Anisotropic symmetries of linear elasticity

Applied Mechanics Reviews

Volumn 48, Issue 5, 1995, Pages 247-285

  Cowin, Stephen C ^a   Mehrabadi, Morteza M ^b  

^a CITY COLLEGE OF NEW YORK   (United States)

^b TULANE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; CRYSTAL SYMMETRY; CRYSTALLOGRAPHY; CRYSTALS; MATHEMATICAL TRANSFORMATIONS; TENSORS;

ANISOTROPIC SYMMETRIES; ELASTICITY THEORY; LINEAR ELASTICITY; MIRROR SYMMETRY; N-FOLD INVERSION AXIS; N-FOLD ROTATION AXIS;

ELASTICITY;

EID: 0029297004     PISSN: 00036900     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.3005102     Document Type: Article

References (40)

1. Beatty MF (1966) Kinematics of finite rigid body displacements. Am J Phys 34 949-956.
2. Beatty MF (1977) Vector analysis of rigid rotations, J Appl Mech 44 501 -507.
3. Billings AR (1969) Tensor Properties of Materials-Generalized Compliance and Conductivity. Wiley-Interscience, London, UK
4. Boulanger P and Hayes M (1995) On Young's Modulus for Anisotropic Media. J Appl Mech, in press.
5. Brand L (1947) Vector and Tensor Analysis, Wiley, New York.
6. Coleman BD and Noll W (1964) Material symmetry and thermostatic inequalities in finite elastic deformations. Arch Rat Mech Anal 15 (2) 87111.
7. Cowin SC and Mehrabadi MM (1987) On the identification of material symmetry for anisotropic elastic materials. Quart J Mech Appl Math 40 (4) 451-476.
8. Cowin SC (1989) Identification of Elastic Material Symmetry by Acoustic Measurements. Elastic Wave Propagation. Proc 2nd IUTAM-IUPAP Symp on Elastic Wave Propagation (MF McCarthy and M Hayes, eds) North Holland, Amsterdam, 511-516.
9. Cowin SC and Mehrabadi MM (1989) Identification of the elastic symmetry of bone and other materials, J Biomech 22 (6/7) 503-515.
10. Cowin SC (1994) On the number of distinct elastic constants associated with certain anisotropic elastic symmetries, ZAngew Math Phys, in press
11. Dana JD and Hurlbut CS (1952) Dana 's Textbook of Minerology, Wiley, New York.
12. Fedorov FI (1964) On the Theory of Waves in Crystals, (in Russian) Mosk. Univ Vestn Fiz Ast 6 36-40.
13. Fedorov FI (1968) Theory of Elastic Waves in Crystals, Plenum Press, New York.
14. Finger J (1892) Über die gegenseitigen Beziehungen gewisser in der Mechanik mit Vortheil anwendbaren Flächen zweiter Ordnung nebst Anwendung auf Probleme der Astatik, Sitzgsber. Akad Wiss Wien (Ila) 101 1105-1142.
15. Goldstein H (1950) Classical Mechanics. Addison-Wesley, Reading. MA.
16. Gurtin ME (1972) The Linear Theory of Elasticity, Handbuch der Physik. Flügge S, ed, Springer Verlag, Berlin.
17. Gurtin ME (1981) An Introduction to Continuum Mechanics, Academic Press, New York.
18. Hearmon RFS (1961) An Introduction to Applied Anisotropic Elasticity, Oxford Univ Press, Oxford.
19. Kiral E and Smith GF (1974) On the constitutive relations for anisotropic materials-triclinic, monoclinic, rhombic, tetragonal and hexagonal systems, Ini JEngng Sei, 12 491-490.
20. Lamb H (1929) Higher Mechanics, Cambridge Univ Press, Cambridge, UK.
21. Landolt HH and Bornstein R (1979) Zahlenwerte und Funktionen aus Naturwissenschaften und Technik. Neue Serie (ed, Hellwege K-H, vol III/ll) Springer Verlag, Berlin.
22. Love AEH (1927) Elasticity, Dover, New York.
23. Lekhnitskii SG (1963) Theory of Elasticity of an Anisotropic Elastic Body, Holden Day, San Francisco.
24. Mehrabadi MM and Cowin SC (1990) Eigentensors of linear anisotropic elastic materials, Quart J Mech Appl Math 43(1) 15-41.
25. Mehrabadi MM, Cowin SC, and Jaric J (1994) Six dimensional orthogonal tensor representation of the rotation about an axis in three dimensions. Int J Solids Struct. 32 439-449, 1995.
26. Norris AN (1989) On the Acoustic Determination of the Elastic Moduli of Anisotropic Solids and Acoustic • Conditions for the Existence of Symmetry Planes. Quart J Medi Appi Math 42, 413-426.
27. Nye JF (1957) Physical Properties of Crystals. Oxford Univ Press, Oxford, UK.
28. Pars LA (1979) Analytical Dynamics, Oxbow Press, Woodbridge, CT.
29. Rychlewski J (1984) On Hooke’s law Prikl Matern Mekhan 48 303-314.
30. Senechal M (1990) Crystalline Symmetries, Adam Hilger, Bristol, UK
31. Shubnikov AV and Koptsik VA (1974) Symmetry in Science and Art, Plenum Press, New York.
32. Smith GF and Rivlin RS (1958) The strain energy function for anisotropic elastic materials, Trans Am Math Soc, 88 (1) 175-193.
33. Thomson WK (Lord Kelvin) (1856) Elements of a mathematical theory of elasticity, Phil Trans R Soc 166 481-498.
34. Thomson WK (Lord Kelvin) (1878) Elasticity, Encyclopaedia Britannica, Adam and Charles Black, Edinburgh, UK.
35. Truesdell CA and Toupin RA (1960) The Classical Field Theories, Handbuch der Physik, S Flügge ed. Springer Verlag, Berlin.
36. Truesdell CA (1966) Existence of Longitudinal Waves, J Acoust Soc Am 40 729-730.
37. Truesdell CA (1968) Comment on Longitudinal Waves, J Acoust Soc Am 43 170.
38. Voigt W (1910) Lehrbuch der Kristallphysik, Leipzig.
39. Whittaker ET (1937) Analytical Dynamics, Cambridge Univ Press, Cambridge, UK.
40. Zhong HY and Del Piero G (1991) On the completeness of the crystallographic symmetries in the description of the symmetries of the elastic tensor, J Elast 25 203-246, 1991.