Bounds on the effective anisotropic elastic constants

Journal of Elasticity

Volumn 57, Issue 1, 1999, Pages 1-24

  Cowin, S C ^a,c   Yang, G ^a   Mehrabadi, M M ^b  

^a CITY UNIVERSITY OF NEW YORK   (United States)

^b Tulane University   (United States)

^c Apartment 4F ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; EIGENVALUES AND EIGENFUNCTIONS; ELASTIC MODULI; MATRIX ALGEBRA; STRAIN; STRESSES; TENSORS;

BOUNDS; COMPLIANCE TENSOR; ELASTICITY TENSOR; TRICLINIC SYMMETRY COEFFICIENTS;

ELASTICITY;

EID: 0033292494     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007669330552     Document Type: Article

References (27)

1. B. Balendran and S. Nemat-Nasser, Bounds on the elastic moduli of composites. J. Mech. Phys. Solids 43 (1995) 1825-1853.
2. S.C. Cowin, The mechanical properties of cortical bone. In: S.C. Cowin (ed.), Bone Mechanics. CRC Press, Boca Raton, FL (1989) pp. 97-127.
3. S.C. Cowin, Properties of the anisotropic elasticity tensor. Quart. J. Mech. Appl. Math. 42 (1989) 249-267.
4. S.C. Cowin and M.M. Mehrabadi, On the structure of the linear anisotropic elastic symmetries. J. Mech. Phys. Solids 40 (1992) 1459-1472.
5. S.C. Cowin and M.M. Mehrabadi, Anisotropic symmetries of linear elasticity. Appl. Mech. Rev. 48 (1995) 247-285.
6. S.C. Cowin, M.M. Mehrabadi and A.M. Sadegh, Kelvin formulation of the anisotropic Hooke's law. In: J.J. Wu, T.C.T. Ting and D.M. Barnett (eds.), Modern Theory of Anisotropic Elasticity and Applications. SIAM, Philadelphia, PA (1991) pp. 340-356.
7. S.C. Cowin and A.M. Sadegh, Non-interacting modes for stress, strain and energy in hard tissue. J. Biomechanics 24 (1991) 859-867.
8. F.I. Fedorov, Theory of Elastic Waves in Crystals. New York, Plenum (1968).
9. I.M. Gelfand, Lectures on Linear Algebra. Dover, New York (1961).
10. M.E. Gurtin, The linear theory of elasticity. In: S. Flugge (ed.), Handbuch der Physik. Springer, Berlin (1972) pp. 1-296.
11. R.F.S. Hearmon, The elastic constants of anisotropic media-II. Phil. Mag. Suppl. 5 (1956) 323-382.
12. R. Hill, The elastic behaviour of crystalline aggregate. Proc. Phys. Soc. A 65 (1952) 349-354.
13. R. Hill, Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids 11 (1963) 357-372.
14. R. James, R. Lipton and A. Lutoborski, Laminar elastic composites with crystallographic symmetry. SIAM J. Appl. Math. 50 (1990) 683-702.
15. F.F.P. Kollmann and W.A. Côté Jr., Principal of Wood Science and Technology, I Solid Wood. Springer, Berlin (1968).
16. R. Lipton, On the behavior of elastic composites with transverse isotropic symmetry. J. Mech. Phys. Solids 39 (1991) 663-681.
17. R. Lipton, Optimal bounds on effective elastic tensors for orthotropic composites. Proc. Roy. Soc. London A 444 (1994) 399-410.
18. R. Lipton, Composites with symmetry and their extremal properties. Internat. J. Solids Struct. 31 (1994) 3407-3417.
19. M.M. Mehrabadi and S.C. Cowin, Eigentensors of linear anisotropic elastic materials. Quart. J. Mech. Appl. Math. 43 (1990) 15-41.
20. L. Mirsky, An Introduction to Linear Algebra. Dover, New York (1990).
21. S. Nemat-Nasser and M. Hori, Micromechanics: Overall Properties of Heterogeneous Materials. North-Holland, Amsterdam (1993).
22. A. Reuss, Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle. ZAMM 9 (1929) 49-58.
23. J. Rychlewski, On Hooke's law. Prikl. Matem. Mekhan. 48 (1984) 303-314.
24. G. Strang, Linear Algebra and Its Applications, 2nd edn. Harcourt-Brace-Jovanovich, Boston (1980).
25. W.K. Thomson (Lord Kelvin), Elements of a mathematical theory of elasticity. Phil. Trans. Roy. Soc. 166 (1856) 481-498.
26. W.K. Thomson (Lord Kelvin), Elasticity. In: Encyclopaedia Britannica. Adam and Charles Black, Edinburgh (1878).
27. W. Voigt, Lehrbuch der Kristallphysik. Teubner, Leipzig (1928).