Making use of an iterated homogenization procedure in finite elasticity, an exact and explicit result is derived for the macroscopic response of Neo-Hookean solids reinforced by a random and isotropic distribution of rigid particles. The key theoretical and practical features of the result are discussed in light of comparisons with recent approximations and full-field simulations.
Issue Section:
Research Papers
1.
Hill
, R.
, 1972, “On Constitutive Macrovariables for Heterogeneous Solids at Finite Strain
,” Proc. R. Soc. London
0370-1662, 326
, pp. 131
–147
.2.
deBotton
, G.
, 2005, “Transversely Isotropic Sequentially Laminated Composites in Finite Elasticity
,” J. Mech. Phys. Solids
0022-5096, 53
, pp. 1334
–1361
.3.
Idiart
, M. I.
, 2008, “Modeling the Macroscopic Behavior of Two-Phase Nonlinear Composites by Infinite-Rank Laminates
,” J. Mech. Phys. Solids
0022-5096, 56
, pp. 2599
–2617
.4.
Idiart
, M. I.
, and Lopez-Pamies
, O.
, 2009, “Two-Phase Hyperelastic Composites: A Realizable Homogenization Constitutive Theory
,” in preparation.5.
Lopez-Pamies
, O.
, and Ponte Castañeda
, P.
, 2006, “On the Overall Behavior, Microstructure Evolution, and Macroscopic Stability in Reinforced Rubbers at Large Deformations: I—Theory
,” J. Mech. Phys. Solids
0022-5096, 54
, pp. 807
–830
.6.
Lopez-Pamies
, O.
, and Ponte Castañeda
, P.
, 2006, “On the Overall Behavior, Microstructure Evolution, and Macroscopic Stability in Reinforced Rubbers at Large Deformations: II—Application to Cylindrical Fibers
,” J. Mech. Phys. Solids
0022-5096, 54
, pp. 831
–863
.7.
Bruggeman
, D. A. G.
, 1935, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen (Calculation of Various Physical Constants in Heterogeneous Substances. I. Dielectric Constants and Conductivity of Composites From Isotropic Substances)
,” Ann. Phys.
0003-3804, 416
, pp. 636
–664
.8.
Roscoe
, R.
, 1952, “The Viscosity of Suspensions of Rigid Spheres
,” Br. J. Appl. Phys.
0508-3443, 8
, pp. 1
–16
.9.
Norris
, A. N.
, 1985, “A Differential Scheme for the Effective Moduli of Composites
,” Mech. Mater.
0167-6636, 4
, pp. 1
–16
.10.
Milton
, G. W.
, 2002, “The Theory of Composites
,” Cambridge Monographs on Applied and Computational Mathematics
, Cambridge University Press
, Cambridge, England
, Vol. 6
.11.
Duva
, J. M.
, 1984, “A Self-Consistent Analysis of the Stiffening Effect of Rigid Inclusions on a Power-Law Material
,” ASME J. Eng. Mater. Technol.
0094-4289, 106
, pp. 317
–321
.12.
Eshelby
, J. D.
, 1957, “The Determination of the Elastic Field of an Ellipsoidal Inclusion and Related Problems
,” Proc. R. Soc. London
0370-1662, 241
, pp. 376
–396
.13.
Lopez-Pamies
, O.
, 2009, “Onset of Cavitation in Compressible, Isotropic, Hyperelastic Solids
,” J. Elast.
0374-3535, 94
, pp. 115
–145
.14.
Lopez-Pamies
, O.
, and Idiart
, M. I.
, 2009, “An Exact Result for the Macroscopic Response of Porous Neo-Hookean Solids
,” J. Elast.
0374-3535, 95
, pp. 99
–105
.15.
Triantafyllidis
, N.
, Nestorovic
, M. D.
, and Schraad
, M. W.
, 2006, “Failure Surfaces for Finitely Strained Two-Phase Periodic Solids Under General In-Plane Loading
,” ASME J. Appl. Mech.
0021-8936, 73
, pp. 505
–515
.16.
Michel
, J. C.
, Lopez-Pamies
, O.
, Ponte Castañeda
, P.
, and Triantafyllidis
, N.
, “Microscopic and Macroscopic Instabilities in Finitely Strained Reinforced Elastomers
,” in preparation. 1051-981517.
Moraleda
, J.
, Segurado
, J.
, and Llorca
, J.
, 2009, “Finite Deformation of Incompressible Fiber-Reinforced Elastomers: A Computational Micromechanics Approach
,” J. Mech. Phys. Solids
0022-5096, 57
, pp. 1596
–1613
.18.
Eischen
, J. W.
, and Torquato
, S.
, 1993, “Determining Elastic Behavior of Composites by the Boundary Element Method
,” J. Appl. Phys.
0021-8979, 74
, pp. 159
–170
.19.
Christensen
, R. M.
, 2005, Mechanics of Composite Materials
, Dover
, New York
.20.
Mullins
, L.
, and Tobin
, N. R.
, 1965, “Stress Softening in Rubber Vulcanizates. Part I. Use of a Strain Amplification Factor to Describe the Elastic Behavior of Filler-Reinforced Vulcanized Rubber
,” J. Appl. Polym. Sci.
0021-8995, 9
, pp. 2993
–3009
.Copyright © 2010
by American Society of Mechanical Engineers
You do not currently have access to this content.