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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2012002133
pages 307-326


Tianxiang Liu
Department of Engineering, University of Leicester, Leicester, LE1 7RH, United Kingdom
Peter Wriggers
Institute of Mechanics and Computational Mechanics, University of Hannover Appelstrasse 9a D - 30167 Hannover, Germany
Geng Liu
School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an, 710072, China


Analyzing contact performances between two surfaces plays a key role in studying friction, wear, and lubrication in tribological systems. Advancements of micro/nano-electromechanical system (MEMS/NEMS) and nanotechnology in recent years demand the developments of multiscale contact mechanics. By using multiscale methods, calculation domains which consider local mechanical behaviors with nanoscale characteristics could be simulated by atomistic methods, and other domains can still use conventional methods for larger lengths and time scales in order to save computational costs or achieve high-performance calculations for larger scale systems. A molecular dynamics-continuum concurrent multiscale model for quasi-static nanoscale contacts is presented, which can both implement equilibrium of the energy field and force field in different scale domains. In molecular dynamics simulations, since the speed of the approaching probe is very small in comparison with the longitudinal sound speed, which is usually in the order of 103 m/s, the results of the contact process can be treated approximately as the quasi-static case in nature. For continuum simulations, the Cauchy-Born rule is employed to evaluate the nonlinear constitutive relationship of the coarse scale. By using the present multiscale model, simulations of nanoscale adhesive contacts between a cylinder and a substrate are implemented. The results show that the boundary conditions are effective for the contact problems. Furthermore, 2-D adhesive contacts of rough surfaces are investigated. Some behaviors of the nanoscale contact processes are discussed, and differences between the multiscale model and the pure molecular dynamics simulation are revealed.


  1. Agrawal, P. M., Rice, B. M., and Thompson, D. L., Predicting trends in rate parameters for self-diffusion on FCC metal surfaces. DOI: 10.1016/S0039-6028(02)01916-7

  2. Allen, N. P. and Tildesley, D. J., Computer Simulation of Liquids. DOI: 10.1063/1.2810937

  3. Arndt, M. and Griebel, M., Derivation of higher order gradient continuum models from atomistic models for crystalline solids. DOI: 10.1137/040608738

  4. Bandeira, A. A., Wriggers, P., Pimenta, P., and de Mattos, P., Numerical derivation of contact mechanics interface laws using a finite element approach for large 3D deformation. DOI: 10.1002/nme.867

  5. Belytschko, T. and Xiao, S. P., Coupling methods for continuum model with molecular model. DOI: 10.1615/IntJMultCompEng.v1.i1.10

  6. Belytschko, T. and Xiao, S. P., Multiscale analysis with atomistic/continuum models for fracture.

  7. E, W. and Ming, P., Cauchy-born rule and the stability of crystalline solids: Static problems. DOI: 10.1007/s00205-006-0031-7

  8. Farrell, D. E., Karpov, E. G., and Liu, W. K., Algorithms for bridging scale method parameter. DOI: 10.1007/s00466-007-0156-z

  9. Ghazali, A. and Levy, J. C. S., Low temperature Pb deposits on Cu(001): Monte Carlo structural studies. DOI: 10.1016/S0039-6028(01)01060-3

  10. Guan, P., Mckenzie, D. R., and Pailthorpe, B. A., MD simulations of Ag film growth using the Lennard-Jones potential. DOI: 10.1088/0953-8984/8/45/011

  11. Guan, P., Mckenzie, D. R., and Paithorpe, B. A., Patterns of energy dissipation in three-dimensional face-centered cubic lattices after ion impact. DOI: 10.1088/0953-8984/9/23/025

  12. Harold, S. P., Eduard, G. K., and Liu, W. K., The bridging scale for two-dimensional atomistic/continuum coupling. DOI: 10.1080/14786430412331300163

  13. Hoekstra, J., Yan, H., and Kalonji, G., Structural variations in strained crystalline multilayers. DOI: 10.1557/JMR.1994.2190

  14. Israelachvili, J. N., Skimming the surface. DOI: 10.1038/435893a

  15. Karpov, E. G., Yu, H., Park, H. S., Liu,W. K.,Wang, Q., and Qian, D., Multiscale boundary conditions in crystalline solids: Theory and application to nanoindentation. DOI: 10.1016/j.ijsolstr.2005.10.003

  16. Ladeveze, P., Nouy, A., and Loiseau, O., A multiscale computational approach for contact problems. DOI: 10.1016/S0045-7825(02)00406-1

  17. Li, X., Yang, J. Z., and E, W., A multiscale coupling method for the modeling of dynamics of solids with application to brittle cracks. DOI: 10.1016/

  18. Liu, W. K., Karpov, E. G., Zhang, S., and Park, H. S., An introduction to computational nanomechanics and materials. DOI: 10.1016/j.cma.2003.12.008

  19. Liu, T., Liu, G., Wriggers, P., and Zhu, S., Study on contact characteristic of nanoscale asperities by using molecular dynamics simulations. DOI: 10.1115/1.3063812

  20. Luan, B. and Robbins, M. O., The breakdown of continuum models for mechanical contacts. DOI: 10.1038/nature03700

  21. Luan, B. Q., Hyun, S., Molinari, J. F., Bernstein, N., and Robbins, M. O., Multiscale modeling of two-dimensional contacts. DOI: 10.1103/PhysRevE.74.046710

  22. McVeigh, C. and Liu, W. K., Linking microstructure and properties through a predictive multiresolution continuum. DOI: 10.1016/j.cma.2007.12.020

  23. Morrey, W. C. and Wille, L. T., Large-scale molecular dynamics simulation of fracture growth in alloys. DOI: 10.1016/0921-5107(95)01482-9

  24. Park, H. S., Karpov, E. G., and Liu, W. K., Non-reflecting boundary conditions for atomistic, continuum and coupled atomistic/ continuum simulations. DOI: 10.1002/nme.1357

  25. Paskin, A. and Gohar, A., Computer simulation of crack propagation. DOI: 10.1103/PhysRevLett.44.940

  26. Persson, B. N. J. and Ballone, P., Squeezing lubrication films: Layering transition for curved solid surfaces with long-range elasticity. DOI: 10.1063/1.481589

  27. Qi,W. H.,Wang, M. P., and Hu,W. Y., Calculation of the cohesive energy of metallic nanoparticles by the Lennard-Jones potential. DOI: 10.1016/j.matlet.2003.10.048

  28. Qian, D. and Gondhalekar, R. H., A virtual atom cluster approach to the mechanics of nanostructures. DOI: 10.1615/IntJMultCompEng.v2.i2.70

  29. Rapaport, D. C., The Art of Molecular Dynamics Simulation. DOI: 10.1017/CBO9780511816581

  30. Sauer, R. A. and Li, S., An atomic interaction-based continuum model for adhesive contact mechanics. DOI: 10.1016/j.finel.2006.11.009

  31. Sauer, R. A. and Li, S., A contact mechanics model for quasi-continua. DOI: 10.1002/nme.1970

  32. Song, J.-H. and Belytschko, T., Multiscale aggregating discontinuities method for micro-macro failure of composites. DOI: 10.1016/j.compositesb.2009.01.007

  33. Swope, W. C., Andersen, H. C., Berens, P. H., and Wilson, K. R., Computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters. DOI: 10.1063/1.442716

  34. Tadmor, E. B., Ortiz, M., and Phillips, R., Quasicontinuum analysis of defects in solids. DOI: 10.1080/01418619608243000

  35. Tan, S., Ghazali, A., and Levy, J. C. S., Pb/Cu(100) surface superstructures: Monte Carlo and molecular dynamics simulations. DOI: 10.1016/S0039-6028(97)00540-2

  36. Tang, S., Hou, T. Y., and Liu, W. K., A mathematical framework of the bridging scale method. DOI: 10.1002/nme.1514

  37. Tang, S., A finite difference approach with velocity interfacial conditions for multiscale computations of crystalline solids. DOI: 10.1016/

  38. Temizer, I. and Wriggers, P., A multiscale contact homogenization technique for the modeling of third bodies in the contact interface. DOI: 10.1016/j.cma.2008.08.008

  39. Tian, R., Chan, S., Tang, S., Kopacz, A. N., Wang, J.-S., Jou, H.-J., Siad, L., Lindgren, L.-E., Olsen, G. B., and Liu, W. K., A multiresolution continuum simulation of the ductile fracture process. DOI: 10.1016/j.jmps.2010.07.002

  40. Verlet, L., Computer “experiments” on classical fluids, I. Thermodynamical properties of Lennard-Jones molecules. DOI: 10.1103/PhysRev.159.98

  41. Wagner, G. J. and Liu, W. K., Coupling of atomistic and continuum simulations using a bridging scale decomposition. DOI: 10.1016/S0021-9991(03)00273-0

  42. Xiao, S. P. and Belytschko, T., A bridging domain method for coupling continua with molecular dynamics. DOI: 10.1016/j.cma.2003.12.053

  43. Yang, C., Tartaglino, U., and Persson, B. N. J., A multiscale molecular dynamics approach to contact mechanics. DOI: 10.1140/epje/e2006-00004-9

  44. Yu, N. and Polycarpou, A. A., Adhesive contact based on the Lennard-Jones potential: A correction to the value of the equilibrium distance as used in the potential. DOI: 10.1016/j.jcis.2004.06.029

  45. Yuan, Z. and Fish, J., Multiple scale Eigendeformation-based reduced order homogenization. DOI: 10.1016/j.cma.2008.12.038

  46. Zeng, X. and Li, S., Multiscale modeling and simulation of soft adhesion and contact of stem cells. DOI: 10.1016/j.jmbbm.2010.06.002

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