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• W2891348992 abstract "The fundamental assumption of continuous systems in classical physics is the conjecture that the physical space is densely filled with matter. This hypothesis is applied to single and multiphase continua as well as mixtures consisting of a finite number of constituents. Three classes of mixtures are defined: In the most complex case, class III, balance laws of mass, momenta, energy are formulated for each constituent, which possess their own mass, momenta, energy (and, therefore temperature). In class II mixtures, all components possess the same temperature, but the constituents possess their individual momenta and masses. Finally, in class I mixtures, the constituents do have the same temperature and common velocity—there is no slip between them—but each component has its own mass. The modern theories of continuous bodies differentiate between Boltzmann and polar continua. In the former, the balance of angular momentum is applied as moment of momentum. In such continua, the Cauchy stress tensor of the mixture is symmetric. In the latter, angular momentum is expressed as moment of momentum plus spin with all its peculiar consequences. The balance laws of mass, momenta, and energy are formulated for the constituents for both cases in global and local forms in detail. The results for Boltzmann continua are well known. However, for polar media, different sub-theories emerge, depending upon how the specific spin is parameterized. In Cosserat continua, the specific spin is motivated by rigid body dynamics as the “product of the tensor moment of inertia times angular velocity”, see (21.32). If the micromotion is a pure rotation of the particles, i.e., the tensors of moments of inertia of the constituents do not change under motion, the mixture is called micro-polar, else micro-morphic. The chapter is closed by formulating the physical balance laws of the mixture as a whole and stating the relations of the physical variables of the mixture in terms of those of the constituents." @default.
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• W2891348992 date "2018-01-01" @default.
• W2891348992 modified "2023-10-03" @default.
• W2891348992 title "Balance Laws of Continuous System" @default.
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• W2891348992 doi "https://doi.org/10.1007/978-3-319-77745-0_21" @default.
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