A constitutive framework for tubular structures that enables a semi-inverse solution to extension and inflation

Journal of Elasticity

Volumn 77, Issue 1, 2004, Pages 57-81

  Criscione, John C ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Anisotropic material; Biomechanics; Cardiovascular mechanics; Constitutive behavior; Finite elasticity

Indexed keywords

DEFORMATION; FUNCTIONS; PRESSURE EFFECTS; PROBABILITY DENSITY FUNCTION; PROBLEM SOLVING; SET THEORY; STRAIN; TENSORS;

ANISOTROPIC MATERIALS; CARDIOVASCULAR MECHANICS; CONSTITUTIVE BEHAVIOR; FINITE ELASTICITY;

TUBES (COMPONENTS);

EID: 20644440383     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10659-005-2155-7     Document Type: Article

References (15)

1. S.N. Atluri, Alternate stress and conjugate strain measures, and mixed variational formulations involving rigid rotations, for computational analyses of finitely deformed solids, with application to plates and shells - I. Computers Structures 18(1) (1984) 93-116.
2. J.C. Criscione, Rivlin's representation formula is ill-conceived for the determination of response functions via biaxial testing. J. Elasticity 70 (2003) 129-147.
3. J.C. Criscione, A.S. Douglas and W.C. Hunter, Physically based strain invariant set for materials exhibiting transversely isotropic behavior. J. Mech. Phys. Solids 49 (2001) 871-897.
4. J.C. Criscione, J.D. Humphrey, A.S. Douglas and W.C. Hunter, An invariant basis for natural strain which yields orthogonal stress response terms in isotropic hyperelasticity. J. Mech. Phys. Solids 48 (2000) 2445-2465.
5. J.C. Criscione and W.C. Hunter, Kinematic framework for materials with two separate families of parallel fibers. Continuum Mech. Thermodynamics 15 (2003) 613-628.
6. J.C. Criscione, A.D. McCulloch and W.C. Hunter, Constitutive framework optimized for myocardium and other high-strain, laminar materials with one fiber family. J. Mech. Phys. Solids 50 (2002) 1681-1702.
7. P.J. Flory, Thermodynamic relations for high elastic materials. Trans. Faraday Soc. 57 (1961) 829-838.
8. Y.C. Fung, Biomechanics: Mechanical Properties of Living Tissues. Springer, New York (1993) p. 281.
9. M.E. Gurtin, An Introduction to Continuum Mechanics. Academic Press, San Diego (1981) pp. 63, 71, 110.
10. J.D. Humphrey, Cardiovascular Solid Mechanics: Cells, Tissues, and Organs. Springer, New York (2002) Chapters 4, 7.
11. L.E. Malvern, Introduction to the Mechanics of a Continuous Medium. Prentice-Hall, Englewood Cliffs, NJ (1969) p. 284.
12. R.W. Ogden, Non-linear Elastic Deformations. Dover Press, Mineola, NY (1997) pp. 88, 122, 156.
13. G.R Smith, Constitutive Equations for Anisotropic and Isotropic Materials. North-Holland, Amsterdam (1994).
14. G.R Smith and R.S. Rivlin, The strain-energy function for anisotropic elastic materials. Trans. Amer. Math. Soc. 88 (1958) 175-193.
15. A.J.M. Spencer, Constitutive theory for strongly anisotropic solids. In: A.J.M. Spencer (ed.), Continuum Theory of the Mechanics of Fibre-Reinforced Composites. Springer, New York (1984) pp. 1-32.