On the deformation of transversely isotropic porous elastic circular cylinder

• Autorzy: Ghiba I.-D.
• Języki publikacji: EN

Abstrakty

EN

In this paper we study the deformation of right circular cylinders filled by a linear transversely isotropic porous material. We construct a solution of the relaxed Saint-Venant's problem using the results established for anisotropic porous cylinders. Firstly, we decompose the relaxed Saint-Venant's problem into two problems: extension-bending-torsion problem and flexure problem. Then, for each of them we give the exact expressions of the solutions.

Słowa kluczowe

EN

transversely isotropic porous materials; relaxed Saint-Venant's problem; circular cylinder

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2009
• Tom: Vol. 61, nr 5
• Strony: 407--421
• Opis fizyczny: Bibliogr. 34 poz.

Twórcy

autor

Ghiba I.-D.

• "Octav Mayer" Mathematics Institute Romanian Academy of Science, Iaşi Branch Bd. Carol I, nr. 8, 700506-Iaşi, Romania,

Bibliografia

• 1. S.C. COWIN, J.W. NUNZIATO, Linear elastic materials with voids, J. Elasticity, 13, 125-147, 1983.
• 2. M.A. GOODMAN, S.C. COWIN, A continuum theory for granular materials, Arch. Rational Mech. Anal., 44, 249-266, 1972.
• 3. J.W. NUNZIATO, S.C. COWIN, A nonlinear theory of elastic materials with voids, Arch. Rational Mech. Anal., 72, 175-201, 1979.
• 4. D. IE§AN, A theory of thermoelastic materials with voids, Acta Mech., 60, 67-89, 1986.
• 5. D. IE§AN, M. CIARLETTA, Non-classical elastic solids, Longman Scientific and Technical, Harlow, Essex, UK and John Wiley&Sons, Inc., New York 1993.
• 6. D. IE§AN, Thermoelastic m,odels of continua, Kluwer Academic Publishers, Boston/Dordrecht/London 2004.
• 7. R.A. TOUPIN, Saint-VenanVs principle, Arch. Rational Mech. Anal., 18, 83-96, 1965.
• 8. R.C. BATRA, J.S. YANG, Saint-VenanVs principle for linear elastic porous materials, J. Elasticity, 39, 265-271, 1995.
• 9. S.G. LEKHNITSKI, Theory of elasticity of an anisotropic body, Mir Publishers, Moscow 1981.
• 10. H. DING, W. CHEN, L. ZHANG, Elasticity of transversely isotropic materials, Series: Solid mechanics and its applications, 126, Springer-Verlag, New York 2006.
• 11. R.E. GOODMAN, Introduction to rock mechanics, second edition, John Wiley & Sons, New York, 1988.
• 12. J.J. LIAO, T.B. Hu, C.W. CHANG, Determination of dynamic elastic constants of transversely isotropic rocks using a single cylindrical specimen, International Journal of Rock Mechanics And Mining Sciences, 34, 1045-1054, 1997.
• 13. D.C. WYLLIE, Foundations on rock: second edition, Taylor h Francis, 1999.
• 14. Y.M TIEN, P.F. TSAO, Preparation and mechanical proprieties of artificial transversely isotropic rock, International Journal of Rock Mechanics and Mining Sciences, 37, 1001-1012, 2000.
• 15. G.E. EXADAKTYLOS, On the constraints and relations of elastic constants of transversely isotropic geomaterials, International Journal of Rock Mechanics and Mining Sciences, 38, 941-956, 2001.
• 16. J.C. JAEGER, N.G.W. COOK, R.W. ZIMMERMAN, Fundamentals of rock mechanics, Edition: 4, Blackwell Publishing, 2007.
• 17. G,E. KEMPSON, Mechanical proprieties of articular cartilage, [in:] Adult Cartilage, M.A.R. FREEMAN [Ed.], 2nd edition, pp. 333-414, Pitman Medical, Kent 1979.
• 18. J.D. HUMPHREY, Cardiovascular solid mechanics, Springer-Verlag, New York 2002.
• 19. X.N. DONG, X.E. GUO, The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity, Journal of Biomechanics, 37, 1281-1287, 2004.
• 20. T. GOLDMANN, H. SEINER, M. LANDA, Experimental determination of elastic coefficients of dry bovine bone, Bulletin of Applied Mechanics, 1, 262-275, 2005.
• 21. C. CHUI, E. KOBAYASHI, X. CHEN, T. HISADA, I. SAKUMA, Transversely isotropic properties of porcine liver tissue: experiments and constitutive modelling, Medical & Biological engineering & Computing, 45, 99-106, 2007.
• 22. A.J.M. SPENCER, Continuum theory of the mechanics of fiber-reinforced composites, Springer-Verlag, New York 1992.
• 23. A.R. BUNSELL, J. RENARD, Fundamentals of fibre reinforced composite materials, CRC. Series: Series in Material Science and Engineering 13, CRC Press Taylor & Francis Group, 2005.
• 24. I.D. GHIBA, Semi-inverse solution for Saint-Venant's problem in the theory of porous elastic materials, European Journal of Mechanics, 27, 1060-1074, 2008.
• 25. D. IE§AN, Saint-Venant's problem, Lecture Notes in Mathematics, Springer-Verlag, Berlin-Heidelberg-New York-London-Paris-Tokyo 1987.
• 26. D. IE§AN, Classical a,nd generalized models of elastic rods, CRC. Series: Modern Mechanics and Mathematics, CRC Press Taylor & Francis Group, Boca Raton/London/New York 2009.
• 27. F. DELLTSOLA, R.C. BATRA, Saint-Venant's problem for porous linear elastic materials, J. Elasticity, 47, 73-81, 1997.
• 28. S. CHIRITA, Saint-Venant's problem and semi-inverse solutions in linear viscoelasticity, Acta Mechanica, 94, 221-232, 1992.
• 29. D. IE§AN, L. NAPPA, Extension and bending of microstretch elastic circular cylinders, Int. J. Engng. Sci., 33, 1139-1151, 1995.
• 30. S. DE CICCO, L. NAPPA, Torsion and flexure of microstretch elastic circular cylindes, Int. J. Engng. Sci., 35, 573-583, 1997.
• 31. A. SCALIA, Extension, bending and torsion of anisotropic microstretch elastic cylinders, Mathematics and Mechanics of Solids, 5, 31-40, 2000.
• 32. D. IE§AN, A. SCALIA, On the deformation of functionally graded porous elastic cylinder, J. Elasticity, 87, 147-159, 2007.
• 33. D. IEŞAN, Thermal effects in orthotropic porous elastic beams, Z. Angew. Math. Phys., 60,138-153, 2009.
• 34. A. BONA, I. BUCATARU, M.A. SLAWINSKI, Coordinate-free characterization of the symmetry classes of elasticity tensors, J. Elasticity, 87, 109-132, 2007.