This article presents a method for the evaluation of effective material properties of transversely randomly distributed unidirectional piezoelectric fiber composites using homogenization techniques based on the finite element method (FEM) and representative volume element (RVE) method. Modified random sequential adsorption (RSA) algorithm is used to generate three-dimensional (3D) RVE models of transversely randomly distributed unidirectional fiber composites. Numerical studies are carried out to estimate the influence of diameter and arrangement of fibers on the effective material properties. Using different diameters of fibers, RVE models are generated up to 80% volume fraction. All effective material properties of transversely randomly distributed unidirectional piezoelectric fiber composites are evaluated and comparisons are made with regular packing like square and hexagonal arrangement of piezoelectric fiber composites.
Bakhvalov, N. and Panasenko, G.1989. Homogenization: Averaging Processes in Periodic Media — Mathematical Problems in the Mechanics of Composite Materials, Kluwer, Dordrecht.
2.
Bensoussan, A., Lions, J.L. and Papanicolaou, G.1978. Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam .
3.
Benveniste, Y.1992. ``The Determination of Elastic and Electric Fields in a Piezoelectric Inhomogeneity,'' J. Appl. Phys, 72(3):1086—1095.
4.
Benveniste, Y.1993. ``Universal Relations in Piezoelectric Composites with Eigenstress and Polarization Fields. Part I: Binary Media — Local Fields and Effective Behavior,'' J. Appl. Mech., 60(2):265—269.
5.
Berger, H., Kari, S., Gabbert, U., Rodriguez-Ramos, R., Guinovart-Diaz, R., Otero, J.A. and Bravo-Castillero, J.2005. ``An Analytical and Numerical Approach for Calculating Effective Material Coefficients of Piezoelectric Fiber Composites,'' Int. J. Sol. Struct., 42:5692—5714.
6.
Bisegna, P. and Luciano, R.1996. ``Variational Bounds for the Overall Properties of Piezoelectric Composites,'' J. Mech. Phys. Solids, 44(4):583—602.
7.
Bisegna, P. and Luciano, R.1997. ``On Methods for Bounding the Overall Properties of Periodic Piezoelectric Fibrous Composites,'' J. Mech. Phys. Solids , 45(8):1329—1356.
8.
Böhm, H.J.1993. ``Numerical Investigation of Microplasticity Effects in Unidirectional Long Fiber Reinforced Metal Matrix Composites,'' Modell. Simul. Mater. Sci. Engng., 1(5):649—671.
9.
Brockenbrough, J.R. and Suresh, S.1990. ``Plastic Deformation of Continuous Fiber-reinforced Metal-matrix Composites: Effects of Fiber Shape and Distribution,'' Scr. Metall. Mater., 24:325—330.
10.
Chan, H.L. and Unsworth, J.1989. ``Simple Model for Piezoelectric Polymere 1-3 Composites used in Ultrasonic Transducer Applications,'' IEEE Trans. Ultrason. Ferroelectrics Frequency Control, 36(4):434—441.
11.
Chen, T.1993. ``Piezoelectric Properties of Multiphase Fibrous Composites: Some Theoretical Results,'' J. Mech. Phys. Sol., 41(11):1781—1794.
12.
Cleveringa, H.H.M., van der Giessen, E. and Needleman, A.1997. ``Comparison of Discrete Dislocations and Continuum Plasticity Predictions for a Composite Material,'' Acta Metall. Mater. , 45(8):3163—3179.
13.
Dunn, M.L. and Taya, M.1993. ``Micromechanics Predictions of the Effective Electroelastic Moduli of Piezoelectric Composites,'' Int. J. Sol. Struct. , 30(2):161—175.
14.
Dunn, M.L. and Wienecke, H.A.1997. ``Inclusions and Inhomogeneities in Transversely Isotropic Piezoelectric Solids,'' Int. J. Sol. Struct., 34(27):3571—3582.
15.
Gaudenzi, P.1997. ``On the Electromechanical Response of Active Composite Materials with Piezoelectric Inclusions,'' Comput. Struct. , 65(2):157—168.
16.
Gunawardena, S.R., Jansson, S. and Leckie, A.1993. ``Modeling of Anisotropic Behavior of Weakly Bonded Fiber Reinforced MMC's,''. Acta Metall. Mater., 41(11):3147—3156.
17.
Levin V.M., Rakovskaja M.I. and Kreher, W.S.1999. ``The Effective Thermoelectroelastic Properties of Microinhomogeneous Materials,'' Int. J. Solids Struct., 36:2683—2705.
18.
Schulgasser, K.1992. ``Relationships between the Effective Properties of Transversely Isotropic Piezoelectric Composites,'' J. Mech. Phys. Solids , 40:473—479.
19.
Silva, E.C.N., Fonseca, J.S.O. and Kikuchi, N.1998. ``Optimal Design of Periodic Piezocomposites,'' Comput . Methods Appl. Engng., 159:49—77.
20.
Smith W.A. and Auld, B.A.1991. ``Modeling 1-3 Composite Piezoelectrics: Thickness-mode Oscillations,'' IEEE Trans. Ultrason. Ferroelectrics Frequency Control, 38:40—47.
21.
Suquet, P.1987. ``Elements of Homogenization Theory for Inelastic Solid Mechanics,'' In: Sanchez-Palencia, E. and Zaoui, A. (eds), Homogenization Techniques for Composite Media, Springer-Verlag, Berlin, pp.194—275.
22.
Wang J.S.1998. ``Random Sequential Adsorption, Series Expansion and Monte Carlo Simulation,'' Physics A, 254:179—184.
23.
Wang, B.1992. ``Three-dimensional Analysis of an Ellipsoidal Inclusion in a Piezoelectric Material,'' Int. J. Sol. Struct., 29:293—308.
24.
Xia, Z., Zhang, Y. and Ellyin, F.2003. ``A Unified Periodical Boundary Conditions for Representative Volume Elements of Composites and Applications,'' Int. J. Sol. Struct., 40:1907—1921.
