Computational Mechanics

, Volume 56, Issue 2, pp 277–290 | Cite as

A technique for calculating particle systems containing rigid and soft parts

  • Nima Nouri
  • Saeed Ziaei-Rad
Original Paper


In this paper, a method was proposed that can simulate the systems containing both rigid and soft parts with rigid body constraints. The idea was to consider the characteristics of rigid parts in their center of mass with three rotational degrees of freedom. In order to compute the systems containing both flexible and rigid parts, standard techniques in molecular dynamics were utilized for flexible parts. However, special procedures were proposed and formulated for rigid parts. Some details on the implementation of the proposed algorithm on GPU were also presented. Next, two case studies were solved. In the first example, a ball mill with the rigid particle of different shapes was considered and the performance of the proposed algorithm was checked and compared with the results obtained from others. In the second example, different self-assembly phases of a mixed rigid and non-rigid polymer molecule with Lennard–Jones pairwise interaction were studied. It was shown that the obtained self-assembly phases were identical to those reported by other researchers.


Many-particle dynamics GPU  Rigid and soft parts Ball mill Self assembly 


  1. 1.
    Alder BJ, Wainwright TE (1959) Studies in molecular dynamics. I. General method. J Chem Phys 31:459MathSciNetCrossRefGoogle Scholar
  2. 2.
    Rahman A (1964) Correlations in the motion of atoms in liquid argon. Phys Rev 136:A405–A411CrossRefGoogle Scholar
  3. 3.
    Nguyen H (2008) GPU Gems 3. Addison-Wesley, Boston (Chapter 31)Google Scholar
  4. 4.
    Ryckaert J, Ciccotti G, Berendsen H (1977) Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes. J Comput Phys 23:327CrossRefGoogle Scholar
  5. 5.
    Dubbeldam D, Oxford GAE, Krishna R, Broadbelt LJ, Snurr RQ (2010) Distance and angular holonomic constraints in molecular simulations. J Chem Phys 133:034114CrossRefGoogle Scholar
  6. 6.
    Eastman P, Pande VS (2010) Constant constraint matrix approximation: a robust, parallelizable constraint method for molecular simulations. J Chem Theory Comput 6:434CrossRefGoogle Scholar
  7. 7.
    Zhang Zh, Glotzer ShC (2004) Self-assembly of patchy particles. Nanoletters 4:1407–1413CrossRefGoogle Scholar
  8. 8.
    Zohdi TI (2011) Dynamics of clusters of charged particulates in electromagnetic fields. Int J Numer Methods Eng 85:1140–1159MathSciNetCrossRefGoogle Scholar
  9. 9.
    Zohdi TI (2012) Dynamics of charged particulate systems. Modeling, theory and computation. Springer, New YorkCrossRefGoogle Scholar
  10. 10.
    Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117:1CrossRefGoogle Scholar
  11. 11.
    Heine DR, Petersen MK, Grest GS (2010) Effect of particle shape and charge on bulk rheology of nanoparticle suspensions. J Chem Phys 132:184509CrossRefGoogle Scholar
  12. 12.
    Mountain R (2007) Solvation structure of ions in water. Int J Thermophys 28:536–543CrossRefGoogle Scholar
  13. 13.
    Johnson SD, Mountain RD, Meijer PHE (1995) Simulation of C60 through the plastic transition temperatures. J Chem Phys 103:1106CrossRefGoogle Scholar
  14. 14.
    CUDA toolkit 4.2 programming manualGoogle Scholar
  15. 15.
    Meel JA, Arnold A, Frenkel D, Zwart SFP, Belleman RG (2008) Harvesting graphics power for MD simulations. Mol Simul 34:259–266CrossRefGoogle Scholar
  16. 16.
    Miller TF III, Eleftheriou M, Pattnaik P, Ndirango A, Newns D, Martyna GJ (2002) Symplectic quaternion scheme for biophysical molecular dynamics. J Chem Phys 116(20):8649CrossRefGoogle Scholar
  17. 17.
    LAMMPS source code, (2010)
  18. 18.
    Andersen HC (1980) Molecular dynamics simulations at constant pressure and/or temperature. J Chem Phys 72:2384–2393CrossRefGoogle Scholar
  19. 19.
    Tuckerman ME, Alejandre J, Lopez-Rendon R, Jochim AL, Martyna GJ (2006) A Liouville-operator derived measure-preserving integrator for molecular dynamics simulations in the isothermal-isobaric ensemble. J Phys A 39:5629–5651MathSciNetCrossRefGoogle Scholar
  20. 20.
    Bitzek E, Koskinen P, Gahler F, Moseler M, Gumbsch P (2006) Structural relaxation made simple. PRL 97:170201CrossRefGoogle Scholar
  21. 21.
    Zhang HP, Makse HA (2005) Jamming transition in emulsions and granular materials. Phys Rev E 72:011301CrossRefGoogle Scholar
  22. 22.
    Yoneya M, Berendsen HJC, Hirasawa K (1994) A noniterative matrix method for constraint molecular-dynamics simulations. Mol Simul 13:395–405CrossRefGoogle Scholar
  23. 23.
    Forester TR, Smith W (1998) SHAKE, rattle, and roll: efficient constraint algorithms for linked rigid bodies. J Comput Chem 19:102–111CrossRefGoogle Scholar
  24. 24.
    McBride C, Wilson MR, Howard JAK (1998) Molecular dynamics simulations of liquid crystal phases using atomistic potentials. Mol Phys 93:955–964CrossRefGoogle Scholar
  25. 25.
    Andersen HC (1983) RATTLE: a ”Velocity” version of the SHAKE algorithm for molecular dynamics calculations. J Comput Phys 52:24–34CrossRefGoogle Scholar
  26. 26.
    Sang-Ho L, Palmo K, Krimm S (2005) WIGGLE: a new constrained molecular dynamics algorithm in Cartesian coordinates. J Comput Phys 210:171–182CrossRefGoogle Scholar
  27. 27.
    Lambrakos SG, Boris JP, Oran ES, Chandrasekhar I, Nagumo M (1989) A modified SHAKE algorithm for maintaining rigid bonds in molecular dynamics simulations of large molecules. J Comput Phys 85:473–486CrossRefGoogle Scholar
  28. 28.
    Leimkuhler B, Skeel R (1994) Symplectic numerical integrators in constrained Hamiltonian systems. J Comput Phys 112:117–125MathSciNetCrossRefGoogle Scholar
  29. 29.
    Gonnet P (2007) P-SHAKE: a quadratically convergent SHAKE in \({\cal O} (n^2)\). J Comput Phys 220:740–750MathSciNetCrossRefGoogle Scholar
  30. 30.
    CUDA toolkit 4.2 reference manualGoogle Scholar
  31. 31.
    Stone AJ, Dullweber A, Hodges MP, Popelier PLA, Wales DJ (1995–1996) ORIENT 3.2: A program for studying interactions between molecules. University of Cambridge, CambridgeGoogle Scholar
  32. 32.
    Höhner D, Wirtz S, Kruggel-Emden H, Scherer V (2011) Comparison of the multi-sphere and polyhedral approach to simulate non-spherical particles within the discrete element method: Influence on temporal force evolution for multiple contacts. Powder Technol 208:643–656CrossRefGoogle Scholar
  33. 33.
    Mishra BK, Murty CVR (2001) On the determination of contact parameters for realistic DEM simulations of ball mills. Powder Technol 115:290–297CrossRefGoogle Scholar
  34. 34.
    Crane AJ, Francisco J, Veracoechea M, Escobedob FA, Muller EA (2008) Molecular dynamics simulation of the mesophase behaviour of a model bolaamphiphilic liquid crystal with a lateral flexible chain. Soft Mater 4:1820–1829CrossRefGoogle Scholar
  35. 35.
    Tschierske C (2007) Liquid crystal engineering—new complex mesophase structures and their relations to polymer morphologies, nanoscale patterning and crystal engineering. Chem Soc Rev 36:1930–1970CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIsfahan University of TechnologyIsfahanIran

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