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Tytuł artykułu

Theory of residual stresses with application to an arterial geometry

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Konferencja
Solid Mechanics Conference (35 ; 04-08.09.2006 ; Cracow, Poland)
Języki publikacji
EN
Abstrakty
EN
This paper presents a theory of residual stresses, with applications to biomechanics, especially to arteries. For a hyperelastic material, we use an initial local deformation tensor K as a descriptor of residual strain. This tensor, in general, is not the gradient of a global deformation, and a stress-free reference configuration, denoted ..., therefore, becomes incompatible. Any compatible reference configuration ... will, in general, be residually stressed. However, when a certain curvature tensor vanishes, there actually exists a compatible and stress-free configuration, and we show that the traditional treatment of residual stresses in arteries, using the opening-angle method, relates to such a situation. Boundary value problems of nonlinear elasticity are preferably formulated on a fixed integration domain. For residually stressed bodies, three such formulations naturally appear: (i) a formulation relating to ... with a non-Euclidean metric structure; (ii) a formulation relating to ... with a Euclidean metric structure; and (iii) a formulation relating to the incompatible configuration ... . We state these formulations, show that (i) and (ii) coincide in the incompressible case, and that an extra term appears in a formulation on ... , due to the incompatibility.
Rocznik
Strony
341--364
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
autor
autor
  • Division of Mechanics Institute of Technology, Linkoping University SE 581 83 Linkoping, Sweden
Bibliografia
  • 1. R.N. VAISHNAV and J. VOSSOUGHI, Estimation of residual strains in aortic segments, [in:] C.W. HALL [Ed.], Biomedical engineering II, Recent developments, Pergamon Press, New York 1983.
  • 2. Y.C. FUNG, On the foundations of biomechanics, Journal of Applied Mechanics, 50, 1003-1009, 1983.
  • 3. E.K. RODRIGUEZ, A. ROGER and A.D. McCuLLOCH, Stress-Dependent Finite Growth in Soft Elastic Tissues, Journal of Biomechanics, 27, 455-467, 1994.
  • 4. R. SKALAK, S. ZARGARYAN, R. JAIN, P. NETTI and A. HOGER, Compatibility and the genesis of residual stress by volumetric growth. Journal of Mathematical Biology, 34, 889-914, 1996.
  • 5. G.A. MAUGIN, Geometry and thermodynamics of structural rearangements: Ekkehart Kroner's legacy, ZAMM, 83, 2, 75-84, 2003.
  • 6. C. TRUESDELL and W. NOLL, The nonlinear field theories of mechanics, Springer, New York 1965.
  • 7. W. NOLL, Materially uniform simple bodies with inhomogeneities, Archive for Rational Mechanics and Analysis, 27, 1-32, 1967.
  • 8. M.E. GURTIN, An introduction to continuum mechanics, Academic Press, Orlando 1981.
  • 9. B.E. JOHNSON and A. HOGER, The use of a virtual configuration in formulating constitutive equations for residually stressed elastic materials, Journal of Elasticity, 41, 177-215, 1995.
  • 10. K. TAKAMIZAWA and T. MATSUDA, Kinematics for bodies undergoing residual stress and its applications to the left ventricle, Journal of Applied Mechanics, 57, 321-329, 1990.
  • 11. C.J. CHOUNG and Y.C. FUNG, Residual stress in arteries, [in:] G.W. SCHMID-SCHONBEIN, S.L-Y. Woo and B.W. ZWEIFACH [Eds.], Frontiers in Biomechanics, Springer-Verlag, 117-129, New York 1986.
  • 12. J. STALHAND, A. KL ARE RING and M. KARLSSON, Towards in vivo aorta material identification and stress estimation, Biomechanics and Modeling in Mechanobiology, 2, 169-186, 2004.
  • 13. J. STALHAND and A. KL ARE RING, Aorta in vivo parameter identification using an axial force constraint, Biomechanics and Modeling in Mechanobiology, 3, 191-199, 2005.
  • 14. T. OLSSON, J. STALHAND and A. KLARBRING, Modeling initial strain distribution in soft tissues with application to arteries, Biomechanics and Modeling in Mechanobiology, 5, 27-38, 2006.
  • 15. J.A. BLUME, Compatibility conditions for a left Cauchy-Green strain field, Journal of Elasticity, 21, 271-308, 1989.
  • 16. A. KLARBRING and T. OLSSON, On compatible strain with reference to biomechanics of soft tissue, ZAMM, 85, 6, 440-448, 2005.
  • 17. P. STEINMANN, Views om multiplicative elastoplasticity and the continuum theory of dislocations, International Journal of Engineering Science, 34, 15, 1717-1735, 1996.
  • 18. J.F. GANGHOFFER and B. HAUSSY, Mechanical modeling of growth considering domain variation. Part I: Constitutive framework, International Journal of Solids and Structures, 42, 4311-4337, 2005.
  • 19. B. SONNESON, T. LANNE, E. VERNERSSON and F. HANSEN, Sex difference in the mechanical properties of the abdominal aorta in human beings, J. Vac. Surg., 20, 959-969, 1994.
  • 20. G.A, HOLZAPFEL, T.C. GASSER and R.W. OGDEN, New constitutive framework for arterial wall mechanics and a comparative study of material models. Journal of Elasticity, 61, 1-48, 2000.
  • 21. J.E. MARSDEN and T.J.R. HUGHES, Mathematical Foundations of Elasticity, Prentice-Hall, New Jersey 1983.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT7-0007-0012
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