On conservation integrals in micropolar elasticity

Philosophical Magazine

Volumn 83, Issue 11, 2003, Pages 1365-1377

  Lubarda, V A ^a   Markenscoff, X ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DEFORMATION; MATHEMATICAL TRANSFORMATIONS; STRESS ANALYSIS; TENSORS; THEOREM PROVING;

MICROPOLAR ELASTICITY;

ELASTICITY;

EID: 0037943139     PISSN: 14786435     EISSN: None     Source Type: Journal    
DOI: 10.1080/1478643031000072491     Document Type: Article

References (62)

1. AERO, E. L., and KUVSHINSKII, E. V., 1960, Fiz. tverd. Tela, 2, 1399.
2. APARICIO, N. D., 2000, Int. J. Solids Struct., 37, 3873.
3. ATKINSON, C., and LEPPINGTON, F. G., 1974, Int. J. Fracture, 10, 599; 1977, Int. J. Solids Struct., 13, 1103.
4. ATKINSON, C., and LEPPINGTON, F. G., 1974, Int. J. Fracture, 10, 599; 1977, Int. J. Solids Struct., 13, 1103.
5. BRULIN, O., and HSIEH, R. K. T. (editors), 1982, Mechanics of Micropolar Media (World Scientific: Singapore).
6. BUDIANSKY, B., and RICE, J. R., 1973, J. appl. Mech., 40, 201.
7. BUI, H. D. and PROIX, J. M., 1984, C. R. Acad. Sci. Paris, II, 298, 325.
8. COSSERAT, E., and COSSERAT, F., 1909, Thèorie des Corps Dèformables (Paris: Hermann).
9. DAI, T.-A., 1986, Int. J. Solids Struct., 22, 729.
10. DE BORST, R., and VAN DER GIESSEN, E. (editors), 1998, Material Instabilities in Solids (Chichester, West Sussex: Wiley).
11. DHALIWAL, R. S., and SINGH, A., 1987, Thermal Stresses II, edited by R. B. Hetnarski (Amsterdam: Elsevier Science), pp. 269-328.
12. ERINGEN, A. C., 1968, Fracture - An Advanced Treatise, edited by H. Liebowitz (New York: Academic Press), pp. 621-729; 1999, Microcontinuum Field Theories (New York: Springer).
13. ERINGEN, A. C., 1968, Fracture - An Advanced Treatise, edited by H. Liebowitz (New York: Academic Press), pp. 621-729; 1999, Microcontinuum Field Theories (New York: Springer).
14. ERINGEN, A. C., and SUHUBI, E. S., 1964, Int. J. Engng Sci., 2, 189, 389.
15. ESHELBY, J. D., 1951, Phil. Trans. R. Soc. A, 244, 87; 1956, Solid St. Phys., 3, 79; 1970, Inelastic Behavior of Solids, edited by M. F. Kanninen, W. F. Adler, A. R. Rosenfield and R. I. Jaffee (New York: McGraw-Hill), pp. 77-115; 1975, J. Elasticity, 5, 321.
16. ESHELBY, J. D., 1951, Phil. Trans. R. Soc. A, 244, 87; 1956, Solid St. Phys., 3, 79; 1970, Inelastic Behavior of Solids, edited by M. F. Kanninen, W. F. Adler, A. R. Rosenfield and R. I. Jaffee (New York: McGraw-Hill), pp. 77-115; 1975, J. Elasticity, 5, 321.
17. ESHELBY, J. D., 1951, Phil. Trans. R. Soc. A, 244, 87; 1956, Solid St. Phys., 3, 79; 1970, Inelastic Behavior of Solids, edited by M. F. Kanninen, W. F. Adler, A. R. Rosenfield and R. I. Jaffee (New York: McGraw-Hill), pp. 77-115; 1975, J. Elasticity, 5, 321.
18. ESHELBY, J. D., 1951, Phil. Trans. R. Soc. A, 244, 87; 1956, Solid St. Phys., 3, 79; 1970, Inelastic Behavior of Solids, edited by M. F. Kanninen, W. F. Adler, A. R. Rosenfield and R. I. Jaffee (New York: McGraw-Hill), pp. 77-115; 1975, J. Elasticity, 5, 321.
19. FLECK, N. A., and HUTCHINSON, J. W., 1997, Adv. appl. Mech., 33, 295.
20. FLECK, N. A., MULLER, G. M., ASHBY, M. F., and HUTCHINSON, J. W., 1994, Acta metall. mater., 42, 475.
21. FLETCHER, D. C., 1975, Archs ration. Mech. Analysis, 60, 329.
22. FREUND, L. B., 1978, Int. J. Solids Struct., 14, 241.
23. GOLEBIEWSKA-HERRMANN, A., 1981, Int. J. Solids Struct., 17, 1.
24. GRIOLI, G., 1960, Ann. Mat. Pura Appl., Ser. 4, 50, 389.
25. GÜNTHER, W., 1958, Abh. Braunschweigischen Wiss. Ges., 10, 195; 1962, ibid., 14, 53.
26. GÜNTHER, W., 1958, Abh. Braunschweigischen Wiss. Ges., 10, 195; 1962, ibid., 14, 53.
27. HONEIN, T., and HERRMANN, G., 1997, J. Mech. Phys. Solids, 45, 789.
28. HUANG, Y. N., and BATRA, R. C., 1996, J. Elasticity, 2, 275.
29. JARIĆ, J. P., 1979, Theor. appl. Mech., 5, 20; 1986, Int. J. Solids Struct., 22, 767.
30. JARIĆ, J. P., 1979, Theor. appl. Mech., 5, 20; 1986, Int. J. Solids Struct., 22, 767.
31. KALONI, P. N., and ARIMAN, T., 1967, Z. angew. Math. Phys., 18, 136.
32. KOITER, W. T., 1964, Proc., Koninklijke Ned. Akad. Wetenschappen B, 67, 17, 30.
33. KNOWLES, J. K., and STERNBERG, E., 1972, Archs ration. Mech. Analysis, 44, 187.
34. KUBO, S., 1982, Int. J. Fracture, 20, R27.
35. LUBARDA, V. A., 1993, J. appl. Mech., 60, 29.
36. LUBARDA, V. A., and MARKENSCOFF, X., 1999, Proceedings of the Conference on the Integration of Material, Process and Product Design, edited by N. Zabaras, R. Becker, S. Ghosh and L. Lalli (Rotterdam: Balkema), pp. 53-58; 2000, J. Mech. Phys. Solids, 48, 553.
37. LUBARDA, V. A., and MARKENSCOFF, X., 1999, Proceedings of the Conference on the Integration of Material, Process and Product Design, edited by N. Zabaras, R. Becker, S. Ghosh and L. Lalli (Rotterdam: Balkema), pp. 53-58; 2000, J. Mech. Phys. Solids, 48, 553.
38. MAUGIN, G. A., 1990, C. hebd. Séanc. Acad. Sci., Paris, 311, 763.
39. MINDLIN, R. D., 1963, Exp. Mech., 3, 573; 1964, Archs ration. Mech. Analysis, 16, 51.
40. MINDLIN, R. D., 1963, Exp. Mech., 3, 573; 1964, Archs ration. Mech. Analysis, 16, 51.
41. MINDLIN, R. D., and TIERSTEN, H. F., 1962, Archs ration. Mech. Analysis, 11, 415.
42. MUKI, R., and STERNBERG, E., 1965, Z. angew. Math. Phys., 16, 611.
43. NIKITIN, E., and ZUBOV, L. M., 1998, J. Elasticity, 51, 1.
44. NOETHER, E., 1918, Nachr. k. Gess. Wissen. Göttingen, math.-phys. Klasse, 2, 235 (Engl. transl., 1971, Transport Theory statist. Phys., 1, 186).
45. NOETHER, E., 1918, Nachr. k. Gess. Wissen. Göttingen, math.-phys. Klasse, 2, 235 (Engl. transl., 1971, Transport Theory statist. Phys., 1, 186).
46. NOWACKI, W., 1986, Theory of Asymmetrie Elasticity, translated by H. Zorski (Oxford: Pergamon) (Warsawa: Panstwave Wydawnictwo Naulcowe).
47. OLVER, P. J., 1984, Archs ration. Mech. Analysis, 85, 111, 131; 1986, Applications of Lie Groups to Differential Equations (New York: Springer).
48. OLVER, P. J., 1984, Archs ration. Mech. Analysis, 85, 111, 131; 1986, Applications of Lie Groups to Differential Equations (New York: Springer).
49. PUCCI, E., and SACCOMANDI, G., 1990, Int. J. Engng Sci., 28, 557.
50. RICE, J. R., 1968, J. appl. Mech., 35, 379; 1985, Fundamentals of Deformation and Fracture, edited by B. A. Bilby, K. J. Miller and J. R. Willis (Cambridge University Press), pp. 33-56.
51. RICE, J. R., 1968, J. appl. Mech., 35, 379; 1985, Fundamentals of Deformation and Fracture, edited by B. A. Bilby, K. J. Miller and J. R. Willis (Cambridge University Press), pp. 33-56.
52. STOJANOVIĆ, R., 1970, Recent Developments in the Theory of Polar Continua (Berlin: Springer).
53. TOUPIN, R. A., 1962, Archs ration. Mech. Analysis, 11, 385.
54. VALIEV, R. Z., Islamgaliev, R. K., and ALEXANDROV, I. V., 2000, Prog. Mater. Sci., 45, 103.
55. VOIGT, W., 1887, Abh. Ges. Wiss. Göttingen, 34, 3.
56. VUKOBRAT, M. Dj., 1989, Int. J. Engng Sci., 27, 1093.
57. VUKOBRAT, M., and JARIĆ, J., 1981, Theor. appl. Mech., 7, 73.
58. VUKOBRAT, M., and KUZMANOVIĆ, D., 1992, Acta mech., 92, 1.
59. XIA, Z. C., and HUTCHINSON, J. W., 1996, J. Mech. Phys. Solids, 44, 1621.
60. YANG, J. S., and BATRA, R. C., 1995, Engng Fracture Mech., 51, 1041.
61. YAVARI, A., SARKANI, S., and MOVER, E. T., 2002, J. appl. Mech., 69, 45.
62. ZBIB, H., and AIFANTIS, E. C., 1989, Appl. Mech. Rev., 42, S292.