Emergence and disappearance of load induced fiber kinking surfaces in transversely isotropic hyperelastic materials

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 61, Issue 4, 2010, Pages 745-772

  Baek, Seungik ^a   Pence, Thomas J ^a  

^a Michigan State University   (United States)

Author keywords

Constitutive behavior; Fiber reinforcement; Hyperelastic; Kink surfaces; Transverse isotropy

Indexed keywords

ABRUPT CHANGE; CONSTITUTIVE BEHAVIORS; DEFORMATION GRADIENTS; FIBER ORIENTATIONS; FIBER REINFORCEMENT; HIGHLY SENSITIVE; HYPER ELASTIC; HYPERELASTIC MATERIALS; IN-FIBER; MATRIX; NONMONOTONE; PAIR CREATION; SHEARING DEFORMATION; SPATIAL VARIATIONS; TRANSVERSE ISOTROPY; TRANSVERSELY ISOTROPIC;

DEFORMATION; FIBER REINFORCED MATERIALS; FIBERS; REINFORCED PLASTICS; REINFORCEMENT;

SURFACES;

DEFORMATION; ELASTOMERS; EMISSION; FIBER ORIENTATION; FIBERS; REINFORCED PLASTIC; REINFORCEMENT; SHEAR STRESS; SURFACES;

EID: 77955317514     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00033-009-0029-8     Document Type: Article

References (30)

1. Abeyaratne R. C., Knowles J. K.: Discontinuous deformation gradients in plane finite elastostatics of incompressible materials. J. Elast. 10, 255-293 (1980).
2. Abeyaratne R. C.: Discontinuous deformation gradients in the finite twisting of an incompressible elastic tube. J. Elast. 11, 43-80 (1981).
3. Abeyaratne R. C., Knowles J. K.: On the dissipative response due discontinuous strains in bars of unstable elastic material. Int. J. Solids Struct. 24, 1021-1044 (1988).
4. Abeyaratne R., Knowles J. K.: Evolution of phase transitions: a continuum theory. Cambridge University Press, London (2006).
5. Atkin R. J., Fox N.: An Introduction to the Theory of Elasticity. Longman, London (1980).
6. Bhattacharya K.: Phase boundary propagation in heterogeneous bodies. Proc. R. Soc. London A 455, 757-766 (1999).
7. Ericksen J. L.: Equilibrium of bars. J. Elast. 5, 191-201 (1975).
8. Fu Y. B., Zhang Y. T.: Continuum mechanical modeling of kink-band formation in fibre-reinforced composites. Int. J. Solids Struct. 43, 3306-3323 (2006).
9. Gao D. Y., Ogden R. W.: Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem. ZAMP 59, 498-517 (2008).
10. Gasser T. C., Ogden R. W., Holzapfel G. A.: Hyperelastic modeling of arterial layers with distributed collagen fibre orienations. Proc. R. Soc. Interface 3, 15-35 (2006).
11. Guo, Z. Y., Peng, X. Q., Moran, B.: Mechanical response of neo-Hookean fiber reinforced incompressible nonlinearly elastic solids. Int. J. Solids Struct. (2006). doi: 10. 1016/j. ijsolstr. 2006. 08. 018.
12. Kassianidis F., Ogden R. W., Merodio J., Pence T. J.: Azimuthal shear of a transversely isotropic elastic solid. Math. Mech. Solids 13, 690-724 (2008).
13. Knowles J. K., Sternberg E.: On the ellipticity of the equations of elastostatics for a special material. J. Elast. 5, 341-361 (1975).
14. Knowles J. K.: On the dissipation associated with equilibrium shocks in finite elasticity. J. Elast. 9, 131-158 (1979).
15. Knowles J. K.: Hysteresis in stress-cycling of bars undergoing solid-solid phase transitions. Q. J. Mech. Appl. Math. 55, 69-91 (2002).
16. Kumar B., Chaudury S. R.: Finite inhomogeneous shearing deformations of a transversely isotropic incompressible material. J. Elast. 51, 81-87 (1998).
17. Merodio J., Pence T. J.: Kink surfaces in a directionally reinforced neo-Hookean material under plane deformation: I Mechanical equilibrium. J. Elast. 62, 119-144 (2001).
18. Merodio J., Pence T. J.: Kink surfaces in a directionally reinforced neo-Hookean material under plane deformation: II Kink band stability and maximally dissipative band broadening. J. Elast. 62, 145-170 (2001).
19. Merodio J., Ogden R. W.: Material instabilities in fiber-reinforced nonlinearly elastic solids under plane deformation. Arch. Mech. 54, 525-552 (2002).
20. Merodio J., Ogden R. W.: Mechanical response of fiber-reinforced incompressible non-linearly elastic solids. Int. J. Non Linear Mech. 40, 213-227 (2005).
21. Merodio J., Saccomandi G., Sgura I.: The rectilinear shear of fiber-reinforced incompressible non-linearly elastic solids. I. J. Non Linear Mech. 42, 342-354 (2007).
22. Polignone D. A., Horgan C. O.: Cavitation for incompressible anisotropic nonlinearly elastic spheres. J. Elast. 33, 27-65 (1993).
23. Qiu G. Y., Pence T. J.: Remarks on the behavior of simple directionally reinforced incompressible nonlinearly elastic solids. J. Elast. 49, 1-30 (1997).
24. Qiu G. Y., Pence T. J.: Loss of ellipticity in plane deformation of a simple directionally reinforced incompressible nonlinearly elastic solid. J. Elast. 49, 31-63 (1997).
25. Spencer A. J. M.: Deformations of fiber-reinforced materials. Oxford University Press, London (1972).
26. Triantafyllidis N., Abeyaratne R.: Instability of a finitely deformed fiber reinforced elastic material. J. Appl. Mech. 50, 149-156 (1983).
27. Truskinovsky L.: Structure of an isothermal discontinuity. Sov. Phys. Doklady 30, 945-948 (1985).
28. Wineman A. S., Pipken A. C.: Material symmetry restrictions on constitutive equations. Arch. Rat. Mech. Anal. 17, 184-215 (1965).
29. Zhang J. P., Rajagopal K. R.: Some inhomogeneous motions and deformations within the context of a non linear elastic solid. Int. J. Eng. Sci. 30, 919-938 (1992).
30. Zee L., Sternberg E.: Ordinary and strong ellipticity in the equilibrium theory of incompressible hyperelastic solids. Arch. Rat. Mech. Anal. 83, 53-90 (1983).