The effective elastic constants of solids containing spherical exclusions

Journal of Composite Materials

Volumn 31, Issue 9, 1997, Pages 910-934

  O'Rourke, John P ^a   Ingber, Marc S ^b   Weiser, Martin W ^c  

^a Delphi Packard Electric Systems   (United States)

^b University of New Mexico   (United States)

^c Johnson Matthey Electronics   (United States)

Author keywords

Composites with random structure; Effective Poisson's ratio; Effective Young's modulus; Porous elastic materials

Indexed keywords

BOUNDARY ELEMENT METHOD; COMPOSITE MATERIALS; ELASTIC MODULI; MICROSTRUCTURE; SOLIDS; TENSILE TESTING; VOLUME FRACTION;

EFFECTIVE POISSON RATIO; EFFECTIVE YOUNG MODULUS; POROUS ELASTIC MATERIALS; SPHERICAL EXCLUSIONS; THREE DIMENSIONAL RESPONSE; VOID;

ELASTICITY;

EID: 0030643661     PISSN: 00219983     EISSN: None     Source Type: Journal    
DOI: 10.1177/002199839703100905     Document Type: Article

References (21)

1. Bensoussan, A., J.-L. Lions and G. C. Papanicolaou, 1978. Asymptotic Analysis for Periodic Structures, North-Holland. Amsterdam.
2. Berthelot, J. M., A. Cupcic and K. A. Brou, 1993. "Stress Distribution and Effective Longitudinal Young's Modulus of Unidirectional Discontinuous Fibre Composites." J. Comp. Materials, 27:1391-1393.
3. Brebbia, C. A., J. C. F. Telles and L. C. Wrobel. 1984. Boundary Element Techniques. Theory and Applications in Engineering, New York: Springer-Verlag.
4. Coble, R. L. and W. D. Kingery, 1956. "Effect of Porosity of Physical Properties of Sintered Alumina." J. Amer. Cer. Soc., 39(11):377-385.
5. Cowin, S. C. and J. W. Nunziato. 1983. "Linear Elastic Materials with Voids," J. Elas., 13:125-147.
6. Cruz, M. E., C. K. Ghaddar and A. T. Patera. 1994. "Parallel Simulation of Multicomponent Random Media," in Parallel Computing in Multiphase Flow Systems. ASME FED-Vol. 199, S. Kim. G. Karniadakis and M. D. Vernon, eds., New York: ASME, pp. 53-60.
7. Cruz, M. E. and A. T. Patera, 1995. "A Parallel Monle-Carlo Finite-Element Procedure for the Analysis of Multicomponent Random Media." Int. J. Num. Meths. Engrg., 38(7):1087-1121.
8. Hashin, Z. 1983. "Analysis of Composite Materials: A Survey." Journal of Applied Mechanics, 50:481-505.
9. Ingber, M. S., D. E. Womble and L. A. Mondy 1994. "A Parallel Boundary Element Formulation for Determining Effective Properties of Heterogeneous Media," Int. J. Num. Meths. Engrg., 37(22):3905-3920.
10. Mackenzie, J. K. 1949. "The Elastic Constants of a Solid Containing Spherical Holes," Proc. Phys. Soc., B63:2-11.
11. Nemat-Nasser, S. and M. Hori, 1993. "Micromechanics: Overal Properties of Heterogeneous Materials," North-Holland Series in Applied Mathematics and Mechanics. Volume 37.
12. Nemat-Nasser, S., T. Iwakuma and M. Hejazi, 1982. "On Composites with Periodic Structure," Mech. Mater., 1:239-267.
13. Nomura, S. 1987. "Effective Medium Approach to Matrix-Inclusion Type Composite Materials," ASME J. Appl. Mech., 54:880-883.
14. Papathanasiou, T. D., M. S. Ingber, L. A. Mondy and A. L. Graham. 1994. "The Effective Elastic Modulus of Fiber-Reinforced Composites." J. Comp. Materials, 28(4):288-304.
15. Rice, R. W. "Comparison of Stress Concentration Versus Minimum Solid Area Based Mechanical Property-Porosity Relations," J. Mat. Sci., 28:2187-2190.
16. Rodin, G. J. and Y. Hwang. 1989. "On the Problem of Linear Elasticity for an Infinite Region Containing a Finite Number of Non-intersecting Spherical Inhomogeneities." Int. J. Solids Structs., 27(2):145-159.
17. Spriggs, R. M. 1961. "Expression for Effect of Porosity on Elastic Modulus of Polycrystalline Refractory Materials. Particularly Aluminum Oxide," J. Am. Ceram. Soc., 44(12):628-629.
18. Tran-Cong, T., Phan-Thien, N. and A. L. Graham. 1989. "Stokes Problems of Multiparticle Systems," Phys. Fluids, 2(5):666-673.
19. Tandon, G. P. and G. J. Weng. 1986. "Stress Distribution In and Around Spheroidal Inclusions and Voids at Finite Concentrations." J. Appl. Math, 53:511-518.
20. Vekinis, G., M. F. Ashby and P. W. R. Beaumont. 1993. "Plaster of Paris as a Model Material for Brittle Porous Solids," J. Mat. Set., 38:3221-3227.
21. Walsh, J. B., W. F. Brace and A. W. England. 1965. "Effect of Porosity on Compressibility of Glass," J. Amer. Cer. Soc., 48(12):605-608.