Definitions of Continuum Mechanics
The purpose of the present chapter is to provide a systematic introduction of the basic concepts and definitions of the tensors of strains and stress. The presentation begins with a section, in which we briefly present the elements of tensor analysis. Tensor analysis enables one to present in a simple and elegant form the fundamantals of continuum mechanics, and it is used systematically subsequently throughout the book. We then introduce the definition of the tensors of strains and stress, which characterize a continuum, in a reference frame and in an actual frame without any assumptions on the smallness of strains.
KeywordsReference Frame Stress Tensor Basis Vector Strain Tensor Vortex Line
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- 2.Sokolnikov, I.Tensor Analysis (Theory and Applications in Geometry and in Continuum Mechanics(in Russian), Nauka, Moscow, 1971.Google Scholar
- 4.Rashevskii, P.K.The Riemann Geometry and Tensor Analysis(in Russian), Nauka, Moscow, 1967.Google Scholar
- 5.Ilyushin, A.A.Continuum Mechanics(in Russian), Moscow State University, Moscow, 1990.Google Scholar
- 6.Germain, P.Cours de Mécanique des Milieux Continus. Tome L Théorie GénéraleMasson et C1eÉditeurs, Paris, 1973.Google Scholar
- 7.Smirnov, V.I.A Course of Higher Mathematics(in Russian), Vol. 3, Pt. 1, Nauka, Moscow, 1967.Google Scholar
- 8.Godunov, S.K.Elements of Continuum Mechanics(in Russian), Nauka, Moscow, 1978.Google Scholar
- 9.Mase, G.E.Theory and Problems of Continuum MechanicsMcGraw-Hill Book Company, New York, 1970.Google Scholar
- 11.Truesdell, C. and Noll,W., The non-linear field theories of mechanics, inEncyclopedia of Physics III/3Springer-Verlag, Berlin, 1965.Google Scholar