Micromechanical Modeling of the Finite Deformation of Thermoelastic Multiphase Composites

Abstract

A micromechanical model is proposed for the prediction of nonlinearly thermoplastic, multiphase particulate, and/or continuous reinforced composites in which any or all constituents exhibit large strain (finite deformation). The analysis provides closed-form representations for the instantaneous mechanical and thermal concentration tensors, as well as the effective tangent mechanical and thermal properties of the composite. The micromechanical model predictions are assessed by a comparison with an analytical spherical composite model, valid for hydrostatic loadings only Very good agreement between the two approaches was obtained. Similarly, results demonstrating the effects of nonlinearity are given for particulate and continuous fiber-reinforced SiC/Al compositesFinally, the nonlinear response of cellular solids idealized by open-cell and closed-cell structures are compared and contrasted.

Get full access to this article

View all access options for this article.

References

[1] Ogden, R. W. : On the overall moduli of non-linear elastic composite materials. J. Mech. Phys. Solids, 22, 541-553 (1974).

[2] Chen, Y. C. and Jiang, X. : Nonlinear elastic properties of particulate composites. J. Mech. Phys. Solids, 41, 1177-1190 (1993).

[3] Iman, A. , Johnson, G. C. , and Ferrari, M. : Determination of the overall moduli in second order incompressible elasticity. J. Mech. Phys. Solids, 43, 1087-1104 (1995).

[4] Willis, J. R. : Variational estimates for the overall behavior of a nonlinear matrix-inclusion composite, in Micromechanics and Inhomogeneity, pp. 581-597, eds., G. J. Weng , M. Taya , and H. Abe , Springer-Verlag, New York, 1990.

[5] Talbot, D.R.S. and Willis, J. R. : Bounds and self-consistent estimates for the overall properties of nonlinear composites. IMA J. Appl. Math., 39, 215-240 (1987).

[6] Ponte Castaneda, P. and Willis, J. R. : On the overall properties of nonlinearly viscous composites. Proc. Roy. Soc. Lon., A, 416, 217-244 (1988).

[7] Aboudi, J. : Micromechanical analysis of composites by the method of cells. Appl. Mech. Rev., 42, 193-221 (1989).

[8] Aboudi, J. : Micromechanical analysis of composites by the method of cells-Update. Appl. Mech. Rev, 49, S83-S91 (1996).

[9] Aboudi, J. : Overall finite deformation of elastic and elastoplastic composites. Mech. Mat., 5, 73-86 (1986).

10.

[10] Blatz, P. J. and Ko, W. L. : Application of finite elastic theory to the deformation of rubbery materials. Trans. Soc. Rheology, 6, 223-251 (1962).

11.

[11] Horgan, C. O. : On axisymmetric solutions for compressible nonlinearly elastic solids. Z. angew Math. Phys., 46, S107-S125 (1995).

12.

[12] Bland, D. R. : Nonlinear Dynamic Elasticity, Blaisdell, Wltham, 1969.

13.

[13] Murnaghan, E. D. : Finite Deformation of an Elastic Solid, Dover, New York, 1967.

14.

[14] Blatz, P. J. : Application of large deformation theory to the thermomechanical behavior of rubberlike polymers-Porous, unfilled, and filled, in Rheology Theory and Applications, Vol. 5, pp. 1-55, ed., F. R. Eirich , Academic Press, New York, 1969.

15.

[15] Sussman, T. and Bathe, K. J. : A finite element formulation for nonlinear incompressible elastic and inelastic analysis. Computers Struct., 26, 357-409 (1987).

16.

[16] Aboudi, J. : Micromechanical analysis of thermoinelastic multiphase short-fiber composites. Composites Eng., 5, 839-850 (1995).

17.

[17] Herakovich, C. T. : Mechanics of Fibrous Composites, Wiley, New York, 1998.

18.

[18] Hashin, Z. : Large isotropic elastic deformation of composites and porous media. Int. J. Solids Struct., 21, 711-720 (1985).

19.

[19] Aboudi, J. : Mechanics of Composite Materials: A Unified Micromechanical Approach, Elsevier, Amsterdam, 1991.

20.

[20] Carroll, M. M. : Finite strain solutions in compressible isotropic elasticity. J. Elasticity, 20, 65-92 (1988).

21.

[21] Ogden, R. W. : Non-Linear Elastic Deformations, Ellis Horwood, Chichester, 1984.

22.

[22] Murphy, G. J. : Inflation and eversion of spherical shells of a special compressible material. J Elasticity, 30, 251-276 (1993).

23.

[23] Haughton, D. M. : Inflation and bifurcation of thick-walled compressible elastic spherical shells. IMA J. Appl. Math., 39, 259-272 (1987).

24.

[24] Gibson, L. J. and Ashby, M. F. : Cellular Solids, Pergamon Press, Oxford, 1988.

25.

[25] Chou, T.-W. : Microstructural Design of Fiber Composites, Cambridge University Press, Cambridge, 1992.

26.

[26] Ogden, R. W. : On the thermoelastic modeling of rubberlike solids. J. Thermal Stress., 15, 533-557 (1992).