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Locally homogeneous configurations of uniform elastic bodies. (English) Zbl 0785.73020
Summary: This paper deals with one of the fundamental problems of the mathematical theory of inhomogeneities in simple elastic material bodies, namely the availability of local homogeneous configurations. Utilizing the original differential geometric approach of W. Noll [Arch. Ration. Mech. Anal. 27, 1-32 (1967; Zbl 0168.457)] and C.-C. Wang [Arch. Ration. Mech. Anal. 27, 33-94 (1967; Zbl 0187.488)] adopted for our particular needs and restricted to the hyperelastic case, we develop a system of partial differential equations for the locally homogeneous material configurations. The existence and the form of solutions of this system are discussed by means of examples.

74B20 Nonlinear elasticity
35Q72 Other PDE from mechanics (MSC2000)
Full Text: DOI
[1] Noll, W., Arch. rational mech. anal., 27, 1-32, (1967)
[2] Wang, C.-C., Arch. rational mech. anal., 27, 33-94, (1967)
[3] Kondo, K., Proc. 2nd Japan congr. appl. mechs., (1953), Science Council of Japan
[4] Bilby, B.A., Continuous distribution of dislocations, (), 329-398
[5] Kröner, E., Arch. rational mech. anal., 4, 273-334, (1960)
[6] Elżanowski, M.; Epstein, M., International J. non-linear mechanics, 27, 4, 635-638, (1992)
[7] Elżanowski, M.; Epstein, M., Arch. rational mech. anal., 88, 347-357, (1985)
[8] Epstein, M.; Elżanowski, M.; Śniatycki, J., Lecture notes in mathematics, (), 300-310, No. 1139
[9] Elżanowski, M.; Epstein, M.; Śniatycki, J., J. elasticity, 23, 2-3, 167-180, (1990)
[10] Lardner, R.W., Mathematical theory of dislocations and fracture, (1974), University of Toronto Press Toronto · Zbl 0301.73036
[11] Epstein, M.; Maugin, G.A., C. R. acad. sci. Paris, II, 675-678, (1990), Série
[12] Kumosa, M., J. appl. physics, (1992), (to appear).
[13] Wang, C.-C.; Truesdell, C., Introduction to rational elasticity, (1973), Nordhoff International Publishing Leyden · Zbl 0308.73001
[14] Cohen, H.; Epstein, M., Acta mechanica, 47, 207-220, (1983)
[15] Poor, W.A., Differential geometric structures, (1981), McGraw-Hill Book Company New York · Zbl 0493.53027
[16] Okubo, T., Differential geometry, (1987), Marcel Dekker Inc., New York · Zbl 0139.39801
[17] Rawnsley, J.H., Communications of the Dublin institute of advanced studies, 25, (1978), Series A · Zbl 0372.58008
[18] Warner, G., Harmonic analysis on semi-simple Lie groups, Vol. I, (1972), Springer-Verlag New York · Zbl 0265.22020
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