In this paper, a possible
applicability of artificial neural networks to predict the elastic modulus of composites
with ellipsoidal inclusions is investigated. Besides it, based on the general micromechanical
unit cell approach, theoretical formula is also developed, for effective elastic
modulus of composites containing randomly dispersed ellipsoidal in homogeneities. Developed theoretical model considers
the ellipsoidal particles to be arranged in a three-dimensional cubic array. The
arrangement has been divided into unit cells, each of which contains an ellipsoid.
Practically in real composite systems neither isostress is there, nor
isostrain, and besides it due to the effect of random packing of the phases,
non-uniform shape of the particles, we are forced to include an empirical
correction factor. We are forced to include an empirical correction factor in place
of volume fraction which provided a modified expression for effective elastic modulus.
Empirical correction factor is correlated in terms of the ratio of elastic moduli
and the volume fractions of the constituents. Numerical simulations has also been
done using artificial neural network and compared with the results of Halpin-Tsai
and Mori-Tanaka models as well as with experimental results
as cited in the literature. Calculation has been done for the samples of Glass fiber/nylon 6 composite (MMW nylon
6/glass fiber), Organically modified montmorillonite (MMT)/High molecular
weight (HMW) nylon 6 nanocomposite ((HE)2M1R1-HMW
nylon 6), Epoxy-alumina composites and MXD6- clay nanocomposite. It is found that
both the theoretical predictions by the proposed model and ANN results are in close
agreement with the experimental results.
Cite this paper
Upadhyay, A. and Singh, R. (2014). Use of Artificial Neural Network and Theoretical Modeling to Predict the Effective Elastic Modulus of Composites with Ellipsoidal Inclusions. Open Access Library Journal, 1, e903. doi: http://dx.doi.org/10.4236/oalib.1100903.
Voigt, W. (1889)Ueber die
Beziehung zwischen den beiden Elastizita tskonstanten isotroper Korper. Annalen der Physik, 38, 573-587. http://dx.doi.org/10.1002/andp.18892741206
Reuss, A. (1929) Berechnung
der Fliessgrenze von Mischkristallen auf Grund der Plastizitatsbedingung für
Einkristalle. ZAMM—Journal
of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 9, 49- 58. http://dx.doi.org/10.1002/zamm.19290090104
Hashin, Z. and Shtrikman, S. (1963) A Variational Approach
to the Theory of Elastic Behaviour of Multiphase Materials. Journal of the Mechanics and Physics of Solids, 11, 127-140. http://dx.doi.org/10.1016/0022-5096(63)90060-7
Gusev, A.A., Hine, P.J. and Ward, I.M. (2000) Fiber Packing and Elastic Properties of Transversely
Random Unidirectional Glass/Epoxy Composite.Composites Science and Technology, 60, 535-541. http://dx.doi.org/10.1016/S0266-3538(99)00152-9
Lusti, H.R., Hine, P.J. and Gusev, A.A. (2002) Direct Numerical Predictions for the
Elastic and Thermo Elastic Properties of Short Fibre Composites. Composites
Science and Technology, 62, 1927-1934. http://dx.doi.org/10.1016/S0266-3538(02)00106-9
Segurado, J. and Llorca, J. (2003) A Numerical Approximation to the Elastic
Properties of Sphere-Reinforced Composites. Journal
of the Mechanics and Physics of Solids, 50, 2107-2121. http://dx.doi.org/10.1016/S0022-5096(02)00021-2
Jweeg, M.J.,
Hammood, A.S. and Al-Waily, M. (2012) Experimental and Theoretical
Studies of Mechanical Properties for Reinforcement Fiber Types of Composite Materials.International Journal of Mechanical &
Mechatronics Engineering, 12, 62-75.
Upadhyay, A. and Singh, R. (2012) Elastic Properties of Al2O3-NiAl: A Modified Version of Hashin-Shtrikman Bounds. Continuum Mechanics and Thermodynamics, 24, 257-266.
Modniks, J. and Andersons, J. (2010) Modeling Elastic Properties of Short Flax
Fiber-Reinforced Composites by Orientation Averaging. Computational
Materials Science, 50, 595-599.
Ji, B. and Wang, T. (2003) Plastic Constitutive Behavior of
Short-Fiber/Particle
Reinforced Composites. International Journal of Plasticity, 19, 565-581. http://dx.doi.org/10.1016/S0749-6419(01)00041-9
Koker, R., Altinkok, N. and Demir, A. (2007) Neural Network Based Prediction of
Mechanical Properties of Particulate Reinforced Metal Matrix Composites Using
Various Training Algorithms. Materials and Design, 28, 616-627. http://dx.doi.org/10.1016/j.matdes.2005.07.021
Sha, W. and Edwards, K.L. (2007) The Use of Artificial Neural Networks in
Materials Science Based Research. Materials and Design, 28, 1747-1752. http://dx.doi.org/10.1016/j.matdes.2007.02.009
Mori, T. and Tanaka, K. (1973) Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions. Acta Metallurgica, 21, 571-574. http://dx.doi.org/10.1016/0001-6160(73)90064-3
Eshelby, J.D. (1957) The Determination of the Elastic Field of an Ellipsoidal
Inclusion and Related Problems. Proceedings
of the Royal Society A, 241, 376-396. http://dx.doi.org/10.1098/rspa.1957.0133
van Es, M., Xiqiao, F., van Turnhout, J. and van der Giessen, E. (2001) Chapter 21: Comparing Polymer-Clay Nanocomposites with Conventional Composites Using Composite Modeling. In: Al-Malaika, S. and Golovoy, A.W., Eds., Specialty Polymer Additives: Principles
and Applications, Blackwell
Science, CA Malden, 391-414.
Hui, C.Y. and Shia, D. (1998) Simple Formulae
for the Effective Moduli of Unidirectional Aligned Composites. Polymer
Engineering & Science, 38, 774-782. http://dx.doi.org/10.1002/pen.10243
Clark, S.P., Ed. (1966) Handbook of Physical Constants, Geological Society of America. Memoir 97, The Geological Society of America, Inc., New York, 50-89.
Alexandrov, K.S. and Ryshova, T.V. (1961) The
Elastic Properties of Rock-Forming Minerals. II: Layered Silicates. Bulletin USSR
Academy of science, Geophysics Series 9, 12, 1165-1168.
Shukla, D.K. and Parameswaran, V. (2007) Epoxy
Composites with 200 nm Thick Alumina
Platelets as Reinforcements. Journal of Materials Science, 42, 5964-5972. http://dx.doi.org/10.1007/s10853-006-1110-8