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http://dx.doi.org/10.3795/KSME-A.2007.31.1.089

Elastic Analysis of an Unbounded Elastic Solid with an Inclusion Considering Composite Fiber Volume Fraction  

Lee, Jung-Ki (홍익대학교 기계정보공학과)
Han, Hui-Duck (홍익대학교 대학원 기계정보공학과)
Publication Information
Transactions of the Korean Society of Mechanical Engineers A / v.31, no.1, 2007 , pp. 89-96 More about this Journal
Abstract
A volume integral equation method (VIEM) is applied for the effective analysis of plane elastostatic problems in unbounded solids containing single isotropic inclusion of two different shapes considering composite fiber volume fraction. Single cylindrical inclusion and single square cylindrical inclusion are considered in the composites with six different fiber volume fractions (0.25, 0.30, 0.35, 0.40, 0.45, 0.50). Using the rule of mixtures, the effective material properties are calculated according to the corresponding composite fiber volume fraction. The analysis of plane elastostatic problems in the unbounded effective material containing single fiber that covers an area corresponding to the composite fiber volume fraction in the bounded matrix material are carried out. Thus, single fiber, matrix material with a finite region, and the unbounded effective material are used in the VIEM models for the plane elastostatic analysis. A detailed analysis of stress field at the interface between the matrix and the inclusion is carried out for single cylindrical or square cylindrical inclusion. Next, the stress field is compared to that at the interface between the matrix and the single inclusion in unbounded isotropic matrix with single isotropic cylindrical or square cylindrical inclusion. This new method can also be applied to general two-dimensional elastodynamic and elastostatic problems with arbitrary shapes and number of inclusions. Through the analysis of plane elastostatic problems, it will be established that this new method is very accurate and effective for solving plane elastic problems in unbounded solids containing inclusions considering composite fiber volume fraction.
Keywords
Volume Integral Equation Method; Inclusions; Composites; Fiber Volume Fraction; Effective Material;
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1 Lee, J. K. and Mal, A. K., 1995, 'A Volume Integral Equation Technique for Multiple Scattering Problems in Elastodynamics,' Applied Mathematics and Computation, Vol. 67, pp. 135-159   DOI   ScienceOn
2 Lee, J. K., Han, H. D. and Mal, A., 2006, 'Effects of Anisotropic Fiber Packing on Stresses in Composites,' Computer Methods in Applied Mechanics and Engineering, Vol. 195, No. 33-36, pp. 4544-4556   DOI   ScienceOn
3 Lee, J. K., Choi, S. J. and Mal, A., 2001, '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), pp. 2789-2802   DOI   ScienceOn
4 Lee, K. J. and Mal, A. K., 1990, 'A boundary element method for plane anisotropic elastic media,' Journal of Applied Mechanics, Vol. 57, pp. 600-606   DOI
5 Mal, A. K. and Knopoff, L., 1967, 'Elastic Wave Velocities in Two Component Systems,' J. Inst. Math. Applics., Vol. 3, pp. 376-387   DOI
6 Yang, R. B., 2003, 'A Dynamic Generalized Self-Consistent Model for Wave Propagation in Particulate Composites,' Transactions of the ASME, Journal of Applied Mechanics, Vol. 70, No. 4, pp. 575-582   DOI   ScienceOn
7 Yang, H. C. and Chou, Y. T., 1976 (Sep.), 'Generalized Plane Problems of Elastic Inclusions in Anisotropic Solids1,' Transactions of the ASME, Journal of Applied Mechanics, Vol. 43, pp. 424-430   DOI
8 Banerjee, P. K., 1993, The Boundary Element Methods in Engineering, McGraw-Hill, England
9 Christensen, R. M., 1991, Mechanics of Composite Materials, Krieger Pub. Co., Florida
10 Hwu, C. and Yen, W. J., 1993 (Sep.), 'On the Anisotropic Elastic Inclusions in Plane Elastostatics,' Transactions of ASME, Journal of Applied Mechanics, Vol. 60, pp. 626-632   DOI   ScienceOn
11 Lee, J. K. and Mal, A. K., 1997 (Mar.), 'A Volume Integral Equation Technique for Multiple Inclusion and Crack Interaction Problems,' Transactions of the ASME, Journal of Applied Mechanics, Vol. 64, pp. 23-31   DOI   ScienceOn
12 Mal, A. K. and Singh, S. J., 1991, Deformation of Elastic Solids, Prentice Hall, New Jersey
13 Yang, R. B. and Mal, A. K., 1995, 'The Effective Transverse Moduli of a Composite with Degraded Fiber-Matrix Interfaces,' International Journal of Engineering Science, Vol. 33, No. 11, pp. 1623-1632   DOI   ScienceOn
14 Jones, R. M., 1999, Mechanics of Composite Materials, Taylor & Francis, Philadelphia