriving non-reflecting boundary conditions in molecular dynamics simulations. Int. J. Numer. Methods Eng. 62, 1250–1262 (2005). doi:10.1002/nme.1234 MATHCrossRef

Knap, J., Ortiz, M.: An analysis of the quasicontinuum method. J. Mech. Phys. Solids 49, 1899–1923 (2001). doi:10.1016/S0022-5096(01)00034-5 MATHCrossRef

Kohlhoff, S., Gumbsch, P., Fischmeister, H.: Crack propagation in b.c.c crystals studied with a combined finite-element and atomistic model. Philos. Mag. A 64(4), 851–878 (1991). doi:10.1080/01418619108213953 CrossRef

Kojic, M., Filipovic, N., Tsuda, A.: A mesoscopic bridging scale method for fluids and coupling dissipative particle dynamics with continuum finite element method. Comput. Methods Appl. Eng. 197, 821–833 (2008). doi:10.1016/j.cma.2007.09.011 CrossRefMathSciNetMATH

Leung, A.Y.T., Guo, X., He, X.Q., Kitipornchai, S.: A continuum model for zigzag single-walled carbon nanotubes. Appl. Phys. Lett. 86, 083110 (2005)

Leung, A.Y.T., Guo, X., He, X.Q., Jiang, H., Hunag, Y.: Postbuckling of carbon nanotubes by atomic-scale finite element. J. Appl. Phys. 99, 124308 (2006)

Li, C., Chou, T.: Elastic moduli of multi-walled carbon nanotubes and the effect of van der waals forces. Compos. Sci. Technol. 63, 1517–1524 (2003a). doi:10.1016/S0266-3538(03)00072-1

Li, C., Chou, T.: A structural mechanics approach for the analysis of carbon nanotubes. Int. J. Solids Struct. 40, 2487–2499 (2003b). doi:10.1016/S0020-7683(03)00056-8 MATHCrossRef

Li, C., Chou, T.: Multiscale modeling of compressive behavior of carbon nanotube/polymer composites. Compos. Sci. Technol. 66, 2409–2414 (2006). doi:10.1016/j.compscitech.2006.01.013 CrossRef

Liew, K.M., Wong, C.H., He, X.Q., Tan, M.J., Meguid, S.A.: Nanomechanics of single and multiwalled carbon nanotubes. Phys. Rev. B. 69, 11 (2004). doi:10.1103/PhysRevB.69.115429 CrossRef

Liu, W., Karpov, E., Zhang, S., Park, H.: An introduction to computational nanomechanics and materials. Comput. Methods Appl. Mech. Eng. 193, 1529–1578 (2004a). doi:10.1016/j.cma.2003.12.008 MATHCrossRefMathSciNet

Liu, B., Huang, Y., Jiang, H., Qu, S., Hwang, K.C.: The atomic-scale finite element method. Comput. Methods Appl. Mech. Eng. 193, 1849–1864 (2004b). doi:10.1016/j.cma.2003.12.037 MATHCrossRef

Liu, B., Jiang, H., Huang, Y., Qu, S., Yu, M.-F., Hwang, K.C.: Atomic-scale finite element method in multiscale computation with applications to carbon nanotubes. Phys. Rev. B. 72, 035435 (2005)

Liu, W.K., Park, H.S., Qian, D., Karpov, E.G., Kadowaki, H., Wagner, G.J.: Bridging scale methods for nanomechanics and materials. Comput. Methods Appl. Mech. Eng. 195, 1407–1421 (2006). doi:10.1016/j.cma.2005.05.042 MATHCrossRefMathSciNet

Lordi, V., Yao, N.: Molecular mechanics of binding in carbon-nanotube-polymer composites. J. Mater. Res. 15, 12 (2000)

Lu, G., Tadmor, E.B., Kaxiras, E.: From electrons to finite elements: a concurrent multiscale approach for metals. Phys. Rev. B. 73, 124108 (2006a)

Lu, H., Daphalapurkar, N., Wang, B., Roy, S., Komanduri, R.: Multiscale simulation from atomistic to continuum–coupling molecular dynamics (MD) with the material point method (MPM). Philos. Mag 86(20), 2971–2994 (2006b). doi:10.1080/14786430600625578 CrossRef

Meguid, S.A., Chen, B.J.: Modelling temperature-dependent fracture nucleation of SWCNTs using atomistic-based continuum theory. Int. J. Sol. Struct. 44(11–12), 3828–3839 (2007)MATH

Meguid, S.A., Sun, Y.: On the tensile and shear strength of nano-reinforced composite interfaces. Mater. Des. 325, 289–296 (2004)

Meguid, S.A., Sun, Y.: Intelligent condition monitoring of aerospace composites: part I—nano reinforced surfaces & interfaces. Int. J. Mech. Mater. Des. 37–52 (2005)

Meguid, S.A., Wang, X.D.: On the dynamic interaction between a microdefect and a main crack. Proc. R. Soc. Lond. A. 448(1934), 449–464 (1995)

Meguid, S.A., Wang, X.D.: The dynamic interaction of a microcrack with a main crack under antiplane loading. Int. J. Solids Struct. 31(8), 1085–1097 (1994). doi:10.1016/0020-7683(94)90165-1 MATHCrossRef

Micheal Lai, W., Rubin, D., Krempl, E.: Introduction to Continuum Mechanics, Revised Edition. Pergamon Press, NY (1978)

Miller, R., Tadmor, E.: The quasicontinuum method: overview, applications and current directions. J. Comput. Aided. Mater. Des. 9, 203–239 (2002). doi:10.1023/A:1026098010127 CrossRef

Miller, R., Tadmor, E., Phillips, R., Ortiz, M.: Quasicontinuum simulation of fracture at the atomic scale. Model. Simul. Mater. Sci. Eng. 6, 607–638 (1998a). doi:10.1088/0965-0393/6/5/008 CrossRef

Miller, R., Ortiz, M., Phillips, R., Shenoy, V., Tadmor, E.: Quasicontinuum models of fracture and plasticity. Eng. Fract. Mech. 61, 427–444 (1998b). doi:10.1016/S0013-7944(98)00047-2 CrossRef

Miller, R.E., Shilkrot, L.E., Curtin, W.A.: A coupled atomistics and discrete dislocation plasticity simulation of nanoindentation into single crystal films. Acta Mater. 52, 271–284 (2004). doi:10.1016/j.actamat.2003.09.011 CrossRefMathSciNet

Mylvaganam, K., Vodenitcharova, T., Zhang, L.C.: The bending-kinking analysis of a single-walled carbon nanotube–a combined molecular dynamics and continuum mechanics technique. J. Mater. Sci. 41, 3341–3347 (2006). doi:10.1007/s10853-005-5389-7 CrossRef

Namilae, S., Chandra, N.: Multiscale model to study the effect of interfaces in carbon nanotube-based composites. J. Eng. Mater. Technol. 127 222–232 (2005)

Odegard, G.M., Frankland, S.J.V.: Effect of nanotube functionalisation on the elastic properties of polyethylene nanotube composites. AIAA J. 43(8), 1828–1835 (2005). doi:10.2514/1.9468 CrossRef

Odegard, G.M., Gates, T.S., Nicholson, L.M., Wise, K.E.: Equivalent-continuum modeling of nano-structured materials. Compos. Sci. Technol. 62, 1869–1880 (2002). doi:10.1016/S0266-3538(02)00113-6 CrossRef

Odegard, M., Gates, T.S., Wise, K.E., Park, C., Siochi, E.J.: Constitutive modeling of nanotube-reinforced polymer composites. Compos. Sci. Technol. 63, 1671–1687 (2003). doi:10.1016/S0266-3538(03)00063-0 CrossRef

Pantano, A., Parks, D.M., Boyce, M.C.: Mechanics of deformation of single- and multi-wall carbon nanotubes. J. Mech. Phys Solids 52, 789–821 (2004). doi:10.1016/j.jmps.2003.08.004 MATHCrossRef

Park, H., Liu, W.: An introduction and tutorial on multiple-scale analysis in solids. Comput. Methods Appl. Mech. Eng. 193, 1733–1772 (2004). doi:10.1016/j.cma.2003.12.054 MATHCrossRefMathSciNet

Park, H.S., Karpov, E.G., Liu, W.K., Klein, P.A.: The bridging scale for two-dimensional atomistic/continuum coupling. Philos. Mag. 85(1), 79–113 (2005). doi:10.1080/14786430412331300163 CrossRef

Qian, D., Wagner, G., Liu, W.: A multiscale projection method for the analysis of carbon nanotubes. Comput. Methods Appl. Mech. Eng. 193(17–20), 1603–1632 (2004). doi:10.1016/j.cma.2003.12.016 MATHCrossRef

Qu, S., Shastry, V., Curtin, W., Miller, R.: A finite-temperature dynamic coupled atomistic/discrete dislocation method. Model. Simul. Mater. Sci. Eng. 13, 1101–1118 (2005). doi:10.1088/0965-0393/13/7/007 CrossRef

Rafii-Tabar, H.: Modelling the nano-scale phenomena in condensed matter physics via computer-based numerical simulations. Phys. Rep. 325, 239–310 (2000). doi:10.1016/S0370-1573(99)00087-3 CrossRef

Rodney, D., Phillips, R.: Structure and strength of dislocation junctions: an atomic level analysis. PRL 82, 1704–1707 (1999). doi:10.1103/PhysRevLett.82.1704 CrossRef

Rudd, R.E.: Coupling of length scales in MEMS modelling: the atomic limit of finite elements. Int. Soc. Opt. Eng. 4019, 16–25 (2000)

Rudd, R.E., Broughton, J.Q.: Coarse-grained molecular dynamics and the atomic limit of finite elements. Phys. Rev. B. 58, 10 (1998). doi:10.1103/PhysRevB.58.R5893 CrossRef

Rudd, R.E., Broughton, J.Q.: Coupling of length scales and atomistic simulation of MEMS resonators. Int. Soc. Opt. Eng. 3680, 104–113 (1999)

Rudd, R., Broughton, J.: Concurrent coupling of length scales in solid state systems. Phys. Status Solidif. 217, 251 (2000). doi :10.1002/(SICI)1521-3951(200001)217:1<251::AID-PSSB251>3.0.CO;2-ACrossRef

Rudd, R.E., Broughton, J.Q.: Coarse-grained molecular dynamics: nonlinear finite elements and finite temperature. Phys. Rev. B. 72, 144104 (2005)

Shenoy, V., Miller, R., Tadmor, E., Phillips, R., Ortiz, M.: Quasicontinuum models of interfacial structure and deformation. Phys. Rev. Lett. 80, 742–745 (1998). doi:10.1103/PhysRevLett.80.742 CrossRef

Shenoy, V., Miller, R., Tadmor, E., Rodney, D., Phillips, R., Ortiz, M.: An adaptive finite element approach to atomic-scale mechanics–the quasicontinuum method. J. Mech. Phys Solids 47, 611–642 (1999a). doi:10.1016/S0022-5096(98)00051-9 MATHCrossRefMathSciNet

Shenoy, V., Miller, R., Tadmor, E., Rodney, D., Phillips, R., Ortiz, M.: An adaptive finite element approach to atomic-scale mechanics—the quasicontinuum method. J. Mech. Phys. Solids 47, 611–642 (1999b). doi:10.1016/S0022-5096(98)00051-9 MATHCrossRefMathSciNet

Shi, D., Feng, X., Hang, H., Huang, Y., Hwang, K.: Multiscale analysis of fracture of carbon nanotubes embedded in composites. Int. J. Fract. 134, 369–386 (2005). doi:10.1007/s10704-005-3073-1 CrossRef

Shiari, B., Miller, R., Curtin, W.: Coupled atomistic/discrete dislocation simulations of nanoindentation at finite temperatures, J. Eng. Mater. Technol. 127, 358–368 (2005)

Shilkrot, L.E., Miller, R.E., Curtin, W.A.: Multiscale plasticity modeling: coupled atomistics and discrete dislocation mechanics. J. Mech. Phys. Solids. 52, 755–787 (2004). doi:10.1016/j.jmps.2003.09.023 MATHCrossRefMathSciNet

Shlarl, B., Miller, R.E., Klug, D.D.: Multiscale modeling of solids at the nanoscale: dynamic approach. Can. J. Phys. 86, 391–400 (2008). doi:10.1139/P07-145 CrossRef

Spencer, A.J.M.: Continuum Mechanics. Dover Publications, Dover edition, NY (2004)MATH

Srivastava, D., Wei, C.: Nanomechanics of carbon nanotubes and composites. Appl. Mech. Rev 56, 2 (2003). doi:10.1115/1.1538625 CrossRef

Stillinger, F., Weber, T.: Computer simulation of local order in condensed phases of silicon. Phys. Rev. B 31, 8 (1985). doi:10.1103/PhysRevB.31.5262 CrossRef

Sulsky, D., Zhou, S., Schreyer, H.: Application of a particle-in-cell-method to solid mechanics. Comput. Phys. Commun. 87, 236–252 (1995). doi:10.1016/0010-4655(94)00170-7 MATHCrossRef

Sun, Y.: Influence of nanofillers on bond strength and toughness, University of Toronto, Ph.D. Thesis, 2007

Tadmor, E., Phillips, R., Ortiz, M.: Mixed atomistic and continuum models of deformation in solids. Langmuir 12, 4529–4534 (1996a). doi:10.1021/la9508912 CrossRef

Tadmor, E., Ortiz, M., Phillips, R.: Quasicontinuum analysis of defects in solids. Philos. Mag. A 73(6), 1529–1563 (1996b). doi:10.1080/01418619608243000 CrossRef

Tadmor, E., Miller, R., Phillips, R., Ortiz, M.: Nanoindentation and incipient plasticity. J. Mater. Res. 14, 2233–2250 (1999). doi:10.1557/JMR.1999.0300 CrossRef

Troya, D., Mielke, S.L., Schatz, G.C.: Carbon nanotube fracture-differences between quantum mechanical mechanisms and those of empirical potentials. Chem. Phys. Lett. 382, 133–141 (2003). doi:10.1016/j.cplett.2003.10.068 CrossRef

Tserpes, K.I., Papanikos, P., Labeas, G.: Sp.G. Pantelakis, Multi-scale modeling of tensile behavior of carbon nanotube-reinforced composites. Theor. Appl. Fract. Mech. 49, 51–60 (2008). doi:10.1016/j.tafmec.2007.10.004 CrossRef

Verlet, L.: Computer experiments on classical fluids. I. Thermodynamical properties of lennard-jones molecules. Phys. Rev. 159, 98–103 (1967). doi:10.1103/PhysRev.159.98 CrossRef

Vvedensky, D.: Multiscale modeling of nanostructures. J. Phys. Condens. Matter 16, R1537–R1576 (2004). doi:10.1088/0953-8984/16/50/R01 CrossRef

Wagner, G.J., Liu, W.K.: Coupling of atomistic and continuum simulations using a bridging scale decomposition. J. Comput. Phys. 190, 249–274 (2003). doi:10.1016/S0021-9991(03)00273-0 MATHCrossRef

Wagner, G., Karpov, E., Liu, W.: Molecular dynamics boundary conditions for regular crystal lattices. Comput. Methods Appl. Mech. Eng. 193, 1579–1601 (2004). doi:10.1016/j.cma.2003.12.012 MATHCrossRefMathSciNet

Wang, X.D., Meguid, S.A.: Dynamic interaction between a matrix crack and a circular inhomogeneity with a distinct interphase. Int. J. Solids Struct. 36, 517–531 (1999). doi:10.1016/S0020-7683(98)00039-0 MATHCrossRef

Wang, C., Zhou, G., Liu, H., Wu, J., Qiu, Y., Gu, B., et al.: Chemical functionalisation of carbon nanotubes by carboxyl groups on stone-wales defects: a density functional theory study. J. Phys. Chem. B 110, 10266–10271 (2006). doi:10.1021/jp060412f CrossRef

Wong, C.H., Liew, K.M., He, X.Q., Tan, M.J., Meguid, S.A.: Modeling and simulation of multi-walled carbon nanotubes using molecular dynamics simulation. NSTI. Nanotech. 3, 2004 (2004)

Yakobson, B.I., Brabec, C.J., Bernhole, J.: Nanomechanics of carbon tubes: instabilities beyond linear response. Phys. Rev. Lett. 76, 14 (1996). doi:10.1103/PhysRevLett.76.2511 CrossRef

Zeng, Q.H., Yu, A.B., Lu, G.Q.: Multiscale modeling and simulation of polymer nanocomposites. Prog. Polym. Sci. 33, 191–269 (2008). doi:10.1016/j.progpolymsci.2007.09.002 CrossRef

Zhao, X., Cummings, P.T.: Molecular dynamics study of carbon nanotube oscillators revisited. J. Chem. Phys. 124, 134–705 (2006)

Zhao, J., Ding, Y.: Silicon carbide nanotubes functionalized by transition metal atoms: a density-functional study. J. Phys. Chem. C 112, 2558–2564 (2008). doi:10.1021/jp073722m CrossRef

Zienkiewicz, O.C.: The Finite Element Method, vol 1–2, 4th edn. McGraw-Hill, London (1991)

Titel: Coupling atomistics and continuum in solids: status, prospects, and challenges
verfasst von: J. M. Wernik
S. A. Meguid
Publikationsdatum: 01.01.2009
Verlag: Springer Netherlands
Erschienen in: International Journal of Mechanics and Materials in Design / Ausgabe 1/2009
Print ISSN: 1569-1713
Elektronische ISSN: 1573-8841
DOI: https://doi.org/10.1007/s10999-008-9087-x

Premium Partner

Marktübersichten

Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.

Zur Marktübersicht

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 1/2009

The elastic displacement and stress in a material to promote reflection and transmission of an incoming wave

Genetic algorithm based optimal design for vibration control of composite shell structures using piezoelectric sensors and actuators

An iterative procedure for determining effective stress–strain curves of sheet metals

Multiscale design of a rectangular sandwich plate with viscoelastic core and supported at extents by viscoelastic materials

Theoretical and experimental sensitivity analysis of extra insensitive input shapers applied to open loop control of flexible arm

Premium Partner

Marktübersichten