PART II—Discrete Element Method (DEM) Approaches: Dynamic Powder Deposition

  • Tarek I. ZohdiEmail author
Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 60)


Dry powders require different modeling and simulation tools to characterize their behavior. One family of methods that is ideally suited to this task are discrete element methods. This chapter introduces the reader to this type of modeling.


  1. 1.
    Zohdi, T.I.: Genetic design of solids possessing a random-particulate microstructure. Philosoph. Trans. R. Soc. Math. Phys. Eng. Sci. 361(1806), 1021–1043 (2003)Google Scholar
  2. 2.
    Zohdi, T.I.: On the compaction of cohesive hyperelastic granules at finite strains. Proc. R. Soc. 454(2034), 1395–1401 (2003)Google Scholar
  3. 3.
    Zohdi, T.I.: Computational design of swarms. Int. J. Numer. Methods Eng. 57, 2205–2219 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Zohdi, T.I.: Constrained inverse formulations in random material design. Comput. Methods Appl. Mech. Eng. 1–20 192, 28–30, 18, 3179–3194 (2003)Google Scholar
  5. 5.
    Zohdi, T.I.: Staggering error control for a class of inelastic processes in random microheterogeneous solids. Int. J. Nonlinear Mech. 39, 281–297 (2004)zbMATHCrossRefGoogle Scholar
  6. 6.
    Zohdi, T.I.: Modeling and simulation of a class of coupled thermo-chemo-mechanical processes in multiphase solids. Comput. Methods Appl. Mech. Eng. 193(6–8), 679–699 (2004)zbMATHCrossRefGoogle Scholar
  7. 7.
    Zohdi, T.I.: Modeling and direct simulation of near-field granular flows. Int. J. Solids Struct. 42(2), 539–564 (2004)zbMATHCrossRefGoogle Scholar
  8. 8.
    Zohdi, T.I.: A computational framework for agglomeration in thermo-chemically reacting granular flows. Proc. R. Soc. 460(2052), 3421–3445 (2004)Google Scholar
  9. 9.
    Zohdi, T.I.: Statistical ensemble error bounds for homogenized microheterogeneous solids. J. Appl. Math. Phys. (Zeitschrift für Angewandte Mathematik und Physik) 56(3), 497–515 (2005)Google Scholar
  10. 10.
    Zohdi, T.I.: Charge-induced clustering in multifield particulate flow. Int. J. Numer. Methods Eng. 62(7), 870–898 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Zohdi, T.I.: On the optical thickness of disordered particulate media. Mech. Mater. 38, 969–981 (2006)CrossRefGoogle Scholar
  12. 12.
    Zohdi, T.I., Kuypers, F.A.: Modeling and rapid simulation of multiple red blood cell light scattering. Proc. R. Soc. Interface 3(11), 823–831 (2006)CrossRefGoogle Scholar
  13. 13.
    Zohdi, T.I.: Computation of the coupled thermo-optical scattering properties of random particulate systems. Comput. Methods Appl. Mech. Eng. 195, 5813–5830 (2006)zbMATHCrossRefGoogle Scholar
  14. 14.
    Zohdi, T.I.: Computation of strongly coupled multifield interaction in particle-fluid systems. Comput. Methods Appl. Mech. Eng. 196, 3927–3950 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Zohdi, T.I.: Particle collision and adhesion under the influence of near-fields. J. Mech. Mater. Struct. 2(6), 1011–1018 (2007)CrossRefGoogle Scholar
  16. 16.
    Zohdi, T.I.: On the computation of the coupled thermo-electromagnetic response of continua with particulate microstructure. Int. J. Numer. Methods Eng. 76, 1250–1279 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Zohdi, T.I.: Mechanistic modeling of swarms. Comput. Methods Appl. Mech. Eng. 198(21–26), 2039–2051 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Zohdi, T.I.: Charged wall-growth in channel-flow. Int. J. Eng. Sci. 48, 1520 (2010)Google Scholar
  19. 19.
    Zohdi, T.I.: On the dynamics of charged electromagnetic particulate jets. Arch. Comput. Methods Eng. 17(2), 109–135 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Zohdi, T.I., Kuypers, F.A., Lee, W.C.: Estimation of Red Blood Cell volume fraction from overall permittivity measurement. Int. J. Eng. Sci. 48, 1681–1691 (2010)zbMATHCrossRefGoogle Scholar
  21. 21.
    Zohdi, T.I.: Simulation of coupled microscale multiphysical-fields in particulate-doped dielectrics with staggered adaptive FDTD. Comput. Methods Appl. Mech. Eng. 199, 79–101 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Zohdi, T.I.: Dynamics of clusters of charged particulates in electromagnetic fields. Int. J. Numer. Methods Eng. 85, 1140–1159 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Zohdi, T.I.: Joule-heating field phase-amplification in particulate-doped dielectrics. Int. J. Eng. Sci. 49, 30–40 (2011)CrossRefGoogle Scholar
  24. 24.
    Zohdi, T.I.: Estimation of electrical-heating load-shares for sintering of powder mixtures. Proc. R. Soci. 468, 2174–2190 (2012)CrossRefGoogle Scholar
  25. 25.
    Zohdi, T.I.: Modeling and simulation of the optical response rod-functionalized reflective surfaces. Comput. Mech. 50(2), 257–268 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Zohdi, T.I.: On the reduction of heat generation in lubricants using microscale additives. Int. J. Eng. Sci. 62, 84–89 (2013)CrossRefGoogle Scholar
  27. 27.
    Zohdi, T.I.: Electromagnetically-induced vibration in particulate-doped materials. ASME J. Vib. Acoust. 135(3) (2013).
  28. 28.
    Zohdi, T.I.: Numerical simulation of charged particulate cluster-droplet impact on electrified surfaces. J. Comput. Phys. 233, 509–526 (2013)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Zohdi, T.I.: On inducing compressive residual stress in microscale print-lines for flexible electronics. Int. J. Eng. Sci. 62, 157–164 (2013)CrossRefGoogle Scholar
  30. 30.
    Zohdi, T.I.: Rapid simulation of laser processing of discrete particulate materials. Arch. Comput. Methods Eng. 20, 309–325 (2013)CrossRefGoogle Scholar
  31. 31.
    Zohdi, T.I.: A direct particle-based computational framework for electrically-enhanced thermo-mechanical sintering of powdered materials. Math. Mech. Solids 19(1), 93–113 (2014)Google Scholar
  32. 32.
    Zohdi, T.I.: On cross-correlation between thermal gradients and electric fields. Int. J. Eng. Sci. 74, 143–150 (2014)CrossRefGoogle Scholar
  33. 33.
    Zohdi, T.I.: Mechanically-driven accumulation of microscale material at coupled solid-fluid interfaces in biological channels. Proc. R. Soc. Interface 11, 20130922 (2014)CrossRefGoogle Scholar
  34. 34.
    Zohdi, T.I.: A computational modeling framework for heat transfer processes in laser-induced dermal tissue removal. Comput. Mech. Eng. Sci. 98(3), 261–277 (2014)Google Scholar
  35. 35.
    Zohdi, T.I.: Additive particle deposition and selective laser processing-a computational manufacturing framework. Comput. Mech. 54, 171–191 (2014)zbMATHCrossRefGoogle Scholar
  36. 36.
    Zohdi, T.I.: Embedded electromagnetically sensitive particle motion in functionalized fluids. Comput. Part. Mech. 1, 27–45 (2014)CrossRefGoogle Scholar
  37. 37.
    Zohdi, T.I.: Rapid computation of statistically-stable particle/feature ratios for consistent substrate stresses in printed flexible electronics. J. Manuf. Sci. Eng. ASME (2015). MANU-14-1476.
  38. 38.
    Zohdi, T.I.: A computational modelling framework for high-frequency particulate obscurant cloud performance. Int. J. Eng. Sci. 89, 75–85 (2015)CrossRefGoogle Scholar
  39. 39.
    Zohdi, T.I.: On necessary pumping pressures for industrial process-driven particle-laden fluid flows. J. Manuf. Sci. Eng. ASME (2015).
  40. 40.
    Zohdi, T.I.: On the thermal response of a laser-irradiated powder particle in additive manufacturing. CIRP J. Manuf. Sci. Technol. 10, 7783, Aug 2015Google Scholar
  41. 41.
    Zohdi, T.I.: Modeling and simulation of cooling-induced residual stresses in heated particulate mixture depositions. Comput. Mech. 56, 613–630 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  42. 42.
    Zohdi, T.I.: Modeling and efficient simulation of the deposition of particulate flows onto compliant substrates. Int. J. Eng. Sci. 99, 74–91 (2015).
  43. 43.
    Zohdi, T.I.: Modeling and simulation of laser processing of particulate-functionalized materials. Arch. Comput. Methods Eng. 1–25 (2015).
  44. 44.
    Duran, J.: Sands, powders and grains. An introduction to the physics of Granular Matter. Springer (1997)Google Scholar
  45. 45.
    Pöschel, T., Schwager, T.: Computational Granular Dynamics. Springer (2004)Google Scholar
  46. 46.
    Onate, E., Idelsohn, S.R., Celigueta, M.A., Rossi, R.: Advances in the particle finite element method for the analysis of fluid-multibody interaction and bed erosion in free surface flows. Comput. Methods Appl. Mech. Eng. 197(19–20), 1777–1800 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  47. 47.
    Onate, E., Celigueta, M.A., Idelsohn, S.R., Salazar, F., Surez, B.: Possibilities of the particle finite element method for fluid-soil-structure interaction problems. Comput. Mech. 48, 307–318 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  48. 48.
    Rojek, J., Labra, C., Su, O., Onate, E.: Comparative study of different discrete element models and evaluation of equivalent micromechanical parameters. Int. J. Solids Struct. 49, 1497–1517 (2012).
  49. 49.
    Carbonell, J.M., Onate, E., Suarez, B.: Modeling of ground excavation with the particle finite element method. J. Eng. Mech. ASCE 136, 455–463 (2010)CrossRefGoogle Scholar
  50. 50.
    Labra, C., Onate, E.: High-density sphere packing for discrete element method simulations. Commun. Numer. Methods Eng. 25(7), 837–849 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  51. 51.
    Mukherjee, D., Zohdi, T.I.: Electromagnetic control of charged particulate spray systems—Models for planning the spray gun operations. Comput.-Aided Des. 46, 211–215 (2014)CrossRefGoogle Scholar
  52. 52.
    Mukherjee, D., Zaky, Z., Zohdi, T.I., Salama, A., Sun, S.: Investigation of guided particle transport for noninvasive healing of damaged piping system using electro-magneto-mechanical methods. J. Soc. Pet. Eng. J. SPE 169639, 1–12 (2015)Google Scholar
  53. 53.
    Mukherjee, D., Zohdi, T.I.: A discrete element based simulation framework to investigate particulate spray deposition processes. J. Comput. Phys. 290, 298–317 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  54. 54.
    Mukherjee, D., Zohdi, T.I.: Computational modeling of the dynamics and interference effects of an erosive granular jet impacting a porous, compliant surface. Granul. Matter 17, 231–252 (2015)CrossRefGoogle Scholar
  55. 55.
    Akisanya, A.R., Cocks, A.C.F., Fleck, N.A.: The yield behavior of metal powders. Int. J. Mech. Sci. 39, 1315–1324 (1997)CrossRefGoogle Scholar
  56. 56.
    Anand, L., Gu, C.: Granular materials: constitutive equations and shear localization. J. Mech. Phys. Solids 48, 1701–1733 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  57. 57.
    Brown, S., Abou-Chedid, G.: Yield behavior of metal powder assemblages. J. Mech. Phys. Solids 42, 383–398 (1994)CrossRefGoogle Scholar
  58. 58.
    Domas, F.: Eigenschaft profile und Anwendungsübersicht von EPE und EPP. Technical report of the BASF Company (1997)Google Scholar
  59. 59.
    Fleck, N.A.: On the cold compaction of powders. J. Mech. Phys. Solids 43, 1409–1431 (1995)zbMATHCrossRefGoogle Scholar
  60. 60.
    Gethin, D.T., Lewis, R.W., Ransing, R.S.: A discrete deformable element approach for the compaction of powder systems. Model. Simul. Mater. Sci. Eng. 11(1), 101–114 (2003)Google Scholar
  61. 61.
    Gu, C., Kim, M., Anand, L.: Constitutive equations for metal powders: application to powder forming processes. Int. J. Plast. 17, 147–209 (2001)zbMATHCrossRefGoogle Scholar
  62. 62.
    Lewis, R.W., Gethin, D.T., Yang, X.S.S., Rowe, R.C.: A combined finite-discrete element method for simulating pharmaceutical powder tableting. Int. J. Numer. Methods Eng. 62, 853869 (2005)zbMATHCrossRefGoogle Scholar
  63. 63.
    Ransing, R.S., Lewis, R.W., Gethin, D.T.: Using a deformable discrete-element technique to model the compaction behaviour of mixed ductile and brittle particulate systems. Philos. Trans. R. Soc.—Ser. A: Math. Phys. Eng. Sci. 362(1822), 1867–1884 (2004)Google Scholar
  64. 64.
    Tatzel, H.: Grundlagen der Verarbeitungstechnik von EPP-Bewährte und neue Verfahren. Technical report of the BASF Company (1996)Google Scholar
  65. 65.
    Martin, P.: (2009). Handbook of Deposition Technologies for Films and Coatings, 3rd edn. ElsevierGoogle Scholar
  66. 66.
    Martin, P. (2011). Introduction to Surface Engineering and Functionally Engineered Materials. Scrivener and ElsevierGoogle Scholar
  67. 67.
    Choi, S., Park, I., Hao, Z., Holman, H.Y., Pisano, A.P., Zohdi, T.I.: Ultra-fast self-assembly of micro-scale particles by open channel flow. Langmuir 26(7), 4661–4667 (2010)CrossRefGoogle Scholar
  68. 68.
    Choi, S., Jamshidi, A., Seok, T.J., Zohdi, T.I., Wu, M.C., Pisano, A.P.: Fast, High-throughput creation of size-tunable micro, nanoparticle clusters via evaporative self-assembly in picoliter-scale droplets of particle suspension. Langmuir 28(6), 3102–11 (2012)CrossRefGoogle Scholar
  69. 69.
    Choi, S., Pisano, A.P., Zohdi, T.I.: An analysis of evaporative self-assembly of micro particles in printed picoliter suspension droplets. J. Thin Solid Films 537(30), 180–189 (2013)CrossRefGoogle Scholar
  70. 70.
    Demko, M., Choi, S., Zohdi, T.I., Pisano, A.P.: High resolution patterning of nanoparticles by evaporative self-assembly enabled by in-situ creation and mechanical lift-off of a polymer template. Appl. Phys. Lett. 99, 253102-1–253102-3 (2012)Google Scholar
  71. 71.
    Torquato, S.: Random Heterogeneous Materials: Microstructure and Macroscopic Properties. Springer, New York (2002)Google Scholar
  72. 72.
    Kansaal, A., Torquato, S., Stillinger, F.: Diversity of order & densities in jammed hard-particle packings. Phys. Rev. E 66, 041109 (2002)CrossRefGoogle Scholar
  73. 73.
    Donev, A., Cisse, I., Sachs, D., Variano, E. A., Stillinger, F., Connelly, R., Torquato, S., Chaikin, P.: Improving the density of jammed disordered packings using ellipsoids. Science 13, 303, 990–993, Feb 2004Google Scholar
  74. 74.
    Donev, A., Stillinger, F.H., Chaikin, P.M., Torquato, S.: Unusually dense crystal ellipsoid packings. Phys. Rev. Lett. 92, 255506 (2004b)CrossRefGoogle Scholar
  75. 75.
    Donev, A., Torquato, S., Stillinger, F.: Neighbor list collision-driven molecular dynamics simulation for nonspherical hard particles-I. Algorithmic details. J. Comput. Phys. 202, 737 (2005a)MathSciNetzbMATHCrossRefGoogle Scholar
  76. 76.
    Donev, A., Torquato, S., Stillinger, F.: Neighbor list collision-driven molecular dynamics simulation for nonspherical hard particles-II. Application to ellipses and ellipsoids. J. Comput. Phys. 202, 765 (2005b)MathSciNetzbMATHGoogle Scholar
  77. 77.
    Donev, A., Torquato, S., Stillinger, F.H.: Pair correlation function characteristics of nearly jammed disordered and ordered hard-sphere packings. Phys. Rev. E 71, 011105 (2005c)MathSciNetCrossRefGoogle Scholar
  78. 78.
    Jaeger, H.M., Nagel, S.R.: La Physique de l’Etat Granulaire. La Recherche 249, 1380 (1992)Google Scholar
  79. 79.
    Jaeger, H.M., Nagel, S.R.: Physics of the Granular State. Science 255, 1523 (1992)CrossRefGoogle Scholar
  80. 80.
    Nagel, S.R.: Instabilities in a Sandpile. Rev. Mod. Phys. 64, 321 (1992)CrossRefGoogle Scholar
  81. 81.
    Liu, Y., Nakamura, T., Dwivedi, G., Valarezo, A., Sampath, S.: Anelastic behavior of plasma sprayed zirconia coatings. J. Am. Ceram. Soc. 91, 4036–4043 (2008)CrossRefGoogle Scholar
  82. 82.
    Liu, Y., Nakamura, T., Srinivasan, V., Vaidya, A., Gouldstone, A., Sampath, S.: Nonlinear elastic properties of plasma sprayed zirconia coatings and associated relationships to processing conditions. Acta Materialia 55, 4667–4678 (2007)CrossRefGoogle Scholar
  83. 83.
    Jaeger, H.M., Nagel, S.R.: La Fisica del Estado Granular. Mundo Cient. 132, 108 (1993)Google Scholar
  84. 84.
    Jaeger, H.M., Knight, J.B., Liu, C.H., Nagel, S.R.: What is shaking in the sand box? Mat. Res. Soc. Bull. 19, 25 (1994)CrossRefGoogle Scholar
  85. 85.
    Jaeger, H.M., Nagel, S.R., Behringer, R.P.: The Physics of Granular Materials. Phys. Today 4, 32 (1996)CrossRefGoogle Scholar
  86. 86.
    Jaeger, H.M., Nagel, S.R., Behringer, R.P.: Granular Solids, Liquids & Gases. Rev. Mod. Phys. 68, 1259 (1996)CrossRefGoogle Scholar
  87. 87.
    Jaeger, H.M., Nagel, S.R.: Dynamics of Granular material. Am. Sci. 85, 540 (1997)Google Scholar
  88. 88.
    Tai, Y.-C., Noelle, S., Gray, J.M.N.T., Hutter, K.: Shock capturing & front tracking methods for granular avalanches. J. Comput. Phy. 175, 269–301 (2002)zbMATHCrossRefGoogle Scholar
  89. 89.
    Tai, Y.-C., Noelle, S., Gray, J.M.N.T., Hutter, K.: An accurate shock-capturing finite-difference method to solve the Savage-Hutter equations in avalanche dynamics. Ann. Glaciol. 32, 263–267 (2001)CrossRefGoogle Scholar
  90. 90.
    Jenkins, J.T., La Ragione, L.: Particle spin in anisotropic granular materials. Int. J. Solids Struct. 38, 1063–1069 (1999)zbMATHCrossRefGoogle Scholar
  91. 91.
    Gray, J.M.N.T., Wieland, M., Hutter, K.: Gravity-driven free surface flow of granular avalanches over complex basal topography. Proc. R. Soc. Lond. A 455, 1841–1874 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  92. 92.
    Wieland, M., Gray, J.M.N.T., Hutter, K.: Channelized free-surface flow of cohesionless granular avalanches in a chute with shallow lateral curvature. J. Fluid Mech. 392, 73–100 (1999)zbMATHCrossRefGoogle Scholar
  93. 93.
    Berezin, Y.A., Hutter, K., Spodareva, L.A.: Stability properties of shallow granular flows. Int. J. Nonlinear Mech. 33(4), 647–658 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  94. 94.
    Gray, J.M.N.T., Hutter, K.: Pattern formation in granular avalanches. Contin. Mech. Thermodyn. 9, 341–345 (1997)CrossRefGoogle Scholar
  95. 95.
    Gray, J.M.N.T.: Granular flow in partially filled slowly rotating drums. J. Fluid Mech. 441, 1–29 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  96. 96.
    Hutter, K.: Avalanche dynamics. In: Singh, V.P. (ed.) Hydrology of Disasters, pp. 317–394. Kluwer Academic Publishers, Dordrecht etc (1996)Google Scholar
  97. 97.
    Hutter, K., Koch, T., Plüss, C., Savage, S.B.: The dynamics of avalanches of granular materials from initiation to runout. Part II. Experiments. Acta Mechanica 109, 127–165 (1995)MathSciNetCrossRefGoogle Scholar
  98. 98.
    Hutter, K., Rajagopal, K.R.: On flows of granular materials. Contin. Mech. Thermodyn. 6, 81–139 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  99. 99.
    Koch, T., Greve, R., Hutter, K.: Unconfined flow of granular avalanches along a partly curved surface. II. Experiments & numerical computations. Proc. R. Soc. Lond. A 445, 415–435 (1994)Google Scholar
  100. 100.
    Greve, R., Hutter, K.: Motion of a granular avalanche in a convex & concave curved chute: experiments & theoretical predictions. Philos. Trans. R. Soc. Lond. A 342, 573–600 (1993)CrossRefGoogle Scholar
  101. 101.
    Hutter, K., Siegel, M., Savage, S.B., Nohguchi, Y.: Two-dimensional spreading of a granular avalanche down an inclined plane. Part I: Theory. Acta Mechanica 100, 37–68 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  102. 102.
    Behringer, R.P.: The dynamics of flowing sand. Nonlinear Sci Today 3, 1 (1993)zbMATHCrossRefGoogle Scholar
  103. 103.
    Behringer, R.P., Baxter, G.W.: Pattern formation, complexity & time-dependence in granular flows. In: Mehta, A. (ed.) Granular Matter—An Interdisciplinary Approach, pp. 85–119. Springer, New York (1993)Google Scholar
  104. 104.
    Behringer, R.P., Miller, B.J.: Stress fluctuations for sheared 3D granular materials. In: Behringer, R., Jenkins, J. (eds.) Proceedings, Powders & Grains, vol. 97, pp. 333–336. Balkema (1997)Google Scholar
  105. 105.
    Behringer, R.P., Howell, D., Veje, C.: Fluctuations in Granular flows. Chaos 9, 559–572 (1999)zbMATHCrossRefGoogle Scholar
  106. 106.
    Jenkins, J.T., Strack, O.D.L.: Mean-field inelastic behavior of random arrays of identical spheres. Mech. Mater. 16, 25–33 (1993)CrossRefGoogle Scholar
  107. 107.
    Jenkins, J.T., Koenders, M.A.: The incremental response of random aggregates of identical round particles. Eur. Phys. J. E-Soft Matter. 13, 113–123 (2004)CrossRefGoogle Scholar
  108. 108.
    Jenkins, J.T., Johnson, D., La Ragione, L., Makse, H.: Fluctuations and the effective moduli of an isotropic, random aggregate of identical, frictionless spheres. J. Mech. Phys. Solids 53, 197–225 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  109. 109.
    Jackson, J.D.: Classical Electrodynamics, 3rd edn. Wiley (1998)Google Scholar
  110. 110.
    Frenklach, M., Carmer, C.S.: Molecular dynamics using combined quantum & empirical forces: application to surface reactions. Adv. Class. Trajectory Methods 4, 27–63 (1999)Google Scholar
  111. 111.
    Haile, J.M.: Molecular Dynamics Simulations: Elementary Methods. Wiley (1992)Google Scholar
  112. 112.
    Hase, W.L.: Molecular dynamics of clusters, surfaces, liquids, & interfaces. Advances in classical trajectory methods, vol. 4. JAI Press (1999)Google Scholar
  113. 113.
    Schlick, T.: Molecular Modeling & Simulation. An Interdisciplinary Guide. Springer, New York (2000)zbMATHGoogle Scholar
  114. 114.
    Rapaport, D.C.: The Art of Molecular Dynamics Simulation. Cambridge University Press (1995)Google Scholar
  115. 115.
    Moelwyn-Hughes, E.A.: Physical Chemistry. Pergamon (1961)Google Scholar
  116. 116.
    Stillinger, F.H., Weber, T.A.: Computer simulation of local order in condensed phases of silicon. Phys. Rev. B 31, 5262–5271 (1985)CrossRefGoogle Scholar
  117. 117.
    Tersoff, J.: Empirical interatomic potential for carbon, with applications to amorphous carbon. Phys. Rev. Lett. 61, 2879–2882 (1988)CrossRefGoogle Scholar
  118. 118.
    Feynman, R.P., Leighton, R.B., Sands, M.: Feynman Lect. Phys. 2 (2006). ISBN 0-8053-9045-6Google Scholar
  119. 119.
    Cullity, B.D., Graham, C.D.: Introduction to Magnetic Materials, 2nd edn. p. 103. Wiley-IEEE Press (2008). ISBN 0-471-47741-9Google Scholar
  120. 120.
    Boyer, T.H.: The force on a magnetic dipole. Am. J. Phys. 56(8), 688692 (1988). Bibcode:1988AmJPh.56.688B.
  121. 121.
    Avci, B., Wriggers, P.: A DEM-FEM coupling approach for the direct numerical simulation of 3D particulate flows. J. Appl. Mech. 79, 010901-1–7 (2012)Google Scholar
  122. 122.
    Zienkiewicz, O.C.: Coupled problems & their numerical solution. In: Lewis, R.W., Bettes, P., Hinton, E. (eds.) Numerical Methods in Coupled Systems, pp. 35–58. Wiley, Chichester (1984)Google Scholar
  123. 123.
    Zienkiewicz, O.C., Paul, D.K., Chan, A.H.C.: Unconditionally stable staggered solution procedure for soil-pore fluid interaction problems. Int. J. Numer. Methods Eng. 26, 1039–1055 (1988)zbMATHCrossRefGoogle Scholar
  124. 124.
    Lewis, R.W., Schrefler, B.A., Simoni, L.: Coupling versus uncoupling in soil consolidation. Int. J. Numer. Anal. Methods Geomech. 15, 533–548 (1992)CrossRefGoogle Scholar
  125. 125.
    Lewis, R.W., Schrefler, B.A.: The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media. 2nd edn. Wiley Press (1998)Google Scholar
  126. 126.
    Park, K.C., Felippa, C.A.: Partitioned analysis of coupled systems. In: Belytschko, T., Hughes, T.J.R. (eds.) Computational Methods for Transient Analysis (1983)Google Scholar
  127. 127.
    Farhat, C., Lesoinne, M., Maman, N.: Mixed explicit/implicit time integration of coupled aeroelastic problems: three-field formulation, geometric conservation and distributed solution. Int. J. Numer. Methods Fluids 21, 807–835 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  128. 128.
    Farhat, C., Lesoinne, M.: Two efficient staggered procedures for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems. Comput. Methods Appl. Mech. Eng. 182, 499–516 (2000)zbMATHCrossRefGoogle Scholar
  129. 129.
    Farhat, C., van der Zee, G., Geuzaine, P.: Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity. Comput. Methods Appl. Mech. Eng. 195, 1973–2001 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  130. 130.
    Piperno, S.: Explicit/implicit fluid/structure staggered procedures with a structural predictor & fluid subcycling for 2D inviscid aeroelastic simulations. Int. J. Numer. Meth. Fluids 25, 1207–1226 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  131. 131.
    Piperno, S., Farhat, C., Larrouturou, B.: Partitioned procedures for the transient solution of coupled aeroelastic problems—Part I: model problem, theory, and two-dimensional application. Comput. Methods Appl. Mech. Eng. 124(1–2), 79–112 (1995)zbMATHCrossRefGoogle Scholar
  132. 132.
    Piperno, S., Farhat, C.: Partitioned procedures for the transient solution of coupled aeroelastic problems—Part II: energy transfer analysis and three-dimensional applications. Comput. Methods Appl. Mech. Eng. 190, 3147–3170 (2001)zbMATHCrossRefGoogle Scholar
  133. 133.
    Michopoulos, J., Farhat, C., Fish, J.: Modeling and simulation of multiphysics systems. J. Comput. Inf. Sci. Eng. 5(3), 198–213 (2005)Google Scholar
  134. 134.
    Steuben, J.C., Iliopoulos, A.P., Michopoulos, J.G.: Discrete element modeling of particle-based additive manufacturing processes. Comput Methods Appl M 305(0045-7825), 537–561 (2016).
  135. 135.
    Steuben, J.C., Iliopoulos, A.P., Michopoulos, J.G.: On Multiphysics Discrete Element Modeling of Powder-Based Additive Manufacturing Processes. V01AT02A032 (2016).
  136. 136.
    Steuben, J.C., Iliopoulos, A.P., Michopoulos, J.G.: Recent developments of the multiphysics discrete element method for additive manufacturing modeling and simulation. In: ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC/CIE2017-67597, DETC2017-DVD, ASME (2017)Google Scholar
  137. 137.
    Lesoinne, M., Farhat, C.: Free staggered algorithm for nonlinear transient aeroelastic problems. AIAA J. 36(9), 1754–1756 (1998)Google Scholar
  138. 138.
    Le Tallec, P., Mouro, J.: Fluid structure interaction with large structural displacements. Comput. Methods Appl. Mech. Eng. 190(24–25), 3039–3067 (2001)Google Scholar
  139. 139.
    Widom, B.: Random sequential addition of hard spheres to a volume. J. Chem. Phys. 44, 3888–3894 (1966)Google Scholar
  140. 140.
    Ridley, B.A., Nivi, B., Jacobson, J.M.: All-inorganic field effect transistors fabricated by printing. Science 286, 746–749 (1999)CrossRefGoogle Scholar
  141. 141.
    Huang, D., Liao, F., Molesa, S., Redinger, D., Subramanian, V.: Plastic-compatible low-resistance printable gold nanoparticle conductors for flexible electronics. J. Electrochem. Soc. 150(7), G412–417 (2003)CrossRefGoogle Scholar
  142. 142.
    Sirringhaus, H., Kawase, T., Friend, R.H., Shimoda, T., Inbasekaran, M., Wu, W., Woo, E.P.: High-resolution inkjet printing of all-polymer transistor circuits. Science 290, 2123–2126 (2000)CrossRefGoogle Scholar
  143. 143.
    Ahmad, Z., Rasekh, M., Edirisinghe, M.: Electrohydrodynamic direct writing of biomedical polymers and composites. Macromol. Mater. Eng. 295, 315–319 (2010)CrossRefGoogle Scholar
  144. 144.
    Samarasinghe, S.R., Pastoriza-Santos, I., Edirisinghe, M.J., Reece, M.J., Liz-Marzan, L.M.: Printing gold nanoparticles with an electrohydrodynamic direct write device. Gold Bull. 39, 48–53 (2006)CrossRefGoogle Scholar
  145. 145.
    Wang, J.Z., Zheng, Z.H., Li, H.W., Huck, W.T.S., Sirringhaus, H.: Dewetting of conducting polymer inkjet droplets on patterned surfaces. Nat. Mater. 3, 171–176 (2004)CrossRefGoogle Scholar
  146. 146.
    Dornfeld, D., Wright, P.: Technology wedges for implementing green manufacturing. Trans. N. Am. Manuf. Res. Inst. 35, 193–200 (2007)Google Scholar
  147. 147.
    Allwood, J.: What is sustainable manufacturing? Lecture. Cambridge University (2005)Google Scholar
  148. 148.
    Reich-Weiser, C., Vijayaraghavan, A., Dornfeld, D.A.: Metrics for manufacturing sustainability. In: Proceedings of the IMSEC. ASME, Evanston, IL, 7–10 Oct 2008Google Scholar
  149. 149.
    Rosen, M., Dincer, I., Kanoglu, M.: Role of exergy in increasing efficiency and sustainability and reducing environmental impact. Energy Policy 36, 128–137 (2008)CrossRefGoogle Scholar
  150. 150.
    Grigoropoulos, C.P.: Transport in Laser Microfabrication. Cambridge University Press (2009)Google Scholar
  151. 151.
    Wellmann, C., Lillie, C., Wriggers, P.: A contact detection algorithm for superellipsoids based on the common-normal concept. Eng. Comput. 25, 432–442 (2008)Google Scholar
  152. 152.
    Lagaros, N., Papadrakakis, M., Kokossalakis, G.: Structural optimization using evolutionary algorithms. Comput. Struct. 80, 571–589 (2002)CrossRefGoogle Scholar
  153. 153.
    Leonardi, A., Wittel, F.K., Mendoza, M., Herrmann, H.J.: Coupled DEM-LBM method for the free-surface simulation of heterogeneous suspensions. Comput. Part. Mech. 1(1), 3–13 (2014)CrossRefGoogle Scholar
  154. 154.
    Wellmann, C., Wriggers, P.: A two-scale model of granular materials. Comput. Methods Appl. Mech. Eng. 205–208, 46–58 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  155. 155.
    Johnson, K.: Contact Mechanics. Cambridge University Press (1985)Google Scholar
  156. 156.
    Wriggers, P.: Computational Contact Mechanics. Wiley (2002)Google Scholar
  157. 157.
    Wriggers, P.: Nonlinear Finite Element Analysis. Springer (2008)Google Scholar
  158. 158.
    Davis, S.H.: Theory of Solidification. Cambridge University Press (2001)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.University of CaliforniaBerkeleyUSA

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