Skip to main content

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 60))

  • 2289 Accesses

Abstract

During the development of new particulate-functionalized materials, experiments to determine the appropriate combinations of particulate and matrix phases are time-consuming and expensive.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    There are, of course, only 21 constants, since \({{\varvec{I}}}\!{{\varvec{E}}}^*\) is symmetric.

References

  1. Maxwell, J.C.: On the dynamical theory of gases. Philos. Trans. Soc. London. 157, 49 (1867)

    Article  Google Scholar 

  2. Maxwell, J.C.: A treatise on electricity and magnetism, 3rd edn. Clarendon Press, Oxford (1873)

    MATH  Google Scholar 

  3. Rayleigh, J.W.: On the influence of obstacles arranged in rectangular order upon properties of a medium. Phil. Mag. 32, 481–491 (1892)

    Article  MATH  Google Scholar 

  4. Torquato, S.: Random Heterogeneous Materials: Microstructure and Macroscopic Properties. Springer, New York (2002)

    Google Scholar 

  5. Jikov, V.V., Kozlov, S.M., Olenik, O.A.: Homogenization of Differential Operators and Integral Functionals. Springer (1994)

    Google Scholar 

  6. Hashin, Z.: Analysis of composite materials: a survey. ASME J. Appl. Mech. 50, 481–505 (1983)

    Article  MATH  Google Scholar 

  7. Mura, T.: Micromechanics of Defects in Solids, 2nd edn. Kluwer Academic Publishers (1993)

    Google Scholar 

  8. Nemat-Nasser, S., Hori, M.: Micromechanics: Overall Properties of Heterogeneous Solids, 2nd edn. Elsevier, Amsterdam (1999)

    MATH  Google Scholar 

  9. Huet, C.: Universal conditions for assimilation of a heterogeneous material to an effective medium. Mecha. Res. Commun. 9(3), 165–170 (1982)

    Article  MATH  Google Scholar 

  10. Huet, C.: On the definition and experimental determination of effective constitutive equations for heterogeneous materials. Mech. Res. Commun. 11(3), 195–200 (1984)

    Article  Google Scholar 

  11. Sevostianov, I., Kachanov, M.: Effective properties of heterogeneous materials: proper application of the non-interaction and the “dilute limit” approximations. Int. J. Eng. Sci. 58, 124–128 (2012)

    Article  Google Scholar 

  12. 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 

  13. Zohdi, T.I.: On the compaction of cohesive hyperelastic granules at finite strains. Proc. R. Soc. 454(2034), 1395–1401 (2003)

    Google Scholar 

  14. 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 

  15. 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)

    MathSciNet  MATH  Google Scholar 

  16. Zohdi, T.I., Kachanov, M.: A note on the micromechanics of plastic yield of porous solids. Int. J. Fract./Lett. Micromechanics 133, L31–L35 (2005)

    Google Scholar 

  17. Zohdi, T.I.: Particle collision and adhesion under the influence of near-fields. J. Mech. Mater. Struct. 2(6), 1011–1018 (2007)

    Article  Google Scholar 

  18. 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)

    Article  MathSciNet  MATH  Google Scholar 

  19. Zohdi, T.I.: Mechanistic modeling of swarms. Comput. Methods Appl. Mech. Eng. 198(21–26), 2039–2051 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  20. Zohdi, T.I.: Charged wall-growth in channel-flow. Int. J. Eng. Sci. 48, 1520 (2010)

    Google Scholar 

  21. Zohdi, T.I.: On the dynamics of charged electromagnetic particulate jets. Arch. Comput. Methods Eng. 17(2), 109–135 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  22. 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)

    Article  MATH  Google Scholar 

  23. 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)

    Article  MathSciNet  MATH  Google Scholar 

  24. Zohdi, T.I.: Dynamics of clusters of charged particulates in electromagnetic fields. Int. J. Numer. Methods Eng. 85, 1140–1159 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  25. Zohdi, T.I.: Joule-heating field phase-amplification in particulate-doped dielectrics. Int. J. Eng. Sci. 49, 30–40 (2011)

    Article  Google Scholar 

  26. Zohdi, T.I.: Electromagnetically-induced deformation of functionalized fabric. J. Elast. 105(1–2), 381–398 (2011)

    Google Scholar 

  27. Zohdi, T.I.: Estimation of electrical-heating load-shares for sintering of powder mixtures. Proc. R. Soc. 468, 2174–2190 (2012)

    Article  Google Scholar 

  28. Zohdi, T.I.: Modeling and simulation of the optical response rod-functionalized reflective surfaces. Comput. Mech. 50(2), 257–268 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  29. Zohdi, T.I.: On the reduction of heat generation in lubricants using microscale additives. Int. J. Eng. Sci. 62, 84–89 (2013)

    Article  Google Scholar 

  30. Zohdi, T.I.: Electromagnetically-induced vibration in particulate-doped materials. ASME J. Vib. Acoust. 135(3) (2013). https://doi.org/10.1115/1.4023251

  31. Zohdi, T.I.: Numerical simulation of charged particulate cluster-droplet impact on electrified surfaces. J. Comput. Phys. 233, 509–526 (2013)

    Article  MathSciNet  Google Scholar 

  32. Zohdi, T.I.: On inducing compressive residual stress in microscale print-lines for flexible electronics. Int. J. Eng. Sci. 62, 157–164 (2013)

    Article  Google Scholar 

  33. Zohdi, T.I.: Rapid simulation of laser processing of discrete particulate materials. Arch. Comput. Methods Eng. 20, 309–325 (2013)

    Article  Google Scholar 

  34. 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 

  35. Zohdi, T.I.: On cross-correlation between thermal gradients and electric fields. Int. J. Eng. Sci. 74, 143–150 (2014)

    Article  Google Scholar 

  36. Zohdi, T.I.: Mechanically-driven accumulation of microscale material at coupled solid-fluid interfaces in biological channels. Proc. R. Soc. Interface 11, 20130922 (2014)

    Article  Google Scholar 

  37. 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 

  38. Zohdi, T.I.: Additive particle deposition and selective laser processing-a computational manufacturing framework. Comput. Mech. 54, 171–191 (2014)

    Article  MATH  Google Scholar 

  39. Zohdi, T.I.: Embedded electromagnetically sensitive particle motion in functionalized fluids. Computat. Part. Mech. 1, 27–45 (2014)

    Article  Google Scholar 

  40. Zohdi, T.I.: Impact and penetration resistance of network models of coated lightweight fabric shielding. GAMM-Mitteilungen, vol. 37, Issue 1, p. 124150 (2014)

    Google Scholar 

  41. 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

  42. Zohdi, T.I.: A computational modelling framework for high-frequency particulate obscurant cloud performance. Int. J. Eng. Sci. 89, 75–85 (2015)

    Article  Google Scholar 

  43. Ghosh, S.: Micromechanical Analysis and Multi-Scale Modeling Using the Voronoi Cell Finite Element Method. CRC Press/Taylor & Francis (2011)

    Google Scholar 

  44. Ghosh, S., Dimiduk, D.: Computational Methods for Microstructure-Property Relations. Springer, NY (2011)

    Google Scholar 

  45. Hill, R.: The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc. (Lond.) A65, 349–354 (1952)

    Article  Google Scholar 

  46. Chandrasekharaiah, D.S., Debnath, L.: Continuum Mechanics. Academic press (1994)

    Google Scholar 

  47. Voigt, W.: Über die Beziehung zwischen den beiden Elastizitätskonstanten isotroper Körper. Wied. Ann. 38, 573–587 (1889)

    Article  MATH  Google Scholar 

  48. Reuss, A.: Berechnung der Fliessgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle. Z. Angew. Math. Mech. 9, 49–58 (1929)

    Article  MATH  Google Scholar 

  49. Terada, K., Hori, M., Kyoya, T., Kikuchi, N.: Simulation of the multi-scale convergence in computational homogenization approaches. Int. J. Solids Struct. 37, 2229–2361 (2000)

    Article  MATH  Google Scholar 

  50. Segurado, J., Llorca, J.: A numerical approximation to the elastic properties of sphere-reinforced composites. J. Mech. Phys. Solids 50 (2002)

    Google Scholar 

  51. Hazanov, S., Huet, C.: Order relationships for boundary conditions effect in heterogeneous bodies smaller than the representative volume. J. Mech. Phys. Solids 42, 1995–2011 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  52. Hashin, Z., Shtrikman, S.: On some variational principles in anisotropic and nonhomogeneous elasticity. J. Mech. Phys. Solids 10, 335–342 (1962)

    Google Scholar 

  53. Hashin, Z., Shtrikman, S.: A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11, 127–140 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  54. Aboudi, J.: Mechanics of Composite Materials-a Unified Micromechanical Approach, p. 29. Elsevier (1992)

    Google Scholar 

  55. Zohdi, T.I., Wriggers, P.: Introduction to computational micromechanics, Springer Verlag (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tarek I. Zohdi .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Zohdi, T.I. (2018). CM Approaches: Characterization of Particle-Functionalized Materials. In: Modeling and Simulation of Functionalized Materials for Additive Manufacturing and 3D Printing: Continuous and Discrete Media. Lecture Notes in Applied and Computational Mechanics, vol 60. Springer, Cham. https://doi.org/10.1007/978-3-319-70079-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-70079-3_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70077-9

  • Online ISBN: 978-3-319-70079-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics