Onset of macroscopic instabilities in fiber-reinforced elastomers at finite strain

Journal of the Mechanics and Physics of Solids

Volumn 57, Issue 11, 2009, Pages 1828-1850

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

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b Stony Brook University   (United States)

Author keywords

Fiber reinforced composite; Finite strain; Homogenization; Instabilities; Microstructures

Indexed keywords

CHARACTERISTIC SIZE; CLOSED-FORM FORMULAE; CONSTITUTIVE RELATIONS; FIBER DIRECTION; FIBER PROPERTIES; FIBER VOLUME FRACTIONS; FIBER-REINFORCED COMPOSITE; FINITE STRAIN; HOMOGENIZATION; IN-FIBER; INSTABILITIES; LOADING CONDITION; LOADING ORIENTATION; MACROSCOPIC DEFORMATIONS; MATERIAL SYSTEMS; MATRIX; PARAMETRIC ANALYSIS; RANDOM MICROSTRUCTURE; REINFORCED ELASTOMERS; SOFT MATERIAL; STRAIN LOADING; VERY STIFF FIBERS;

DEFORMATION; ELASTOMERS; FIBER OPTICS; FIBER REINFORCED PLASTICS; FIBERS; LAMINATES; MICROSTRUCTURE; REINFORCED PLASTICS; RUBBER; STEEL STRUCTURES; THREE DIMENSIONAL;

LOADING;

EID: 70349232215     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2009.08.001     Document Type: Article

References (46)

1. Abdelmoula, R., Krasucki, F., Marigo, J.-J., 1993. Microbuckling analysis of unidirectional fibred composites. In: Mecamat 93-International Seminar on Micromechanics of Materials. Collection de la Direction des Etudes et Recherches d'Electricité de France, Eyrolles, pp. 303-314.
2. Agoras M., Lopez-Pamies O., and Ponte Castañeda P. A general hyperelastic model for incompressible fiber-reinforced elastomers. Journal of the Mechanics and Physics of Solids 57 (2008) 268-286
3. Brun M., Lopez-Pamies O., and Ponte Castañeda P. Homogenization estimates for fiber-reinforced elastomers with periodic microstructures. International Journal of Solids and Structures 44 (2007) 5953-5979
4. deBotton G. Transversely isotropic sequentially laminated composites in finite elasticity. Journal of the Mechanics and Physics of Solids 53 (2005) 1334-1361
5. deBotton, G., 2008. Composites with one and two families of fibers. Presented at the Composites and Polycrystals Mini-Symposium at the 2008 SIAM Conference on Mathematical Aspects of Materials Science, Philadelphia.
6. deBotton G., Hariton I., and Socolsky E.A. Neo-Hookean fiber-reinforced composites in finite elasticity. Journal of the Mechanics and Physics of Solids 54 (2006) 533-559
7. deBotton G., and Ponte Castañeda P. Elastoplastic constitutive relations for fiber-reinforced solids. International Journal of Solids and Structures 30 (1993) 1865-1890
8. Ericksen J.L., and Rivlin R.S. Large elastic deformations of homogeneous anisotropic materials. Indiana University Mathematics Journal 3 (1954) 281-301
9. Finlay H.M., Whittaker P., and Canham P.B. Collagen organization in branching region of human brain arteries. Stroke 29 (1998) 1595-1601
10. Fleck N. Compressive failure of fiber composites. Advances in Applied Mechanics 33 (1997) 43-117
11. Gent A.N. A new constitutive relation for rubber. Rubber Chemistry and Technology 69 (1996) 59-61
12. Geymonat G., Müller S., and Triantafyllidis N. Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity. Archive for Rational Mechanics and Analysis 122 (1993) 231-290
13. Grandidier J.C., and Poitier-Ferry M. Fiber microbuckling in a long fiber composite material. Comptes Rendus de l'Academie des Sciences, Serie II 310 (1990) 1-6
14. Guo Z.Y., Peng X.Q., and Moran B. A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus. Journal of the Mechanics and Physics of Solids 54 (2006) 1952-1971
15. He Q.C., Le Quang H., and Feng Z.Q. Exact results for the homogenization of elastic fiber-reinforced solids at finite strain. Journal of Elasticity 83 (2006) 153-177
16. Hill R. On constitutive macrovariables for heterogeneous solids at finite strain. Proceedings of the Royal Society of London A 326 (1972) 131-147
17. Holzapfel G.A., Gasser T.C., and Ogden R.W. A new constitutive framework for arterial wall mechanics and a comparative study of material models. Journal of Elasticity 61 (2000) 1-48
18. Honeker C.C., and Thomas E.L. Impact of morphological orientation in determining mechanical properties in triblock copolymers. Chemistry of Materials 8 (1996) 1702-1714
19. Honeker C.C., Thomas E.L., Albalak R.J., Hadjuk D.A., Gruner S.M., and Capel M.C. Perpendicular deformation of a near-single crystal triblock copolymer with a cylindrical morphology. 1. Synchrotron SAXS. Macromolecules 33 (2000) 9395-9406
20. Horgan C.O., and Saccomandi G. A new constitutive theory for fiber-reinforced incompressible nonlinearly elastic solids. Journal of the Mechanics and Physics of Solids 53 (2005) 1985-2015
21. Jelf P.M., and Fleck N. Compression failure mechanisms in unidirectional composites. Journal of Composite Materials 26 (1992) 2706-2726
22. Kyriakides S., and Ruff A.E. Aspects of the failure and postfailure of fiber composites in compression. Journal of Composite Materials 31 (1997) 1633-1670
23. Lopez-Pamies O., Garcia R., Chabert E., Cavaillé J.-Y., and Ponte Castañeda P. Multiscale modeling of oriented thermoplastic elastomers with lamellar morphology. Journal of the Mechanics and Physics of Solids 56 (2008) 3206-3223
24. Lopez-Pamies O., and Ponte Castañeda P. On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations: I-Theory. Journal of the Mechanics and Physics of Solids 54 (2006) 807-830
25. 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. Journal of the Mechanics and Physics of Solids 54 (2006) 831-863
26. Lopez-Pamies, O., Ponte Castañeda, P., 2006c. Effective behavior, microstructure evolution and macroscopic instabilities in reinforced elastomers. Presented at the Instabilities in Solids, Structures and Materials Mini-Symposium at the 15th U.S. National Congress of Theoretical and Applied Mechanics, Boulder.
27. Lopez-Pamies O., and Ponte Castañeda P. Microstructure evolution in hyperelastic laminates and implications for overall behavior and macroscopic stability. Mechanics of Materials 41 (2009) 364-374
28. Merodio J., and Ogden R.W. Instabilities and loss of ellipticity in fiber-reinforced nonlinearly elastic solids under plane deformation. International Journal of Solids and Structures 40 (2003) 4707-4727
29. Merodio J., and Ogden R.W. Mechanical response of fiber-reinforced incompressible nonlinear elastic solids. International Journal of Nonlinear Mechanics 40 (2005) 213-227
30. Merodio J., and Pence T.J. Kink surfaces in a directionally reinforced Neo-Hookean material under plane deformation: I. Mechanical equilibrium. Journal of Elasticity 62 (2001) 119-144
31. Michel, J.-C., Lopez-Pamies, O., Ponte Castañeda, P., Triantafyllidis, N., 2009. Microscopic and macroscopic instabilities in finitely strained reinforced elastomers, in preparation.
32. Moraleda J., Segurado J., and Llorca J. Computational micromechanics of fiber-reinforced elastomers. Journal of the Mechanics and Physics of Solids 57 (2009) 1596-1613
33. Nesterovic N., and Triantafyllidis N. Onset of failure in finitely strained layered composites subjected to combined normal and shear loading. Journal of the Mechanics and Physics of Solids 52 (2004) 941-974
34. Ogden R. Non-linear Elastic Deformations (1984), Dover Publications, New York
35. Ogden R. Extremum principles in non-linear elasticity and their application to composites-I. Theory. International Journal of Solids and Structures 14 (1978) 265-282
36. Ponte Castañeda P. The overall constitutive behavior of nonlinearly elastic composites. Proceedings of the Royal Society of London A 422 (1989) 147-171
37. Ponte Castañeda P. Exact second-order estimates for the effective mechanical properties of nonlinear composite materials. Journal of the Mechanics and Physics of Solids 44 (1996) 827-862
38. Ponte Castañeda P. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I-Theory. Journal of the Mechanics and Physics of Solids 50 (2002) 737-757
39. Ponte Castañeda P., and Tiberio E. A second-order homogenization procedure in finite elasticity and applications to black-filled elastomers. Journal of the Mechanics and Physics of Solids 48 (2000) 1389-1411
40. Quapp M.K., and Weiss J.A. Material characterization of human medial collateral ligament. Journal of Biomechanical Engineering 120 (1998) 757-763
41. Qiu G.Y., and Pence T.J. Remarks on the behavior of simple directionally reinforced incompressible nonlinearly elastic solids. Journal of Elasticity 49 (1997) 1-30
42. Rosen, B.W., 1965. Mechanics of Composite Strengthening. In: Fiber Composite Materials. American Society for Metals 37-75.
43. Triantafyllidis N., and Abeyaratne R.C. Instability of a finitely deformed fiber-reinforced elastic material. Journal of Applied Mechanics 50 (1983) 149-156
44. Triantafyllidis N., and Maker B.N. On the comparison between microscopic and macroscopic instability mechanisms in a class of fiber-reinforced composites. Journal of Applied Mechanics 52 (1985) 794-800
45. Triantafyllidis N., Nestorovic M.D., and Schaard M.W. Failure surfaces for finitely strained two-phase periodic solids under general in-plane loading. Journal of Applied Mechanics 73 (2006) 505-516
46. Walpole L.J. On the overall elastic moduli of composite materials. Journal of the Mechanics and Physics of Solids 17 (1969) 235-251