- Volume 34 Issue 7
DOI QR Code
Volume Integral Equation Method for Multiple Isotropic Inclusion Problems in an Infinite Solid Under Uniaxial Tension
인장 하중을 받는 무한 고체에 포함된 다수의 등방성 함유체 문제 해석을 위한 체적 적분방정식법
- Lee, Jung-Ki (Dept. of Mechanical and Design Engineering, Hongik Univ.)
- 이정기 (홍익대학교 기계정보공학과)
- Received : 2010.02.08
- Accepted : 2010.06.08
- Published : 2010.07.01
A volume integral equation method (VIEM) is introduced for solving the elastostatic problems related to an unbounded isotropic elastic solid; this solid is subjected to remote uniaxial tension, and it contains multiple interacting isotropic inclusions. The method is applied to two-dimensional problems involving long parallel cylindrical inclusions. A detailed analysis of the stress field at the interface between the matrix and the central inclusion is carried out; square and hexagonal packing of the inclusions are considered. The effects of the number of isotropic inclusions and different fiber volume fractions on the stress field at the interface between the matrix and the central inclusion are also investigated in detail. The accuracy and efficiency of the method are clarified by comparing the results obtained by analytical and finite element methods. The VIEM is shown to be very accurate and effective for investigating the local stresses in composites containing isotropic fibers.
Volume Integral Equation Method;Boundary Integral Equation Method;Finite Element Method;Isotropic Inclusion;Infinite Solid;Composite Materials;Fiber Volume Fraction
Supported by : 홍익대학교
- Eshelby, J. D., 1957, "The Determination of theElastic Field of an Ellipsoidal Inclusion, andRelated Problems," Proceedings of the RoyalSociety of London, Series A, A241, pp. 376-396.
- Hashin, Z., 1972, Theory of Fiber ReinforcedMaterials, NASA CR-1974.
- Achenbach, J. D. and Zhu, H., 1990, "Effect ofInterphases on Micro and MacromechanicalBehavior of Hexagonal-Array Fiber Composites,"Transactions of ASME, Journal of AppliedMechanics, Vol. 57, pp. 956-963. https://doi.org/10.1115/1.2897667
- Christensen, R. M., 1991, Mechanics of CompositeMaterials, Krieger Pub. Co., Florida.
- Nimmer, R. P., Bankert, R. J., Russel, E. S.,Smith, G. A. and Wright, P.K., 1991, "MicromechanicalModeling of Fiber/Matrix InterfaceEffects in Transversely Loaded SiC/Ti-6-4 MetalMatrix Composites," Journal of CompositesTechnology & Research, Vol. 13, pp. 3-13. https://doi.org/10.1520/CTR10068J
- Zahl, D. B. and Schmauder, S., 1994,"Transverse Strength of Continuous Fiber MetalMatrix Composites," Computational MaterialsScience, Vol. 3, pp. 293-299. https://doi.org/10.1016/0927-0256(94)90144-9
- Lee, J. K. and Mal, A. K., 1997 (Mar.), “AVolume Integral Equation Technique for MultipleInclusion and Crack Interaction Problems,”Transactions of the ASME, Journal of AppliedMechanics, Vol. 64, pp. 23-31. https://doi.org/10.1115/1.2787282
- Lee, J. and Mal, A., 1998, "Characterization ofMatrix Damage in Metal Matrix Compositesunder Transverse Loads," ComputationalMechanics, Vol. 21, pp. 339-346. https://doi.org/10.1007/s004660050310
- Naboulsi, S., 2003, "Modeling TransverselyLoaded Metal-Matrix Composites," Journal ofComposite Materials, Vol. 37, pp. 55-72. https://doi.org/10.1177/0021998303037001468
- Aghdam, M. M. and Falahatgar, S. R., 2004,"Micromechanical Modeling of Interface Damageof Metal Matrix Composites Subjected toTransverse Loading," Composite Structures, Vol.66, pp. 415-420. https://doi.org/10.1016/j.compstruct.2004.04.063
- Lee, J. K., Han, H. D. and Mal, A., 2006,“Effects of Anisotropic Fiber Packing onStresses in Composites,” Computer Methods inApplied Mechanics and Engineering, Vol. 195,No. 33-36, pp. 4544-4556. https://doi.org/10.1016/j.cma.2005.10.012
- Ju, J. W. and Ko, Y. F., 2008,"Micromechanical Elastoplastic Damage Modelingfor Progressive Interfacial Arc Debonding forFiber Reinforced Composites," InternationalJournal of Damage Mechanics, Vol. 17, pp.307-356. https://doi.org/10.1177/1056789508089233
- Mal, A. K. and Knopoff, L., 1967, “ElasticWave Velocities in Two Component Systems,”Journal of the Institute of Mathematics and itsApplications, Vol. 3, pp. 376-387. https://doi.org/10.1093/imamat/3.4.376
- Lee, J. K. and Mal, A. K., 1995, “A VolumeIntegral Equation Technique for MultipleScattering Problems in Elastodynamics,” AppliedMathematics and Computation, Vol. 67, pp.135-159. https://doi.org/10.1016/0096-3003(94)00057-B
- Buryachenko, V. A., 2007, Micromechanics ofHeterogeneous Materials, Springer, New York.
- Banerjee, P. K., 1993, The Boundary ElementMethods in Engineering, McGraw-Hill, England.
- PATRAN User's Manual, 1998, Version 7.0,MSC/PATRAN.
- Hwu, C. and Yen, W. J., 1993 (Sep.), “Onthe Anisotropic Elastic Inclusions in PlaneElastostatics,” Transactions of ASME, Journal ofApplied Mechanics, Vol. 60, pp. 626-632. https://doi.org/10.1115/1.2900850
- Lee, J. K., Choi, S. J. and Mal, A., 2001,"Stress Analysis of an Unbounded Elastic Solidwith Orthotropic Inclusions and Voids Using aNew Integral Equation Technique," InternationalJournal of Solids And Structures, Vol. 38 (16),pp. 2789-2802. https://doi.org/10.1016/S0020-7683(00)00182-7
- Mal, A. K. and Singh, S. J., 1991, Deformationof Elastic Solids, Prentice Hall, New Jersey.
- ADINA User's Manual, 2008, Version 8.5,ADINA R & D, Inc..
- Volume integral equation method for multiple isotropic inclusion problems in an infinite solid under tension or in-plane shear vol.24, pp.12, 2010, https://doi.org/10.1007/s12206-010-0917-z
- Volume Integral Equation Method for Problems Involving Multiple Diamond-Shaped Inclusions in an Infinite Solid under Uniaxial Tension vol.36, pp.1, 2012, https://doi.org/10.3795/KSME-A.2012.36.1.059