Models of Particle Reinforced Nonlinear-Viscous Composite
Publication: Journal of Engineering Mechanics
Volume 125, Issue 3
Abstract
Two new models are described for a composite consisting of a nonlinear viscous matrix reinforced by rigid particulate inclusions: (1) An analytical plane strain solution for a uniform regular array of rigid hexagonal particles separated by a nonlinear viscous material; and (2) a numerical upper-bound solution using Hashin's composite sphere model for a composite consisting of rigid inclusions in a nonlinear viscous matrix. Suquet's closed-form solution for the nonlinear composite, obtained by transforming Hashin's linear solution, is also examined. Predictions of all models are compared with experimental measurements from uniaxial compression tests on composites consisting of bitumen reinforced with various volume fractions of aggregate.
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References
1.
Bao, G., Hutchinson, J. W., and McMeeking, R. M. ( 1991). “Particle reinforcement against plastic flow and creep.” Acta Mettallurgica et Materialia, 39(8), 1871–1882.
2.
Brady, J. F., and Bossis, G. ( 1985). “The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation.” J. Fluid Mech., Cambridge, U.K., 155, 105–128.
3.
Budiansky, B., Hutchinson, J. W., and Slutsky, S. ( 1982). “Void growth and collapse in viscous solids.” Mechanics of solids, H. G. Hopkins and M. J. Sewell, eds., Pergamon, Tarrytown, N.Y., 13–45.
4.
Campbell, G. A., and Forgacs, G. ( 1990). “Viscosity of concentrated suspensions: An approach based on percolation theory.” Physical Rev. A, 41(8), 4570–4573.
5.
Cheung, C. Y. ( 1995). “The mechanical behaviour of bitumens and bituminous mixes,” PhD thesis, Engrg. Dept., University of Cambridge, Cambridge, U.K.
6.
Cheung, C. Y., and Cebon, D. ( 1996a). “Experimental study of pure bitumen in tension, compression and shear.” J. Rheology, 41(1), 45–73.
7.
Cheung, C. Y., and Cebon, D. (1996b). “Thin film deformation behaviour of power law creeping materials.”J. Engrg. Mech., ASCE, 123(11), 1138–1152.
8.
Cocks, A. C. F., and Ashby, M. F. ( 1982). “On creep fractures by void growth.” Progress in material science, J. W. Christian, P. Haasen, and T. B. Massalski, eds., Vol. 27, Pergamon, Tarrytown, N.Y., 189–243.
9.
Deshpande, V. S. ( 1995). “Deformation behaviour of idealised bituminous mixes,” Master's thesis, Engrg. Dept., University of Cambridge, Cambridge, U.K.
10.
Deshpande, V. S. ( 1997). “Steady-state deformation behaviour of bituminous mixes,” PhD thesis, Engrg. Dept., University of Cambridge, Cambridge, U.K.
11.
Drucker, D. C. ( 1964). “Engineering and continuum aspects of high-strength materials.” High strength materials, V. F. Zackay, ed., 803–813.
12.
Duva, J. M. ( 1984). “A self-consistent analysis of the stiffening effect of rigid inclusions on a power law material.” J. Engrg. Mat. and Technol., 106, 317–321.
13.
Forsythe, G. E., Malcolm, M. A., and Moler, C. B. ( 1977). Computer methods for mathematical computations. Prentice-Hall, Englewood Cliffs, N.J.
14.
Hashin, Z. ( 1962). “The elastic moduli of heterogeneous materials.” J. Appl. Mech., 29, 143–150.
15.
Hashin, Z., and Shtrikman, S. ( 1962). “On some variational principles in anisotropic and nonhomogeneous elasticity.” J. Mech. Phys. Solids, 10, 335–342.
16.
Hervé, E., Stolz, C., and Zaoui, A. ( 1991). “On Hashin composite spheres assemblage.” Comptes Rendus de l'Academie des Sciences Series II, 313(8), 857–862.
17.
Hill, R. ( 1956). “New horizons in the mechanics of solids.” J. Mech. Phys. Solids, 5, 66–74.
18.
Love, A. E. H. ( 1944). A treatise on the mathematical theory of elasticity. Dover, New York.
19.
Ponte Castañeda, P. ( 1991). “The effective mechanical properties of nonlinear isotropic composite.” J. Mech. Phys. Solids, 39(1), 45–69.
20.
Ponte Castañeda, P., and Willis, J. R. ( 1988). “On the overall properties of nonlinearly viscous composites.” Proc., Royal Soc., London, A416, 217–244.
21.
Scott, G. D., and Kilgour, D. M. ( 1969). “The density of random close packing of spheres.” British J. Appl. Phys., D2, 863–869.
22.
Shamo, D. F. ( 1970). “Conditioning of quasi-Newton methods for function minimisation.” Mathematics of Computing, 24, 647–652.
23.
Sternberg, E., Eubanks, R. A., and Sadowsky, M. A. ( 1951). “On the axisymmetric problem of elasticity theory for a region bounded by two concentric spheres.” Proc., 1st U.S. Nat. Congr. of Appl. Mech, 209–215.
24.
Suquet, P. M. ( 1993). “Overall potentials and extremal surfaces of power law or ideally plastic composites.” J. Mech. Phys. Solids, 41(6), 981– 1002.
25.
Suquet, P. M., and Ponte Castañeda, P. ( 1993). “Small-contrast perturbation expansions for the effective properties of nonlinear composites.” Comptes Rendus de l'Academie des Sciences Serie II, 317, 1515–1520.
26.
Talbot, D. R. S., and Willis, J. R. ( 1985). “Variational principles for inhomogeneous non-linear media.” J. Appl. Mathematics, 35, 39–54.
27.
Whiteoak, D. ( 1990). Shell bitumen handbook. Shell Bitumen.
28.
Willis, J. R. ( 1983). “The overall elastic response of composite materials.” J. Mech. Phys. Solids, 50, 1202–1209.
29.
Willis, J. R. ( 1989). “The structure of overall constitutive relations for a class of nonlinear composites.” J. Appl. Mathematics, 43, 231–242.
Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 125 • Issue 3 • March 1999
Pages: 255 - 262
History
Received: Mar 26, 1997
Published online: Mar 1, 1999
Published in print: Mar 1999
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