Dynamics of biological soft tissue and rubber: Internally pressurized spherical membranes surrounded by a fluid

International Journal of Non-Linear Mechanics

Volumn 39, Issue 3, 2004, Pages 399-420

  Haslach, Henry W ^a   Humphrey, Jay D ^b  

^a UNIVERSITY OF MARYLAND   (United States)

^b Texas A and M University   (United States)

Author keywords

Bifurcation; Fung model; Global dynamical bifurcation; Intracranial saccular aneurysm; Mooney Rivlin model; Periodic orbits

Indexed keywords

BIOLOGICAL MEMBRANES; INCOMPRESSIBLE FLOW; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; RUBBER; TISSUE;

PERIODIC ORBITS;

BIOMECHANICS;

EID: 0038148102     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7462(02)00196-8     Document Type: Article

References (23)

1. Humphrey J.D. Computer methods in membrane biomechanics. Comp. Meth. Biomech. Biomed. Eng. 1:1998;171-210.
2. Beatty M.F. Topics in finite elasticity. hyperelasticity of rubber, elastomers, and biological tissues - with examples Appl. Mech. Rev. 40:1987;1699-1734.
3. Ogden R.W. Non-linear Elastic Deformations. 1984;Ellis-Horwood, Chichester.
4. Wang C.C. On the radial oscillations of a spherical thin shell in the finite elasticity theory. Q. Appl. Math. 23:1965;270-274.
5. Akkas N. On the dynamic snap-out instability of inflated non-linear spherical membranes. Int. J. Non-Linear Mech. 13:1978;177-183.
6. Jenkins C.H., Leonard J.W. Nonlinear dynamic response of membranes. state of the art Appl. Mech. Rev. 44:1991;319-328.
7. Löw M., Perktold K., Raunig R. Hemodynamics in rigid and distensible saccular aneurysms. a numerical study of pulsatile flow characteristics Biorheol. 30:1993;287-298.
8. Shah A.D., Humphrey J.D. Finite strain elastodynamics of intracranial saccular aneurysms. J. Biomech. 32:1999;593-599.
9. Haslach H.W. Jr. Constitutive models and singularity types for an elastic biaxially loaded rubber sheet. Math. Mech. Solids. 5:2000;41-73.
10. H.W. Haslach Jr., Dynamical effects of degenerate singularities in the potential for mechanical systems, in: C.T. Leondes (Ed.), Nonlinear techniques in structural dynamic systems, Vol. 15 of structural dynamics systems, computational techniques, and optimization, International Series in Engineering, Technology and Applied Science, Gordon and Breach Science Publishers, New York, 1999, pp. 273-330.
11. Fung Y.C. Biomechanics: Mechanical Properties of Living Tissues. 2nd Edition:1993;Springer, New York.
12. Skalak R., Rachev A., Tozeren A. Stress-strain relations for membranes under finite deformations. Bulgarian Acad. Sci. Biomech. 2:1975;24-29.
13. Ogden R.W. Large deformation isotropic elasticity - on the correlation of theory and experiment for incompressible rubberlike solids. Proc. R. Soc. Lond. A. 326:1972;565-584.
14. Alexander H. A constitutive relation for rubberlike materials. Int. J. Eng. Sci. 6:1968;549-562.
15. Alexander H. Tensile instability of initially spherical balloons. Int. J. Eng. Sci. 9:1971;151-162.
16. Poston T., Stewart I. Catastrophe Theory and its Applications. 1978;Pitman, London.
17. Castrigiano D.P.L., Hayes S.A. Catastrophe Theory. 1993;Addison-Wesley, Reading, MA.
18. Carr J. Applications of Center Manifold Theory. 1981;Springer, New York.
19. Dumortier F., Roussarie C. Cubic lienard equations with linear damping. Nonlinearity. 3:1990;1015-1039.
20. Dumortier F. Local study of planar vector fields. Broer H.W., Dumortier F., van Strien S.J., Takens F. Structures in Dynamics. 1991;North-Holland Elsevier Science Publishers, Amsterdam.
21. H.W. Haslach Jr., A nonlinear dynamical mechanism for bruit generation by an intracranial saccular aneurysm, J. Math. Biol., to appear.
22. J.K. Hale, Oscillations in Nonlinear Systems (1992 reprint), Dover Publications, New York, 1963.
23. Guckenheimer J., Holmes P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. 1983;Springer, New York.