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CM Approaches: Numerical Thermo-Mechanical Formulations

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

Abstract

The previous analytical expressions provide good way to estimate and optimize material combination for effective properties, while controlling local field fluctuations. However, in order to probe the response of a given material combination more deeply, in particular the time-dependent behavior when it is thermoformed, one must resort to numerical methods.

References

  1. 1.
    Zohdi, T.I.: Genetic design of solids possessing a random-particulate microstructure. Philos. 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.: Constrained inverse formulations in random material design. Comput. Methods Appl. Mech. Eng. 1–20. 192(18), 28–30, 3179–3194 (2003)Google Scholar
  4. 4.
    Zohdi, T.I.: Staggering error control for a class of inelastic processes in random microheterogeneous solids. Int. J. Nonlinear Mech. 39, 281–297 (2004)CrossRefzbMATHGoogle Scholar
  5. 5.
    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)CrossRefzbMATHGoogle Scholar
  6. 6.
    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
  7. 7.
    Zohdi, T.I., Kachanov, M.: A note on the micromechanics of plastic yield of porous solids. Int. J. Fract. Lett. Micromech. 133, L31–L35 (2005)Google Scholar
  8. 8.
    Zohdi, T.I.: On the optical thickness of disordered particulate media. Mech. Mater. 38, 969–981 (2006)CrossRefGoogle Scholar
  9. 9.
    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
  10. 10.
    Zohdi, T.I.: Computation of the coupled thermo-optical scattering properties of random particulate systems. Comput. Methods Appl. Mech. Eng. 195, 5813–5830 (2006)CrossRefzbMATHGoogle Scholar
  11. 11.
    Zohdi, T.I.: Computation of strongly coupled multifield interaction in particle-fluid systems. Comput. Methods Appl. Mech. Eng. 196, 3927–3950 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    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)CrossRefzbMATHGoogle Scholar
  14. 14.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Zohdi, T.I.: Joule-heating field phase-amplification in particulate-doped dielectrics. Int. J. Eng. Sci. 49, 30–40 (2011)CrossRefGoogle Scholar
  16. 16.
    Zohdi, T.I.: Estimation of electrical-heating load-shares for sintering of powder mixtures. Proc. R. Soc. 468, 2174–2190 (2012)CrossRefGoogle Scholar
  17. 17.
    Zohdi, T.I.: Modeling and simulation of the optical response rod-functionalized reflective surfaces. Comput. Mech. 50(2), 257–268 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Zohdi, T.I.: On the reduction of heat generation in lubricants using microscale additives. Int. J. Eng. Sci. 62, 84–89 (2013)CrossRefGoogle Scholar
  19. 19.
    Zohdi, T.I.: Numerical simulation of charged particulate cluster-droplet impact on electrified surfaces. J. Comput. Phys. 233, 509–526 (2013)MathSciNetCrossRefGoogle Scholar
  20. 20.
    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
  21. 21.
    Zohdi, T.I.: Rapid simulation of laser processing of discrete particulate materials. Arch. Comput. Methods Eng. 20, 309–325 (2013)CrossRefGoogle Scholar
  22. 22.
    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
  23. 23.
    Zohdi, T.I.: On cross-correlation between thermal gradients and electric fields. Int. J. Eng. Sci. 74, 143–150 (2014)CrossRefGoogle Scholar
  24. 24.
    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
  25. 25.
    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
  26. 26.
    Zohdi, T.I.: Additive particle deposition and selective laser processing-a computational manufacturing framework. Comput. Mech. 54, 171–191 (2014)CrossRefzbMATHGoogle Scholar
  27. 27.
    Zohdi, T.I.: Embedded electromagnetically sensitive particle motion in functionalized fluids. Comput. Part. Mech. 1, 27–45 (2014)CrossRefGoogle Scholar
  28. 28.
    Zohdi, T.I.: Rapid computation of statistically-stable particle/feature ratios for consistent substrate stresses in printed flexible electronics. J. Manuf. Sci. Eng. ASME, MANU-14-1476 (2015). https://doi.org/10.1115/1.4029327
  29. 29.
    Zohdi, T.I.: A computational modelling framework for high-frequency particulate obscurant cloud performance. Int. J. Eng. Sci. 89, 75–85 (2015)CrossRefGoogle Scholar
  30. 30.
    Zohdi, T. I.: On the thermal response of a laser-irradiated powder particle in additive manufacturing. CIRP J. Manuf. Sci. Technol. 10, 77–83 (2015)Google Scholar
  31. 31.
    Zohdi, T.I.: Modeling and simulation of cooling-induced residual stresses in heated particulate mixture depositions. Comput. Mech. 56, 613–630 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Zohdi, T.I.: Modeling and efficient simulation of the deposition of particulate flows onto compliant substrates. Int. J. Eng. Sci. 99, 74–91 (2015). https://doi.org/10.1016/j.ijengsci.2015.10.012
  33. 33.
    Zohdi, T.I.: Modeling and simulation of laser processing of particulate-functionalized materials. Arch. Comput. Methods Eng. 1–25 (2015). https://doi.org/10.1007/s11831-015-9160-1
  34. 34.
    Duran, J.: Sands, Powders and Grains. An introduction to the Physics of Granular Matter. Springer (1997)Google Scholar
  35. 35.
    Pöschel, T., Schwager, T.: Computational Granular Dynamics. Springer (2004)Google Scholar
  36. 36.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    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). https://doi.org/10.1016/j.ijsolstr.2012.02.032
  39. 39.
    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
  40. 40.
    Labra, C., Onate, E.: High-density sphere packing for discrete element method simulations. Commun. Numer. Methods Eng. 25(7), 837–849 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    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
  42. 42.
    Cante, J., Davalos, C., Hernandez, J.A., Oliver, J., Jonsen, P., Gustafsson, G., Haggblad, H.A.: PFEM-based modeling of industrial granular flows. Comput. Part. Mech. 1(1), 47–70 (2014)CrossRefGoogle Scholar
  43. 43.
    Rojek, J.: Discrete element thermomechanical modelling of rock cutting with valuation of tool wear. Comput. Part. Mech. 1(1), 71–84 (2014)CrossRefGoogle Scholar
  44. 44.
    Bolintineanu, D.S., Grest, G.S., Lechman, J.B., Pierce, F., Plimpton, S.J., Schunk, P.R.: Particle dynamics modeling methods for colloid suspensions. Comput. Part. Mech. 1(3), 321–356 (2014)Google Scholar
  45. 45.
    Campello, E.M.B., Zohdi, T.I.: A computational framework for simulation of the delivery of substances into cells. Int. J. Numer. Methods Biomed. Eng. 30(11), 1132–1152 (2014)Google Scholar
  46. 46.
    Campello, E.M.B., Zohdi, T.I.: Design evaluation of a particle bombardment system to deliver substances into cells. Comput. Mech. Eng. Sci. 98(2), 221–245 (2014)MathSciNetzbMATHGoogle Scholar
  47. 47.
    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
  48. 48.
    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
  49. 49.
    Brown, S., Abou-Chedid, G.: Yield behavior of metal powder assemblages. J. Mech. Phys. Solids 42, 383–398 (1994)CrossRefGoogle Scholar
  50. 50.
    Domas, F.: Eigenschaft profile und Anwendungsübersicht von EPE und EPP. Technical Report of the BASF Company (1997)Google Scholar
  51. 51.
    Fleck, N.A.: On the cold compaction of powders. J. Mech. Phys. Solids 43, 1409–1431 (1995)CrossRefzbMATHGoogle Scholar
  52. 52.
    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
  53. 53.
    Gu, C., Kim, M., Anand, L.: Constitutive equations for metal powders: application to powder forming processes. Int. J. Plast. 17, 147–209 (2001)CrossRefzbMATHGoogle Scholar
  54. 54.
    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)CrossRefzbMATHGoogle Scholar
  55. 55.
    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. Philosoph. Trans. R. Soc. Ser. A Math. Phys. Eng. Sci. 362(1822), 1867–1884 (2004)Google Scholar
  56. 56.
    Tatzel, H.: Grundlagen der Verarbeitungstechnik von EPP-Bewährte und neue Verfahren. Technical Report of the BASF Company (1996)Google Scholar
  57. 57.
    Kachanov, L.M.: Introduction to Continuum Damage Mechanics. Martinus Nijoff, Dordricht (1986)CrossRefzbMATHGoogle Scholar
  58. 58.
    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
  59. 59.
    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)CrossRefzbMATHGoogle Scholar
  60. 60.
    Lewis, R.W., Schrefler, B.A., Simoni, L.: Coupling versus uncoupling in soil consolidation. Int. J. Num. Anal. Metho. Geomech. 15, 533–548 (1992)CrossRefGoogle Scholar
  61. 61.
    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
  62. 62.
    Schrefler, B.A.: A partitioned solution procedure for geothermal reservoir analysis. Comm. Appl. Num. Meth. 1, 53–56 (1985)CrossRefzbMATHGoogle Scholar
  63. 63.
    Turska, E., Schrefler, B.A.: On consistency, stability and convergence of staggered solution procedures. Rend. Mat. acc. Lincei, Rome, S. 9, 5, 265–271 (1994)Google Scholar
  64. 64.
    Bianco, M., Bilardi, G., Pesavento, F., Pucci, G., Schrefler, B.A.: A frontal solver tuned for fully coupled non-linear hygro-thermo-mechanical problems. Int. J. Numer. Meth. Eng. 57, 18011818 (2003)CrossRefzbMATHGoogle Scholar
  65. 65.
    Wang, X., Schrefler, B.A.: A multifrontal parallel algorithm for coupled thermo-hydro-mechanical analysis of deforming porous media. Int. J. Numer. Meth. Eng. 43, 10691083 (1998)zbMATHGoogle Scholar
  66. 66.
    Young. D.M.: Iterative methods for solving partial difference equations of elliptic type. Doctoral Thesis, Harvard University (1950)Google Scholar
  67. 67.
    Ames, W.F.: Numerical Methods for Partial Differential Equations, 2nd edn. Academic Press (1977)Google Scholar
  68. 68.
    Axelsson, O.: Iterative Solution Methods. Cambridge University Press (1994)Google Scholar
  69. 69.
    Widom, B.: Random sequential addition of hard spheres to a volume. J. Chem. Phys. 44, 3888–3894 (1966)CrossRefGoogle Scholar
  70. 70.
    Torquato, S.: Random Heterogeneous Materials: Microstructure and Macroscopic Properties. Springer, New York (2002)Google Scholar
  71. 71.
    Kansaal, A., Torquato, S., Stillinger, F.: Diversity of order & densities in jammed hard-particle packings. Phys. Rev. E 66, 041109 (2002)CrossRefGoogle Scholar
  72. 72.
    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 303, 990-993 (2004)Google Scholar
  73. 73.
    Donev, A., Stillinger, F.H., Chaikin, P.M., Torquato, S.: Unusually dense crystal ellipsoid packings. Phys. Rev. Lett. 92, 255506 (2004)Google Scholar
  74. 74.
    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 (2005)Google Scholar
  75. 75.
    Householder, R.: Molding Process. U.S. Patent 4,247,508 (1979)Google Scholar
  76. 76.
    Deckard, C.: Method and apparatus for producing parts by selective sintering U.S. Patent 4,863,538 (1986)Google Scholar
  77. 77.
    Joseph, D.D., Preziosi, L.: Heat waves. Rev. Mod. Phys. 61, 41–74 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  78. 78.
    Ignaczak, J., Ostoja-Starzewski, M.: Thermoelasticity with Finite Wave Speeds. Oxford Mathematical Monographs (2010)Google Scholar
  79. 79.
    Onate, E., Celigueta, M.A., Latorre, S., Casas, G., Rossi, R., Rojek, J.: Lagrangian analysis of multiscale particulate flows with the particle finite element method. Comput. Part. Mech. 1(1), 85–102 (2014)CrossRefGoogle Scholar
  80. 80.
    Anand, L., Gu, C.: Granular materials: constitutive equations and shear localization. J. Mech. Phys. Solids 48, 1701–1733 (2000)MathSciNetCrossRefzbMATHGoogle Scholar

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Authors and Affiliations

  1. 1.University of CaliforniaBerkeleyUSA

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