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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
There are, of course, only 21 constants, since \({{\varvec{I}}}\!{{\varvec{E}}}^*\) is symmetric.
References
Maxwell, J.C.: On the dynamical theory of gases. Philos. Trans. Soc. London. 157, 49 (1867)
Maxwell, J.C.: A treatise on electricity and magnetism, 3rd edn. Clarendon Press, Oxford (1873)
Rayleigh, J.W.: On the influence of obstacles arranged in rectangular order upon properties of a medium. Phil. Mag. 32, 481–491 (1892)
Torquato, S.: Random Heterogeneous Materials: Microstructure and Macroscopic Properties. Springer, New York (2002)
Jikov, V.V., Kozlov, S.M., Olenik, O.A.: Homogenization of Differential Operators and Integral Functionals. Springer (1994)
Hashin, Z.: Analysis of composite materials: a survey. ASME J. Appl. Mech. 50, 481–505 (1983)
Mura, T.: Micromechanics of Defects in Solids, 2nd edn. Kluwer Academic Publishers (1993)
Nemat-Nasser, S., Hori, M.: Micromechanics: Overall Properties of Heterogeneous Solids, 2nd edn. Elsevier, Amsterdam (1999)
Huet, C.: Universal conditions for assimilation of a heterogeneous material to an effective medium. Mecha. Res. Commun. 9(3), 165–170 (1982)
Huet, C.: On the definition and experimental determination of effective constitutive equations for heterogeneous materials. Mech. Res. Commun. 11(3), 195–200 (1984)
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)
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)
Zohdi, T.I.: On the compaction of cohesive hyperelastic granules at finite strains. Proc. R. Soc. 454(2034), 1395–1401 (2003)
Zohdi, T.I.: Constrained inverse formulations in random material design. Comput. Methods Appl. Mech. Eng. 1–20 192(28–30), 18, 3179–3194 (2003)
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)
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)
Zohdi, T.I.: Particle collision and adhesion under the influence of near-fields. J. Mech. Mater. Struct. 2(6), 1011–1018 (2007)
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)
Zohdi, T.I.: Mechanistic modeling of swarms. Comput. Methods Appl. Mech. Eng. 198(21–26), 2039–2051 (2009)
Zohdi, T.I.: Charged wall-growth in channel-flow. Int. J. Eng. Sci. 48, 1520 (2010)
Zohdi, T.I.: On the dynamics of charged electromagnetic particulate jets. Arch. Comput. Methods Eng. 17(2), 109–135 (2010)
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)
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)
Zohdi, T.I.: Dynamics of clusters of charged particulates in electromagnetic fields. Int. J. Numer. Methods Eng. 85, 1140–1159 (2011)
Zohdi, T.I.: Joule-heating field phase-amplification in particulate-doped dielectrics. Int. J. Eng. Sci. 49, 30–40 (2011)
Zohdi, T.I.: Electromagnetically-induced deformation of functionalized fabric. J. Elast. 105(1–2), 381–398 (2011)
Zohdi, T.I.: Estimation of electrical-heating load-shares for sintering of powder mixtures. Proc. R. Soc. 468, 2174–2190 (2012)
Zohdi, T.I.: Modeling and simulation of the optical response rod-functionalized reflective surfaces. Comput. Mech. 50(2), 257–268 (2012)
Zohdi, T.I.: On the reduction of heat generation in lubricants using microscale additives. Int. J. Eng. Sci. 62, 84–89 (2013)
Zohdi, T.I.: Electromagnetically-induced vibration in particulate-doped materials. ASME J. Vib. Acoust. 135(3) (2013). https://doi.org/10.1115/1.4023251
Zohdi, T.I.: Numerical simulation of charged particulate cluster-droplet impact on electrified surfaces. J. Comput. Phys. 233, 509–526 (2013)
Zohdi, T.I.: On inducing compressive residual stress in microscale print-lines for flexible electronics. Int. J. Eng. Sci. 62, 157–164 (2013)
Zohdi, T.I.: Rapid simulation of laser processing of discrete particulate materials. Arch. Comput. Methods Eng. 20, 309–325 (2013)
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)
Zohdi, T.I.: On cross-correlation between thermal gradients and electric fields. Int. J. Eng. Sci. 74, 143–150 (2014)
Zohdi, T.I.: Mechanically-driven accumulation of microscale material at coupled solid-fluid interfaces in biological channels. Proc. R. Soc. Interface 11, 20130922 (2014)
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)
Zohdi, T.I.: Additive particle deposition and selective laser processing-a computational manufacturing framework. Comput. Mech. 54, 171–191 (2014)
Zohdi, T.I.: Embedded electromagnetically sensitive particle motion in functionalized fluids. Computat. Part. Mech. 1, 27–45 (2014)
Zohdi, T.I.: Impact and penetration resistance of network models of coated lightweight fabric shielding. GAMM-Mitteilungen, vol. 37, Issue 1, p. 124150 (2014)
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
Zohdi, T.I.: A computational modelling framework for high-frequency particulate obscurant cloud performance. Int. J. Eng. Sci. 89, 75–85 (2015)
Ghosh, S.: Micromechanical Analysis and Multi-Scale Modeling Using the Voronoi Cell Finite Element Method. CRC Press/Taylor & Francis (2011)
Ghosh, S., Dimiduk, D.: Computational Methods for Microstructure-Property Relations. Springer, NY (2011)
Hill, R.: The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc. (Lond.) A65, 349–354 (1952)
Chandrasekharaiah, D.S., Debnath, L.: Continuum Mechanics. Academic press (1994)
Voigt, W.: Über die Beziehung zwischen den beiden Elastizitätskonstanten isotroper Körper. Wied. Ann. 38, 573–587 (1889)
Reuss, A.: Berechnung der Fliessgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle. Z. Angew. Math. Mech. 9, 49–58 (1929)
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)
Segurado, J., Llorca, J.: A numerical approximation to the elastic properties of sphere-reinforced composites. J. Mech. Phys. Solids 50 (2002)
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)
Hashin, Z., Shtrikman, S.: On some variational principles in anisotropic and nonhomogeneous elasticity. J. Mech. Phys. Solids 10, 335–342 (1962)
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)
Aboudi, J.: Mechanics of Composite Materials-a Unified Micromechanical Approach, p. 29. Elsevier (1992)
Zohdi, T.I., Wriggers, P.: Introduction to computational micromechanics, Springer Verlag (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
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)