Browse > Article
http://dx.doi.org/10.7234/kscm.2010.23.4.007

Volume Integral Equation Method for Multiple Anisotropic Inclusion Problems in an Infinite Solid under Uniaxial Tension  

Lee, Jung-Ki (홍익대학교 기계정보공학과)
Publication Information
Composites Research / v.23, no.4, 2010 , pp. 7-13 More about this Journal
Abstract
A volume integral equation method (VIEM) is introduced for the solution of elastostatic problems in an unbounded isotropic elastic solids containing interacting multiple anisotropic inclusions subject to remote uniaxial tension. The method is applied to two-dimensional problems involving long parallel cylindrical inclusions. A detailed analysis of stress field at the interface between the matrix and the central inclusion is carried out for square and hexagonal packing of the inclusions. Effects of the number of anisotropic inclusions and various fiber volume fractions on the stress field at the interface between the matrix and the central inclusion are also investigated in detail. The accuracy of the method is validated by solving the single inclusion problem for which solutions are available in the literature.
Keywords
Volume Integral Equation Method; Anisotropic Inclusion; Fiber Volume Fraction; Composite Materials;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Lee, J.K. and Mal, A.K., "A Volume Integral Equation Technique for Multiple Inclusion and Crack Interaction Problems," Transactions of the ASME, Journal of Applied Mechanics, Vol. 64, 1997 (Mar.), pp. 23-31.   DOI   ScienceOn
2 Eshelby, J.D., "The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems," Proceedings of the Royal Society of London, Series A, A241, 1957, pp. 376-396.
3 Hashin, Z., Theory of Fiber Reinforced Materials, NASA CR-1974, 1972.
4 Yang, H.C. and Chou, Y.T., "Generalized Plane Problems of Elastic Inclusions in Anisotropic Solids1," Transactions of the ASME, Journal of Applied Mechanics, Vol. 43, 1976 (Sep.), pp. 424-430.   DOI
5 Achenbach, J.D. and Zhu, H., "Effect of Interphases on Micro and Macromechanical Behavior of Hexagonal-Array Fiber Composites," Transactions of ASME, Journal of Applied Mechanics, Vol. 57, 1990, pp. 956-963.   DOI
6 Christensen, R.M., Mechanics of Composite Materials, Krieger Pub. Co., Florida, 1991.
7 Nimmer, R.P., Bankert, R.J., Russel, E.S., Smith, G.A. and Wright, P.K., "Micromechanical Modeling of Fiber/Matrix Interface Effects in Transversely Loaded SiC/Ti-6-4 Metal Matrix Composites," Journal of Composites Technology & Research, Vol. 13, 1991, pp. 3-13.   DOI
8 Zahl, D.B. and Schmauder, S., "Transverse Strength of Continuous Fiber Metal Matrix Composites," Computational Materials Science, Vol. 3, 1994, pp. 293-299.   DOI   ScienceOn
9 Lee, J. and Mal, A., "Characterization of Matrix Damage in Metal Matrix Composites under Transverse Loads," Computational Mechanics, Vol. 21, 1998, pp. 339-346.   DOI   ScienceOn
10 Lee, J.K. and Mal, A.K., "A Volume Integral Equation Technique for Multiple Scattering Problems in Elastodynamics," Applied Mathematics and Computation, Vol. 67, 1995, pp. 135-159.   DOI   ScienceOn
11 Lee, K.J. and Mal, A.K., "A Boundary Element Method for Plane Anisotropic Elastic Media," Journal of Applied Mechanics, Vol. 57, 1990, pp. 600-606.   DOI
12 Buryachenko, V.A., Micromechanics of Heterogeneous Materials, Springer, New York, 2007.
13 Lee, J.K., Choi, S.J. and Mal, A., "Stress Analysis of an Unbounded Elastic Solid with Orthotropic Inclusions and Voids Using a New Integral Equation Technique," International Journal of Solids and Structures, Vol. 38 (16), 2001, pp. 2789-2802.   DOI   ScienceOn
14 Banerjee, P.K., The Boundary Element Methods in Engineering, McGraw-Hill, England, 1993.
15 PATRAN User's Manual, Version 7.0, MSC/PATRAN, 1998.
16 Hwu, C. and Yen, W.J., "On the Anisotropic Elastic Inclusions in Plane Elastostatics," Transactions of ASME, Journal of Applied Mechanics, Vol. 60, 1993 (Sep.), pp. 626-632.   DOI   ScienceOn
17 Mal, A.K. and Singh, S.J., Deformation of Elastic Solids, Prentice Hall, New Jersey, 1991.
18 Naboulsi, S., "Modeling Transversely Loaded Metal-Matrix Composites," Journal of Composite Materials, Vol. 37, 2003, pp. 55-72.   DOI   ScienceOn
19 Aghdam, M.M. and Falahatgar, S.R., "Micromechanical Modeling of Interface Damage of Metal Matrix Composites Subjected to Transverse Loading," Composite Structures, Vol. 66, 2004, pp. 415-420.   DOI   ScienceOn
20 Lee, J.K., Han, H.D. and Mal, A., "Effects of Anisotropic Fiber Packing on Stresses in Composites," Computer Methods in Applied Mechanics and Engineering, Vol. 195, No. 33-36, 2006, pp. 4544-4556.   DOI   ScienceOn
21 Ju, J.W. and Ko, Y.F., "Micromechanical Elastoplastic Damage Modeling for Progressive Interfacial Arc Debonding for Fiber Reinforced Composites," International Journal of Damage Mechanics, Vol. 17, 2008, pp. 307-356.   DOI   ScienceOn
22 Mal, A.K. and Knopoff, L., "Elastic Wave Velocities in Two Component Systems," Journal of the Institute of Mathematics and its Applications, Vol. 3, 1967, pp. 376-387.   DOI