Second-order estimates for the large-deformation response of particle-reinforced rubbers

Comptes Rendus - Mecanique

Volumn 331, Issue 1, 2003, Pages 1-8

  Lopez Pamies, Oscar ^a   Ponte Castañeda, Pedro ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Computational solid mechanics; Elastomers; Finite deformations; Homogenization

Indexed keywords

ELASTOMER; RUBBER;

COMPOSITE;

ARTICLE; COMPRESSION; CONFORMATIONAL TRANSITION; DEFORMITY; ELASTICITY; FIBER; MEASUREMENT; MECHANICAL STRESS; MECHANICS; PARTICLE SIZE; TECHNIQUE;

EID: 0037233482     PISSN: 16310721     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1631-0721(03)00021-4     Document Type: Article

References (18)

1. R. Hill, On constitutive macro-variables for heterogeneous solids at finite strain, Proc. Roy. Soc. London Ser. A 326 (1972) 131-147.
2. S. Müller, Homogenization of nonconvex integral functionals and cellular elastic materials, Arch. Rational Mech. Anal. 99 (1987) 189-212.
3. G. Geymonat, S. Müller, N. Triantafyllidis, Homogenization of nonlinearly elastic materials, macroscopic bifurcation and macroscopic loss of rank-one convexity, Arch. Rational Mech. Anal. 122 (1993) 231-290.
4. R. Ogden, Extremun principles in non-linear elasticity and their application to composites - I, Theory, Int. J. Solids Structures 14 (1978) 265-282.
5. P. Ponte Castañeda, The overall constitutive behaviour of nonlinearly elastic composites, Proc. Roy. Soc. London Ser. A 422 (1989) 147-171.
6. L. Mullins, N.R. Tobin, Stress softening in rubber vulcanizates. Part I. Use of strain amplification factor to describe the elastic behavior of filler-reinforced vulcanized rubber, J. Appl. Polymer Sci. 99 (1965) 189-212.
7. L.R. Treolar, The Physics of Rubber Elasticity, Oxford University Press, Oxford, 1975.
8. E.A. Meinecke, M.I. Taftaf, Effect of carbon-black on the mechanical properties of el astomers, Rubber Chem. Technol. 61 (1988) 534-547.
9. S. Govindjee, J. Simo, A micromechanically based continuum damage model for carbon black-filled rubbers incoporating Mullins' effect, J. Mech. Phys. Solids 39 (1991) 87-112.
10. P. Ponte Castañeda, E. Tiberio, A second-order homogenization procedure in finite elasticity and applications to black-filled elastomers, J. Mech. Phys. Solids 48 (2000) 1389-1411.
11. N. Lahellec, Estimates of the homogenized hyperelastic behavior of periodic fiber-reinforced composites using the second-order procedure, C. R. Acad. Sci. Paris IIb 329 (2001) 67-73.
12. P. Ponte Castañeda, Exact second-order estimates for the effective mechanical properties of nonlinear composite materials, J. Mech. Phys. Solids 44 (1996) 827-862.
13. P. Ponte Castañeda, Second-order homogenization estimates for nonlinear composites incorporating field fluctuations. I. Theory, J. Mech. Phys. Solids 50 (2002) 737-757.
14. P. Ponte Castañeda, The effective mechanical properties of nonlinear isotropic composites, J. Mech. Phys. Solids 39 (1991) 45-71.
15. N. Laws, On the thermostatics of composite materials, J. Mech. Phys. Solids 21 (1973) 9-17.
16. P. Suquet, P. Ponte Castañeda, Small-contrast perturbation expansions for the effective properties of nonlinear composites, C. R. Acad. Sci. Paris II 317 (1993) 1515-1522.
17. Z. Hashin, S. Shtrikman, A variational approach to the theory of the elastic behavior of multiphase materials, J. Mech. Phys. Solids 11 (1963) 127-140.
18. V.M. Levin, Thermal expansion coefficients of heterogeneous materials, Mekh. Tverd. Tela 2 (1967) 83-94.