Multiscale modeling of oriented thermoplastic elastomers with lamellar morphology

Journal of the Mechanics and Physics of Solids

Volumn 56, Issue 11, 2008, Pages 3206-3223

  Lopez Pamies, O ^a,b   Garcia, R ^c   Chabert, E ^b   Cavaille J Y ^c   Ponte Castaneda P ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b LABORATOIRE DE MÉCANIQUE DES SOLIDES   (France)

^c UNIVERSITÉ DE LYON   (France)

Author keywords

Block copolymers; Finite strain; Homogenization; Instabilities; Microstructures

Indexed keywords

ABS RESINS; BLOCK COPOLYMERS; CONSTITUTIVE MODELS; CRYSTAL MICROSTRUCTURE; CRYSTAL ORIENTATION; CRYSTAL STRUCTURE; DEFORMATION; ELASTOMERS; MICROSCOPIC EXAMINATION; MICROSTRUCTURAL EVOLUTION; MICROSTRUCTURE; POLYMERS; POWDERS; REINFORCED PLASTICS; RUBBER; SINGLE CRYSTALS; THERMOPLASTIC ELASTOMERS; X RAY SCATTERING;

FINITE STRAIN; HOMOGENIZATION; INSTABILITIES; MICROSTRUCTURES;

LAMELLAR STRUCTURES;

EID: 53249089998     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2008.07.008     Document Type: Article

References (38)

1. Abeyaratne R., and Triantafyllidis N. The emergence of shear bands in plane strain. Int. J. Solids Struct. 17 (1981) 1113-1134
2. Albalak R.J., and Thomas E.L. Microphase separation of block copolymer solution in a flow field. J. Polym. Sci. Part B: Polym. Phys. 31 (1993) 37-46
3. Allan P., Arridge R.G.C., Ehtaiatkar F., and Folkes M.J. The mechanical properties of an oriented lamella stock formed from an S-B-S block copolymer. J. Phys. D 24 (1991) 1381-1390
4. Arruda E.M., and Boyce M.C. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J. Mech. Phys. Solids 41 (1993) 389-412
5. Bockstaller M.R., Mickiewicz R.A., and Thomas E.L. Block copolymer nanocomposites: perspectives for tailored functional materials. Adv. Mater. 17 (2005) 1331-1349
6. Brun M., Lopez-Pamies O., and Ponte Castañeda P. Homogenization estimates for fiber-reinforced elastomers with periodic microstructures. Int. J. Solids Struct. 44 (2007) 5953-5979
7. Cohen Y., Albalak R.J., Dair B.J., Capel M.S., and Thomas E.L. Deformation of oriented lamellar block copolymer films. Macromolecules 33 (2000) 6502-6516
8. Dair B.J., Honeker C.C., Alward D.B., Avgeropoulos A., Hadjichristidis N., Fetters L.J., Capel M., and Thomas E.L. Mechanical properties and deformation behavior of the double gyroid phase in unoriented thermoplastic elastomers. Macromolecules 32 (1999) 8145-8152
9. Fredrickson G.H., and Bates F.S. Dynamics of block copolymers: theory and experiment. Annu. Rev. Mater. Sci. 26 (1996) 501-550
10. Garcia, R., 2006. Etude du comportement sous déformation de copolymère à blocs SBS et SBM à morphologie lamellaire. Ph.D. Dissertation, L'Institut National des Sciences Appliquées de Lyon, France.
11. Gent A. A new constitutive relation for rubber. Rubber Chem. Technol. 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. Arch. Ration. Mech. Anal. 122 (1993) 231-290
13. Gido S.P., Gunther J., and Thomas E.L. Lamellar diblock copolymer grain boundary morphology. 1. Twist boundary characterization. Macromolecules 26 (1993) 4506-4520
14. Hill R. On constitutive macro-variables for heterogeneous solids at finite strain. Proc. R. Soc. London A 326 (1972) 131-147
15. Honeker C.C., and Thomas E.L. Impact of morphological orientation in determining mechanical properties in triblock copolymers. Chem. Mater. 8 (1996) 1702-1714
16. 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
17. Knowles J.K., and Sternberg E. On the ellipticity of the equations of nonlinear elastostatics for a special material. J. Elasticity 5 (1975) 341-361
18. Lopez-Pamies, O., 2008. A new hyperelastic model for rubber elastic materials, submitted for publication.
19. 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
20. 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
21. Lopez-Pamies, O., Ponte Castañeda, P., 2008. Microstructure evolution in hyperelastic laminates and implications for overall behavior and macroscopic stability. Mech. Mater., accepted for publication.
22. Ogden R. Extremum principles in non-linear elasticity and their application to composites-I. Theory. Int. J. Solids Struct. 14 (1978) 265-282
23. Park C., Yoon J., and Thomas E.L. Enabling nanotechnology with self assembled block copolymer patterns. Polymer 44 (2003) 6725-6760
24. Polis D.L., and Winey K.I. Controlling kink band morphology in block copolymers: threshold criteria and stability. Macromolecules 31 (1998) 3617-3625
25. Ponte Castañeda P. Exact second-order estimates for the effective mechanical properties of nonlinear composite materials. J. Mech. Phys. Solids 44 (1996) 827-862
26. Ponte Castañeda P. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations. I. Theory. J. Mech. Phys. Solids 50 (2002) 737-757
27. Ponte Castañeda P., and Suquet P. Nonlinear composites. Adv. Appl. Mech. 34 (1998) 171-302
28. Ponte Castañeda P., and Tiberio E. A second-order homogenization method in finite elasticity and applications to black-filled elastomers. J. Mech. Phys. Solids 48 (2000) 1389-1411
29. Ponte Castañeda P., and Willis J.R. Variational second-order estimates for nonlinear composites. Proc. R. Soc. London A 455 (1999) 1799-1811
30. Prasman E., and Thomas E.L. High-strain tensile deformation of a sphere-forming triblock copolymer/mineral oil. J. Polym. Sci. Part B: Polym. Phys. 36 (1998) 1625-1636
31. Read D.J., Duckett R.A., Sweeney J., and McLeish T.C.B. The chevron folding instability in thermoplastic elastomers and other layered materials. J. Phys. D 32 (1999) 2087-2099
32. Seguela R., and Prud'homme J. Deformation mechanism of thermoplastic 2-phase elastomer of lamellar morphology having a high volume fraction of the rubbery microphase. Macromolecules 14 (1981) 197-202
33. Triantafyllidis N., and Maker B.N. On the comparison between microscopic and macroscopic instability mechanisms in a class of fiber-reinforced composites. J. Appl. Mech. 52 (1985) 794-800
34. Triantafyllidis N., and Nestorvić N. Onset of failure in finitely strained layered composites subjected to combined normal and shear strain. J. Mech. Phys. Solids 52 (2005) 941-974
35. 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
36. Tzianetopoulou T., and Boyce M.C. Micromechanics of PS/PB/PS triblock-copolymer films with lamellar morphology. Materials Research Society Symposium Proceedings vol. 788 (2004) L9.3
37. Willis J.R. Bounds and self-consistent estimates for the overall moduli of anisotropic composites. J. Mech. Phys. Solids 25 (1977) 185-202
38. Willis, J.R., 1982. Elasticity theory of composites. Mech. Solids 653-686.