Homogenization-based constitutive models for porous elastomers and implications for macroscopic instabilities: II-Results

Journal of the Mechanics and Physics of Solids

Volumn 55, Issue 8, 2007, Pages 1702-1728

  Lopez Pamies, O ^a,b   Ponte Castaneda P ^a,b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b LABORATOIRE DE MÉCANIQUE DES SOLIDES   (France)

Author keywords

Constitutive behavior; Finite strain; Microstructures; Porous material; Soft matter

Indexed keywords

COMPUTER SIMULATION; ELASTOMERS; HOMOGENIZATION METHOD; MICROSTRUCTURE; POROSITY;

COMPRESSIVE DEFORMATIONS; CONSTITUTIVE BEHAVIOR; FINITE DEFORMATIONS; SOFT MATTER;

MATHEMATICAL MODELS;

EID: 34250899142     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2007.01.008     Document Type: Article

References (19)

1. Danielsson M., Parks D.M., and Boyce M.C. Constitutive modeling of porous hyperelastic materials. Mech. Mater. 36 (2004) 347-358
2. Gent A.N. A new constitutive relation for rubber. Rubber Chem. Technol. 69 (1996) 59-61
3. Geymonat G., Müller S., and Triantafyllidis N. Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity. Arch. Ration. Mech. Anal. 122 (1993) 231-290
4. Gong L., and Kyriakides S. Compressive response of open-cell foams. Part II: initiation and evolution of crushing. Int. J. Solids Struct. 42 (2005) 1381-1399
5. Gurson A.L. Continuum theory of ductile rupture by void nucleation and growth: part I-yield criteria and flow rules for porous ductile media. J. Eng. Mater. Technol. 99 (1977) 2-15
6. Hashin Z. The elastic moduli of heterogeneous materials. J. Appl. Mech. 29 (1962) 143-150
7. Hashin Z. Large isotropic elastic deformation of composites and porous media. Int. J. Solids Struct. 21 (1985) 711-720
8. Hou H.-S., and Abeyaratne R. Cavitation in elastic and elastic-plastic solids. J. Mech. Phys. Solids 40 (1992) 571-592
9. Kinney J.H., Marshall G.W., Marshall S.J., and Haupt D.L. Three-dimensional imaging of large compressive deformations in elastomeric foams. J. Appl. Polym. Sci. 80 (2001) 1746-1755
10. Lopez-Pamies O., and Ponte Castañeda P. Second-order estimates for the macroscopic response and loss of ellipticity in porous rubbers at large deformations. J. Elasticity 76 (2004) 247-287
11. Lopez-Pamies O., and Ponte Castañeda P. On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations: I-theory. J. Mech. Phys. Solids 54 (2006) 807-830
12. Lopez-Pamies O., and Ponte Castañeda P. On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations. II-application to cylindrical fibers. J. Mech. Phys. Solids 54 (2006) 831-863
13. Lopez-Pamies, O., Ponte Castañeda, P., 2007. Homogenization-based constitutive models for porous elastomers and implications for macroscopic instabilities: I-analysis. J. Mech. Phys. Solids, in press, doi:10.1016/j.jmps.2007.01.007.
14. Michel, J.-C., Lopez-Pamies, O., Ponte Castañeda, P., Triantafyllidis, N., 2007. Microscopic and macroscopic instabilities in finitely strained porous elastomers. J. Mech. Phys. Solids, in press, doi:10.1016/j.jmps.2006.11.006.
15. Ogden R. Extremum principles in non-linear elasticity and their application to composites-I theory. Int. J. Solids Struct. 14 (1978) 265-282
16. Triantafyllidis N., and Bardenhagen S.G. The influence of scale size on the stability of periodic solids and the role of associated higher order gradient continuum models. J. Mech. Phys. Solids 44 (1996) 1891-1928
17. Triantafyllidis N., Nestorvić M.D., and Schraad M.W. Failure surfaces for finitely strained two-phase periodic solids under general in-plane loading. J. Appl. Mech. 73 (2006) 505-515
18. Wang A.S.D., and Ertepinar A. Stability and vibrations of elastic thick-walled cylindrical and spherical shells subjected to pressure. Int. J. Non-Linear Mech. 7 (1972) 539-555
19. Wesolowski Z. Stability of elastic thick-wall spherical shell loaded by external pressure. Arch. Mech. Stosow. 19 (1967) 3-23