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Published online by Cambridge University Press:  12 October 2022

Shaofan Li  and
Jun Li
Shaofan Li
Affiliation:
University of California, Berkeley
Jun Li
Affiliation:
Wuhan University of Technology
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Introduction to Computational Nanomechanics
Multiscale and Statistical Simulations
 , pp. 559 - 564
Publisher: Cambridge University Press
Print publication year: 2022

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References

Abraham, F. F., Broughton, J. Q., Bernstein, N., and Kaxiras, E. 1998. Spanning the length scales in dynamic simulation. Computers in Physics, 12(6), 538–546.Google Scholar
Andersen, H. C. 1980. Molecular dynamics simulations at constant pressure and or temperature. Journal of Chemical Physics, 72, 2384–2393.CrossRefGoogle Scholar
Antoun, T., Curran, D. R., Seaman, L., Kanel, G. I., Razorenov, S. V., and Utkin, A. V. 2003. Spall fracture. Springer Science & Business Media.Google Scholar
Arndt, M., Nairz, O., Vos-Andreae, J., Keller, C., Van der Zouw, G., and Zeilinger, A. 1999. Wave–particle duality of C 60 molecules. Nature, 401(6754), 680–682.Google Scholar
Baskes, M. I. 1999. Many-body effects in fcc metals: A Lennard-Jones embedded-atoms potential. Physical Review Letters, 83(13), 2592.Google Scholar
Belytschko, T. 1983. An overview of semidiscretization and time integration procedures. In Computational methods for transient analysis (A 84-29160 12-64), 1–65. North-Holland.Google Scholar
Born, M. and Huang, K. 1954. Dynamical theory of crystal lattice. Oxford University Press.Google Scholar
Car, R. and Parrinello, M. 1985. Unified approach for molecular dynamics and densityfunctional theory. Physical Review Letters, 55(22), 2471.Google Scholar
Chandler, D. 1987. Introduction to modern statistical mechanics. Oxford University Press.Google Scholar
Chialvo, A. A. and Debenedetti, P. G. 1990. On the use of the Verlet neighbor list in molecular dynamics. Computer Physics Communications, 60(2), 215–224.CrossRefGoogle Scholar
Clatterbuck, D. M., Chrzan, D. C., and Morris, J. W. Jr. 2003. The ideal strength of iron in tension and shear. Acta Materials, 51, 2271–2283.CrossRefGoogle Scholar
Clausius, R. J. E. 1870. On a mechanical theorem applicable to heat. Philosophical Magazine Series 4, 122–127.Google Scholar
Dodson, B. W. 1987. Development of a many-body Tersoff-type potential for silicon. Physical Review B, 35(6), 2795.Google Scholar
Einstein, A. 1905. On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat. Annalen der Physik, 17, 208, 549–560.CrossRefGoogle Scholar
Elder, R. M., Mattson, W. D., and Sirk, T. W. 2019. Origins of error in the localized virial stress. Chemical Physics Letters, 731, 136580.CrossRefGoogle Scholar
Elices, M. G. G. V., Guinea, G. V., Gomez, J., and Planas, J. 2002. The cohesive zone model: Advantages, limitations and challenges. Engineering Fracture Mechanics, 69(2), 137–163.CrossRefGoogle Scholar
Ericson, F. and Schweitz, J. A. 1990. Micromechanical fracture strength of silicon. Journal of Applied Physics, 68, 5840.Google Scholar
Eringen, A. C. and Maugin, G. A. 2012. Electrodynamics of continua I: Foundations and solid media. Springer Science & Business Media.Google Scholar
Español, P. and Warren, P. 1995. Statistical mechanics of dissipative particle dynamics. Europhysics Letters, 30(4), 191–196.Google Scholar
Evans, D. J. and Morriss, G. 2008. Statistical mechanics of nonequilibrium liquids. Cambridge University Press.CrossRefGoogle Scholar
Falk, M. L., Needleman, A., and Rice, J. R. 2001. A critical evaluation of cohesive zone models of dynamic fracture. Journal de Physique IV, France, 11, 43–50.Google Scholar
Fan, H. and Li, S. 2015. Multiscale cohesive zone modeling of crack propagations in polycrystalline solids. GAMM-Mitteilungen, 38, 268–284.Google Scholar
Finnis, M. W. and Sinclair, J. E. 1984. A simple empirical N-body potential for transition metals. Philosophical Magazine, A, 50(1), 45–55.Google Scholar
Finnis, M. W. and Sinclair, J. E. 1986. Erratum: A simple empirical N-body potential for transition metals. Philosophical Magazine, A, 53(1), 161.Google Scholar
Fleck, N. A. and Hutchinson, J. W. 1997. Strain gradient plasticity. Advances in Applied Mechanics, 33, 296–361.Google Scholar
Fock, V. 1930. Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems. Zeitschrift für Physik, 61(1–2), 126–148.Google Scholar
Fokker, A. D. 1914. Die mittlere Energie rotierender elektrischer Dipole im Strahlungsfeld. Annalen der Physik, 348(5), 810–820.CrossRefGoogle Scholar
Frenkel, D. and Smit, B. 1996. Understanding molecular simulation from algorithm to applications. Academic Press.Google Scholar
Gear, C. W. 1966. The numerical integration of ordinary differential equations of various orders. Technical Report 7126. Argonne National Laboratory.CrossRefGoogle Scholar
Gear, C. W. 1971. Numerical initial value problems in ordinary differential equations. Prentice-Hall.Google Scholar
Groot, R. D. and Warren, P. B. 1997. Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation. The Journal of Chemical Physics, 107(11), 4423–4435.Google Scholar
Hardy, R. J. 1982. Formulas for determining local properties in molecular-dynamics simulations: Shock waves. The Journal of Chemical Physics, 76(1), 622–628.Google Scholar
Hartree, D. R. 1957. The calculation of atomic structures. Wiley & Sons.Google Scholar
Hartree, D. R. 1928. The wave mechanics of an atom with a non-coulomb central field. Part II. Theory and method. Mathematical Proceedings of the Cambridge Philosophical Society, 24(1), 89–110.Google Scholar
He, M. and Li, S. 2012. An embedded atom hyperelastic constitutive model and multiscale. Computational Mechanics, 49, 337–355.Google Scholar
Heisenberg, W. 1985. Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Springer. In Original Scientific Papers Wissenschaftliche Originalarbeiten (pp. 478–504).Google Scholar
Hogenberg, P. and Kohn, W. 1964. Inhomogeneous electron gas. Physical Review, 136(3B), B864.CrossRefGoogle Scholar
Hoogerbrugge, P. J. and Koelman, J. M. V. A. 1992. Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhysics Letters, 19(3), 155.Google Scholar
Hoover, W. G. 1985. Canonical dynamics: Equilibrium phase-space distributions. Physical Review A, 31, 1695.CrossRefGoogle ScholarPubMed
Hu, H., Liu, M., Wang, Z. F., Zhu, J., Wu, D., Ding, H., Liu, Z., and Liu, F. 2012. Quantum electronic stress: Density-functional-theory formulation and physical manifestation. Physical Review Letters, 109(5), 055501.Google Scholar
Hughes, T. J. 2012. The finite element method: Linear static and dynamic finite element analysis. Courier Corporation.Google Scholar
Hughes, T. J., Taylor, R. L., Sackman, J. L., Curnier, A., and Kanoknukulchai, W. 1976. A finite element method for a class of contact-impact problems. Computer Methods in Applied Mechanics and Engineering, 8(3), 249–276.Google Scholar
Irving, J. H. and Kirkwood, J. G. 1950. The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics. The Journal of Chemical Physics, 18(6), 817–829.CrossRefGoogle Scholar
Israelachvili, J. N. 2011. Intermolecular and surface forces. Academic Press.Google Scholar
Izumi, S. and Sakai, S. 2004. Internal displacement and elastic properties of the silicon Tersoff model. JSME International Journal Series A Solid Mechanics and Material Engineering, 47, 54–61.CrossRefGoogle Scholar
Kadanoff, L. P. 2000. Statistical physics: Statics, dynamics and renormalization. World Scientific Publishing Company.CrossRefGoogle Scholar
Kelchner, C. L., Plimpton, S. J., and Hamilton, J. C. 1998. Dislocation nucleation and defect structure during surface indentation. Physical Review B, 58(17), 11085.Google Scholar
Khoei, A. R. and DorMohammadi, H. 2012. Validity and size-dependency of Cauchy-Born hypothesis with Tersoff potential in silicon nano-structures. Computational Materials Science, 63, 168–177.CrossRefGoogle Scholar
Khoei, A. R., DorMohammadi, H., and Aramoon, A. 2014. A temperature-related boundary Cauchy-Born method for multi-scale modeling of silicon nano-structures. Physics Letter A, 378, 551–560.Google Scholar
Kinjo, T. and Hyodo, S. A. 2007. Equation of motion for coarse-grained simulation based on microscopic description. Physical Review E, 75(5), 051109.Google Scholar
Koelman, J. M. V. A. and Hoogerbrugge, P. J. 1993. Dynamic simulations of hard-sphere suspensions under steady shear. Europhysics Letters, 21(3), 363.CrossRefGoogle Scholar
Kohn, W. and Sham, J. L. 1965. Self-consistent equations including exchange and correlation effects. Physical Review, 140 (4A), A1133–1138.Google Scholar
Kubo, R. 1966. The fluctuation-dissipation theorem. Reports on Progress in Physics, 29(1), 255.CrossRefGoogle Scholar
Lehoucq, R. B. and Sears, M. P. 2011. Statistical mechanical foundation of the peridynamic nonlocal continuum theory: Energy and momentum conservation laws. Physical Review E, 84(3), 031112.CrossRefGoogle ScholarPubMed
Li, S. and Liu, W. K. 1999. Reproducing kernel hierarchical partition of unity. Part I: Formulation and theory. International Journal of Numerical Methods for Engineering, 45, 251–288.Google Scholar
Li, S., Ren, B., and Minaki, H., , H. 2014. Multiscale crystal defect dynamics: A dual-lattice process zone model. Philosophical Magazine, 94, 1414–1450.Google Scholar
Li, S. and Sheng, N. 2010. On multiscale non-equilibrium molecular dynamics simulations. International Journal for Numerical Methods in Engineering, 83, 998–1038.Google Scholar
Li, S. and Tong, Q. 2015. A concurrent multiscale micromorphic molecular dynamics. Journal of Applied Physics, 117, 154303.Google Scholar
Li, S. and Urata, S. 2016. An atomistic-to-continuum molecular dynamics: Theory, algorithm, and applications. Computer Methods in Applied Mechanics and Engineering, 306, 452–478.Google Scholar
Li, S., Zeng, X., Ren, B., Qian, J., Zhang, J., and Jha, A. J. 2012. An atomistic-based interphase zone model for crystalline solids. Computer Methods in Applied Mechanics and Engineering, 229–232, 87–109.CrossRefGoogle Scholar
Li, X., Kasai, T., Nakao, S., Tanaka, H., Ando, T., Shikida, M., and Sato, K. 2005. Measurement for fracture toughness of single crystal silicon film with tensile test. Sensors and Actuators A: Physical, 119, 229–235.CrossRefGoogle Scholar
Liu, L. and Li, S. 2012. A finite temperature multiscale interphase zone model and simulations of fracture. Journal of Engineering Materials and Technology, 134, 31014.CrossRefGoogle Scholar
Lyu, D. and Li, S. 2017. Multiscale crystal defect dynamics: A coarse-grained lattice defect model based on crystal microstructure. Journal of Mechanics and Physics of Solids, 107, 379–410.Google Scholar
Marsden, J. and Hughes, T. 1983. Mathematical foundations of elasticity. Prentice-Hall.Google Scholar
Martínez, L., Andrade, R., Birgin, E. G., and Martínez, J. M. 2009. Packmol: A package for building initial configurations for molecular dynamics simulations. Journal of Computational Chemistry, 30(13), 2157–2164.Google Scholar
Martyna, G. J., Tuckerman, M. E., Tobias, D. J., and Klein, M. L. 1996. Explicit reversible integrators for extended systems dynamics. Molecular Physics, 87(5), 1117.Google Scholar
Milstein, F. and Farber, B. 1980. Theoretical fcc-bcc transition under [100] tensile loading. Physical Review Letters, 44, 277–280.Google Scholar
Mishin, Y., Mehl, M. J., Papaconstantopoulos, D. A., Voter, A. F., and Kress, J. D. 2001. Structural stability and lattice defects in copper: Ab initio, tight-binding, and embeddedatom calculations. Physical Review B, 63(22), 224106.Google Scholar
Murashima, T., Urata, S., and Li, S. 2019. Coupling finite element method with Large Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) for hierarchical multiscale simulations. The European Physical Journal B, 9, 211–215.CrossRefGoogle Scholar
Murdoch, A. I. 1983. The motivation of continuum concepts and relations from discrete considerations. The Quarterly Journal of Mechanics and Applied Mathematics, 36(2), 163–187.Google Scholar
Murdoch, A. I. 2007. A critique of atomistic definition of the stress tensor. Journal of Elasticity, 88, 113–140.Google Scholar
Nielsen, F. 2010 (September). Legendre transformation and information geometry. Technical Report CIG-MEMO2. www.informationgeometry.org.Google Scholar
Nielsen, O. H. and Martin, R. M. 1983. First-principles calculation of stress. Physical Review Letters, 50(9), 697.Google Scholar
Nielsen, O. H. and Martin, R. M. 1985. Quantum-mechanical theory of stress and force. Physical Review B, 32(6), 3780.Google Scholar
Nosé, S. 1984. A unified formulation of the constant temperature molecular dynamics methods. Journal of Chemical Physics, 81, 511.Google Scholar
Onsager, L. 1944. Crystal statistics. I. A two-dimensional model with an order-disorder transition. Physical Review, 65(3–4), 117.CrossRefGoogle Scholar
Park, H. S. and Klein, P. A. 2008. A surface Cauchy-Born model for silicon nanostructures. Computer Methods in Applied Mechanics and Engineering, 197, 3249–3260.Google Scholar
Parrinello, M. and Rahman, A. 1980. Crystal structure and pair potentials: A molecular dynamics study. Physical Review Letters, 14, 1196–1199.Google Scholar
Parrinello, M. and Rahman, A. 1981. Polymorphic transitions in single crystals: A new molecular dynamics method. Journal of Applied Physics, 12, 7182–7190.Google Scholar
Pelaez, S., Garcia-Mochales, P., and Serena, P. A. 2006. A comparison between EAM interatomic potentials for Al and Ni: From bulk systems to nanowires. Physica Status Solidi (A), 203(6), 1248–1253.Google Scholar
Petersen, K. E. 1982. Silicon as a mechanical material. Proceedings of the IEEE, 70, 420–457.CrossRefGoogle Scholar
Pilar, F. L. 1990. Elementary quantum chemistry. Dover Publication.Google Scholar
Planck, M. 1917. Über einen Satz der statistischen Dynamik und seine Erweiterung in der Quantentheorie. Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin, 24, 324–341.Google Scholar
Podio-Guidugli, P., 2010. On (Andersen–) Parrinello–Rahman molecular dynamics, the related metadynamics, and the use of the Cauchy–Born rule. Journal of Elasticity, 100(1), 145–153.Google Scholar
Qian, J. and Li, S. 2011. Application of multiscale cohesive zone model to simulate fracture in polycrystalline solids. ASME Journal of Engineering Materials and Technology, 133, 011010.Google Scholar
Ren, B. and Li, S. 2013. A three-dimensional atomistic-based process zone finite element simulation of fragmentation in polycrystalline solids. International Journal for Numerical Methods in Engineering, 93, 989–1014.Google Scholar
Roussas, G. G. 2003. An introduction to probability and statistical inference. Elsevier.Google Scholar
Rudd, R. E. and Broughton, J. Q. 1998. Coarse-grained molecular dynamics and the atomic limit of finite elements. Physical Review B, 58(10), R5893–R5896.Google Scholar
Rudd, R. E. and Broughton, J. Q. 2005. Coarse-grained molecular dynamics: Nonlinear finite elements and finite temperature. Physical Review B, 72(14), 144104.Google Scholar
Rudzinski, J. F. 2019. Recent progress towards chemically-specific coarse-grained simulation models with consistent dynamical properties. Computation, 7(3), 42.Google Scholar
The LAMMPS Developers. 2022. LAMMPS Documentation, Sandia National Laboratories (SNL), Albuquerque, NM, https://docs.lammps.org/Manual.pdfGoogle Scholar
Sauer, R. and Li, S. 2007. A contact mechanics model for quasi-continua. International Journal for Numerical Methods in Engineering, 71, 931–962.Google Scholar
Silling, S. A. 2000. Reformulation of elasticity theory for discontinuities and long-range forces. Journal of the Mechanics and Physics of Solids, 48(1), 175–209.Google Scholar
Silling, S. A. and Askari, E. 2005. A meshfree method based on the peridynamic model of solid mechanics. Computers & Structures, 83(17–18), 1526–1535.Google Scholar
Silling, S. A., Epton, M., Weckner, O., Xu, J., and Askari, E. 2007. Peridynamic states and constitutive modeling. Journal of Elasticity, 88(2), 151–184.Google Scholar
Silling, S. A. and Lehoucq, R. B. 2010. Peridynamic theory of solid mechanics. Advances in Applied Mechanics, 44, 73–168.Google Scholar
Slater, J. C. 1928. The self consistent field and the structure of atoms. Physical Review, 32(3), 339–348.Google Scholar
Subramaniyan, A. K. and Sun, C. T. 2008. Continuum interpretation of virial stress in molecular simulations. International Journal of Solids and Structures, 45, 4340–4346.CrossRefGoogle Scholar
Sunyk, R. and Steinmann, P. 2003. On higher gradients in continuum-atomistic modelling. International Journal of Solids and Structures, 40(24), 6877–6896.Google Scholar
Tadmor, E. B., Ortiz, M., and Phillips, R. 1996. Quasicontinuum analysis of defects in solids. Philosophical Magazine A, 73, 1529–1563.Google Scholar
Tang, S., Hou, T. Y., and Liu, W. K. 2006. A pseudo-spectral multiscale method: Interfacial conditions and coarse grid equations. Journal of Computational Physics, 213(1), 57–85.CrossRefGoogle Scholar
Taylor, G. I. 1938. Plastic strain in metals. Journal of the Institute of Metals, 62, 307–324.Google Scholar
Tersoff, J. 1988. Empirical interatomic potential for silicon with improved elastic properties. Physical Review B, 38, 9902.CrossRefGoogle ScholarPubMed
Todd, B. D. and Daivis, P. J. 2017. Nonequilibrium molecular dynamics: Theory, algorithms and applications. Cambridge University Press.Google Scholar
Tong, Q. and Li, S. 2015. From molecular systems to continuum solids: A multiscale structure and dynamics. Journal of Chemical Physics, 143, 064101.Google Scholar
Tong, Q. and Li, S. 2016. Multiscale coupling of molecular dynamics and peridynamics. Journal of Mechanics and Physics of Solids, 95, 169–187.Google Scholar
Tong, Q. and Li, S. 2020. A concurrent multiscale study of dynamic fracture. Computer Methods in Applied Mechanics and Engineering, 366, 113075.Google Scholar
Tretiakov, K. V. and Scandolo, S. 2004. Thermal conductivity of solid argon from molecular dynamics simulations. The Journal of Chemical Physics, 120(8), 3765–3769.Google Scholar
Tsai, D. H. 1979. The virial theorem and stress calculation in molecular dynamics. The Journal of Chemical Physics, 70, 1375.Google Scholar
Urata, S. and Li, S. 2017a. Higher order Cauchy-Born rule based multiscale cohesive zone model and prediction of fracture toughness of Silicon thin films. International Journal of Fracture, 203(1), 159–181.Google Scholar
Urata, S. and Li, S. 2017b. A multiscale model for amorphous materials. Computational Materials Science, 135, 64–77.Google Scholar
Urata, S. and Li, S. 2018. A multiscale shear-transformation-zone (STZ) model and simulation of plasticity in amorphous solids. Acta Materialia, 155, 153–165.Google Scholar
Wagner, G. J. and Liu, W. K. 2003. Coupling of atomistic and continuum simulations using a bridging scale decomposition. Journal of Computational Physics, 190, 249–274.Google Scholar
Wang, S., Li, Z., and Pan, W. 2019. Implicit-solvent coarse-grained modeling for polymer solutions via Mori-Zwanzig formalism. Soft Matter, 15(38), 7567–7582.Google Scholar
Wang, S., Ma, Z., and Pan, W. 2020. Data-driven coarse-grained modeling of polymers in solution with structural and dynamic properties conserved. Soft Matter, 16(36), 8330–8344.Google Scholar
Warren, T. L., Silling, S. A., Askari, A., Weckner, O., Epton, M. A., and Xu, J. 2009. A non-ordinary state-based peridynamic method to model solid material deformation and fracture. International Journal of Solids and Structures, 46(5), 1186–1195.Google Scholar
Wiener, N. 1964. Time series. MIT Press.Google Scholar
Xu, X. P. and Needleman, A. 1994. Numerical simulations of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids, 42(9), 1397–1434.Google Scholar
Zeng, X. 2011. Application of an atomistic field theory to Nano/Micro materials modeling and simulation. Computer Modeling in Engineering and Sciences, 74, 183–201.Google Scholar
Zeng, X. and Li, S. 2010. A multiscale cohesive zone model and simulations of fracture. Computer Methods in Applied Mechanics and Engineering, 199, 547–556.Google Scholar
Zhou, M. 2003. A new look at the atomic level virial stress: On continuum-molecular system equivalence. Proceedings of the Royal Society of London. A: Mathematical, Physical and Engineering Sciences, 459(2037), 2347–2392.Google Scholar

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  • Bibliography
  • Shaofan Li, University of California, Berkeley, Jun Li
  • Book: Introduction to Computational Nanomechanics
  • Online publication: 12 October 2022
  • Chapter DOI: https://doi.org/10.1017/9780511894770.025
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  • Bibliography
  • Shaofan Li, University of California, Berkeley, Jun Li
  • Book: Introduction to Computational Nanomechanics
  • Online publication: 12 October 2022
  • Chapter DOI: https://doi.org/10.1017/9780511894770.025
Available formats
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  • Bibliography
  • Shaofan Li, University of California, Berkeley, Jun Li
  • Book: Introduction to Computational Nanomechanics
  • Online publication: 12 October 2022
  • Chapter DOI: https://doi.org/10.1017/9780511894770.025
Available formats
×