A Statistical Mechanical Formulation of Continuum Fields and Balance Relations for Granular and Other Materials with Internal Degrees of Freedom
In the last fourty years or so, it has become increasingly apparent that the macroscopic behaviour of many materials may under various circumstances be significantly influenced by their fundamentally “heterogeneous” or “structured” nature. A particular class of such materials includes those whose “structure” is characterized by the ability to evolve or “move” relative to the material as a whole, i.e., by additional, internal degrees of freedom. Prominent examples of such materials include liquid crystals, polycrystals with texture, materials undergoing phase transitions, mixtures, as well as granular and porous materials, the subjects of this CISM course.
KeywordsGranular Material Mass Point Momentum Balance Balance Relation Continuum Field
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- Cosserat, E. F., Sur la mecanique générale, C. R. Acad. Paris 145, 1139–1142, 1907.Google Scholar
- Eringen, A. E., and Kadafar, C. B., Polar field theories, in Continuum Physics IV, Academic Press, 1976.Google Scholar
- Capriz, G., Materials with Microstructure, Springer Tracts in Natural Philosophy 35, 1989.Google Scholar
- Svendsen, B., A fibre bundle model for structured continua, ZAMM 76, S209 - S210, 1996.Google Scholar
- Svendsen, B., A fibre bundle model for continua with internal degrees of freedom, in preparation, 1999.Google Scholar
- Ahmadi, G., A generalized continuum theory for flow of granular materials, in Advances in the mechanics and the flow of granular materials, M. Shahinpoor, ed., pp. 497–527, II Gulf Publishing, 1983.Google Scholar
- Pitteri, M., On the objectivity of certain gross fields constructed within classical statistical mechanics, Proceedings of the ISIMM Symposium on Kinetic Theory and Extended Thermodynamics, I. Müller and T. Ruggeri, editors, pp. 291–305, 1987.Google Scholar
- Müller, I., and Ruggeri, T., Extended Thermodynamics, Springer Tracts in Natural Philosophy 37, 1993.Google Scholar
- Truesdell, C., A First Course in Rational Mechanics, 2nd edition, Academic Press, 1993.Google Scholar
- Landau, L., and Lifshitz, E., Théorie du champ, MIR, 1966.Google Scholar