A multiscale component mode synthesis approach for dynamic analysis of nanostructures. (English) Zbl 1352.74222

Summary: A component mode synthesis-based multiscale approach is developed for dynamic analysis of nanostructures. The multiscale approach decomposes a nanostructure into atomistic and continuum regions and employs vibrational modes to connect the regions of different scales, enabling a reflectionless atomistic-to-continuum coupling. Dynamic response of the coupled atomistic and continuum regions is computed concurrently using a common time scale. Numerical results indicate that the multiscale approach has significant condensation and scaling advantages, and it is well suited for modeling and simulation of large and complex systems.


74M25 Micromechanics of solids
74A60 Micromechanical theories
Full Text: DOI


[1] Kohlhoff, Crack propagation in b.c.c crystals studied with a combined finite element and atomistic model, Philosophical Magazine A 64 (4) pp 851– (1991)
[2] Broughton, Concurrent coupling of length scales: Methodology and application, Physical Review B 60 pp 2391– (1999)
[3] Atkas, A combined continuum/dsmc technique for multiscale analysis of microfluidic filters, Journal of Computational Physics 178 (2) pp 342– (2002)
[4] Deymier, Concurrent multiscale model of an atomic crystal coupled with elastic continua, Physical Review B 66 (2) pp 134106– (2002)
[5] Wagner, Coupling of atomistic and continuum simulations using a bridging scale decomposition, Journal of Computational Physics 190 pp 249– (2003) · Zbl 1169.74635
[6] Xiao, A bridging domain method for coupling continua with molecular dynamics, Computer Methods in Applied Mechanics and Engineering 193 pp 1645– (2004) · Zbl 1079.74509
[7] Fish, Discrete-to-continuum bridging based on multigrid principles, Computer Methods in Applied Mechanics and Engineering 193 pp 1693– (2004) · Zbl 1079.74503
[8] Waisman, A space-time multilevel method for molecular dynamics simulations, Computer Methods in Applied Mechanics and Engineering 195 pp 6542– (2006) · Zbl 1126.82001
[9] Tadmor, Mixed atomistic and continuum models of deformation in solids, Langmuir 12 pp 4529– (1996a)
[10] Tadmor, Quasicontinuum analysis of defects in solids, Philosophical Magazine A 73 (6) pp 4529– (1996b)
[11] Jiang, A finite-temperature continuum theory based on interatomic potentials, Journal of Engineering Materials and Technology 127 pp 408– (2005)
[12] Tang, Finite-temperature quasicontinuum method for multiscale analysis of silicon nanostructures, Physical Review B 74 (6) pp 064110– (2006)
[13] Liu, The atomic-scale finite element method, Computer Methods in Applied Mechanics and Engineering 193 pp 1849– (2004) · Zbl 1079.74645
[14] Fish, Heterogeneous multiscale method: A general methodology for multiscale modeling, Physical Review B 67 pp 092101– (2003)
[15] Rudd, Coarse-grained molecular dynamics and the atomic limit of finite elements, Physical Review B 58 (10) pp R5893– (1998)
[16] Rudd, Coarse-grained molecular dynamics: Nonlinear finite elements and finite temperature, Physical Review B 72 (14) pp 144104– (2005)
[17] Liu, An introduction to computational nanomechanics and materials, Computer Methods in Applied Mechanics and Engineering 193 pp 1529– (2004) · Zbl 1079.74506
[18] Fish, Bridging the scales in nano engineering and science, Journal of Nanoparticle Research 8 pp 577– (2006)
[19] Wernik, Coupling atomistics and continuum in solids: status, prospects, and challenges, International Journal of Mechanics and Materials in Design 5 (1) pp 79– (2009)
[20] Liu, Multiscale methods for mechanical science of complex materials: Bridging from quantum to stochastic multiresolution continuum, International Journal of Numerical Methods in Engineering 83 pp 1039– (2010) · Zbl 1197.74007
[21] Kudin, C2F, BN, and C nanoshell elasticity from ab initio computations, Physical Review B 64 (23) pp 235406– (2001)
[22] Nayfeh, Nonlinear Oscillations (1979)
[23] Iwatsubo, Nonlinear vibration analysis of a rotor system using component mode synthesis method, Archive of Applied Mechanics 72 pp 843– (2003) · Zbl 1068.74557
[24] Maradudin, Theory of Lattice Dynamics in the Harmonic Approximation, in Solid State Physics, Suppl. 3 pp 244– (1971)
[25] Girifalco, Energy of cohesion, compressibility, and the potential-energy functions of the graphite system, Journal of Chemical Physics 25 pp 693– (1956)
[26] Morse, Diatomic molecules according to the wave mechanics. ii. vibrational levels, Physical Review 34 pp 57– (1929) · JFM 55.0539.02
[27] Tersoff, Empirical interatomic potential for carbon, with applications to amorphous carbon, Physical Review Letter 61 pp 2879– (1988)
[28] Brenner, Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films, Physical Review B 42 pp 9458– (1990)
[29] Stillinger, Computer simulation of local order in condensed phases of silicon, Physical Review B 31 pp 5262– (1985)
[30] Belytschko, Atomistic simulations of nanotube fracture, Physical Review B 65 (23) pp 235430– (2002)
[31] Mathew, Concurrent coupling of atomistic and continuum models at finite temperature, Computer Methods in Applied Mechanics and Engineering 200 (5-8) pp 765– (2011) · Zbl 1225.74010
[32] Tuckerman, Statistical Mechanics: Theory and Molecular Simulation (2010)
[33] Patera, A spectral element method for fluid dynamics: Laminar flow in a channel expansion, Journal of Computational Physics 54 pp 468– (1984) · Zbl 0535.76035
[34] Karniadakis, Spectral/hp Element Methods for CFD (1999)
[35] Canuto, Spectral Methods: Fundamentals in Single Domains (2006) · Zbl 1093.76002
[36] Gottlieb, Numerical Analysis of Spectral Method: Theory and Applications (1977)
[37] Hurty, Dynamic analysis of structural systems using component modes, AIAA Journal 3 (4) pp 678– (1965)
[38] Craig, Fundamentals of Structural Dynamics (2006)
[39] Li, A multilevel component mode synthesis approach for the calculation of the phonon density of states of nanocomposite structures, Computational Mechanics 42 (4) pp 593– (2008) · Zbl 1310.74003
[40] Li, Component mode synthesis approaches for quantum mechanical electrostatic analysis of nanoscale devices, Journal of Computational Electronics 10 (3) pp 300– (2011)
[41] Craig, Coupling of substructures for dynamic analysis, AIAA Journal 6 (7) pp 1313– (1968) · Zbl 0159.56202
[42] Craig, Free-interface methods of substructure coupling for dynamic analysis, AIAA Journal 14 (11) pp 1633– (1976)
[43] Shyu, On the use of multiple quasi-static mode compensation sets for component mode synthesis of complex structures, Finite Element in Analysis and Design 35 pp 119– (2000)
[44] Xu, In Bridging the Scales in Science and Engineering (2009)
[45] Belytschko, Coupling methods for continuum model with molecular model, International Journal for Multiscale Computational Engineering 1 pp 115– (2003)
[46] Sert, Spectral element formulations on non-conforming grids: A comparative study of pointwise matching and integral projection methods, Journal of Computational Physics 211 (1) pp 300– (2006) · Zbl 1120.65338
[47] Tsai CT Szabo BA A constraint method-a new finite element technique NASA Technical Memorandum, NASA, TM X-2893 1973 551 568
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.