Abstract
In this contribution an analysis of static properties of transversely isotropic, porous and nano-composites is considered. Present work features explicit formulas for effective coefficient in these types of composites. The reinforcements of the composites are a set of spheroidal inclusions with identical size and shape. The center is randomly distributed and the inclusions are embedded in an homogeneous infinite medium (matrix). An study of theoretical predictions obtained by Maxwell approach using two different density distribution functions, which describe the alignment inclusions is done. The method allows to report the static effective elastic coefficients in composites ensemble with inclusions of different geometrical shapes and configurations embedded into a matrix. The effective properties of composites are computed using the Maxwell homogenization method in Matlab software. Another novelty of this contribution is the calculation of new explicit analytical formulas for the control of the alignment tensors N* and Ns∗ which is in charged of the alignment distribution of inclusions within matrix through disorder parameters λ and s, respectively. The alignment tensors N∗ and Ns∗ are obtained as average of all possible alignments of the inclusions inside the composite. Numerical results are obtained and compared with some other theoretical approaches reported in the literature.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bravo-Castillero J, Guinovart-Diaz R, Rodriguez-Ramos R, Sabina FJ, Brenner R (2012) Unified analytical formulae for the effective properties of periodic fibrous composites. Materials Letters 73:68 – 71, doi:https://doi.org/10.1016/j.matlet.2011.12.106
Dong XN, Guo XE (2004) The dependence of transversely isotropic elasticity of hu- man femoral cortical bone on porosity. Journal of Biomechanics 37(8):1281–1287, doi:https://doi.org/10.1016/j.jbiomech.2003.12.011
Dong XN, Zhang X, Huang YY, Guo XE (2005) A generalized self-consistent estimate for the effective elastic moduli of fiber-reinforced composite materials with multiple trans- versely isotropic inclusions. International Journal of Mechanical Sciences 47(6):922 – 940, doi:https://doi.org/10.1016/j.ijmecsci.2005.01.008
Drago AS, Pindera MJ (2008) A locally-exact homogenization theory for periodic microstructures with isotropic phases. Trans ASME Journal of Applied Mechanics 75(5):051,010–051,010–14, doi:https://doi.org/10.1115/1.2913043
El-Eskandarany MS (1998) Mechanical solid state mixing for synthesizing of SiCp/Al nanocompos- ites. Journal of Alloys and Compounds 279(2):263 – 271, doi:https://doi.org/10.1016/s0925-8388(98)00658-6
Giraud A, Huynh Q, Hoxha D, Kondo D (2007) Effective poroelastic properties of transversely isotropic rock-like composites with arbitrarily oriented ellipsoidal inclusions. Mechanics of Materials 39(11):1006 – 1024, doi:https://doi.org/10.1016/j.mechmat.2007.05.005
Guinovart-Diaz R, Bravo-Castillero J, Rodriguez-Ramos R, Sabina FJ, Martinez-Rosado R (2001) Overall properties of piezocomposite materials 1–3. Materials Letters 48(2):93 – 98, doi:https://doi.org/10.1016/s0167-577x(00)00285-8
Hershey AV (1954) The elasticity of an isotropic aggregate of anisotropic cubic crystals. Trans ASME Journal of Applied Mechanics 21(3):236–240, doi:https://doi.org/10.1115/1.2913043
Hill R (1965) A self-consistent mechanics of composite materials. Journal of the Mechanics and Physics of Solids 13(4):213 – 222, doi:https://doi.org/10.1016/0022-5096(65)90010-4
Kanaun S (2016) Efficient homogenization techniques for elastic composites: Maxwell scheme vs. effective field method. International Journal of Engineering Science 103:19 – 34, doi:https://doi.org/10.1016/j.ijengsci.2016.03.004
Kröner E (1958) Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls. Zeischrift für Physik 151(4):504–518, doi:https://doi.org/10.1007/bf01337948
Kumar SS, Bai VS, Rajkumar KV, Sharma GK, Jayakumar T, Rajasekharan T (2009) Elastic modulus of Al-Si/SiC metal matrix composites as a function of volume fraction. Journal of Physics D: Applied Physics 42(17):175,504, doi:https://doi.org/10.1088/0022-3727/42/17/175504
Kushch VI, Sevostianov I (2016) Maxwell homogenization scheme as a rigorous method of micromechanics: Application to effective conductivity of a composite with spheroidal particles. International Journal of Engineering Science 98:36 – 50, doi:https://doi.org/10.1016/j.ijengsci.2015.07.003, special Issue Dedicated to Sergey Kanaun’s 70th Birthday
Levin V, Kanaun S, Markov M (2012) Generalized Maxwell’s scheme for homogeniza- tion of poroelastic composites. International Journal of Engineering Science 61:75 – 86, doi:https://doi.org/10.1016/j.ijengsci.2012.06.011, the special issue in honor of Nikita F. Morozov
Levin VM, Kanaun SK (2012) Application of Maxwell method in solution of homogenization problem for anizotropic elastic media with ellipsoidal inclusions. Proceedings of Petrozavodsk State University 1(8):86–89
Liaw PK, Shannon RE, Clark WG, Harrigan WC, Jeong H, Hsu DK (1995) Nondestructive characterization of material properties of metal-matrix composites. Materials Chemistry and Physics 39(3):220 – 228, doi:https://doi.org/10.1016/0254-0584(94)01431-f
Martinez-Ayuso G, Friswell MI, Adhikari S, Khodaparast HH, Berger H (2017) Homogenization of porous piezoelectric materials. International Journal of Solids and Structures 113-114:218–229, doi:https://doi.org/10.1016/j.ijsolstr.2017.03.003
Maxwell J (1954) A Treatise on Electricity and Magnetism, 3rd edn. Dover, New York
McCartney LN, Kelly A (2008) Maxwell’s far-field methodology applied to the prediction of proper- ties of multi-phase isotropic particulate composites. Proceedings of the Royal Society A: Mathe- matical, Physical and Engineering Sciences 464(2090):423–446, doi:https://doi.org/10.1098/rspa.2007.0071
Mogilevskaya SG, Kushch VI, Nikolskiy D (2014) Evaluation of some approximate estimates for the effective tetragonal elastic moduli of two-phase fiber-reinforced composites. Journal of Composite Materials 48(19):2349–2362, doi:https://doi.org/10.1177/0021998313498103
Otero JA, Rodriguez-Ramos R, Bravo-Castillero J, Guinovart-Diaz R, Sabina FJ, Monsivais G (2013) Semi-analytical method for computing effective properties in elastic composite under imperfect contact. International Journal of Solids and Structures 50(3):609 – 622, doi:https://doi.org/10.1016/j.ijsolstr.2012.11.001
Otero JA, Rodriguez-Ramos R, Monsivais G (2017) Computation of effective properties in elastic composites under imperfect contact with different inclusion shapes. Mathematical Methods in the Applied Sciences 40(9):3290–3310, doi:https://doi.org/10.1002/mma.3956
Premkumar MK, Hunt Jr WH, Sawtell RR (1992) Aluminum composite materials for multichip modules. JOM 44(7):24–28, doi:https://doi.org/10.1007/bf03222271
Qu J, Cherkaoui M (2006) Fundamentals of Micromechanics of Solids. John Wiley & Sons, New Jersey
Qu SG, Lou HS, Li XQ (2016) Influence of particle size distribution on properties of sic particles reinforced aluminum matrix composites with high sic particle content. Journal of Composite Materials 50(8):1049–1058, doi:https://doi.org/10.1177/0021998315586864
Roger D, Dieulesaint E (2000) Elastic Waves in Solids, vol I. Springer, New York
Selmi A, Friebel C, Doghri I, Hassis H (2007) Prediction of the elastic properties of single walled car- bon nanotube reinforced polymers: A comparative study of several micromechanical models. Com- posites Science and Technology 67(10):2071 – 2084, doi:https://doi.org/10.1016/j.compscitech.2006.11.016
Sevostianov I (2014) On the shape of effective inclusion in the Maxwell homogeniza- tion scheme for anisotropic elastic composites. Mechanics of Materials 75:45 – 59, doi:https://doi.org/10.1016/j.mechmat.2014.03.003
Sevostianov I, Giraud A (2013) Generalization of Maxwell homogenization scheme for elastic material containing inhomogeneities of diverse shape. International Journal of Engineering Science 64:23 – 36, doi:https://doi.org/10.1016/j.ijengsci.2012.12.004
Upadhyay A, Singh R (2012) Prediction of effective elastic modulus of biphasic composite materials. Modern Mechanical Engineering 2(1):6–13, doi:https://doi.org/10.4236/mme.2012.21002
Vilchevskaya E, Sevostianov I (2015) Effective elastic properties of a particulate composite with transversely-isotropic matrix. International Journal of Engineering Science 94:139 – 149, doi:https://doi.org/10.1016/j.ijengsci.2015.05.006
Wang G, Pindera MJ (2016) Locally-exact homogenization theory for transversely isotropic unidirectional composites. Mechanics Research Communications 78:2 – 14, doi:https://doi.org/10.1016/j.mechrescom.2015.09.011, Recent Advances in Multiscale, Multifunctional and Functionally Graded Materials
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Alfonso, L.D.L. et al. (2019). Effective Elastic Properties Using Maxwell’s Approach for Transversely Isotropic Composites. In: Altenbach, H., Öchsner, A. (eds) State of the Art and Future Trends in Material Modeling . Advanced Structured Materials, vol 100. Springer, Cham. https://doi.org/10.1007/978-3-030-30355-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-30355-6_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-30354-9
Online ISBN: 978-3-030-30355-6
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)