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References
J. B. Alblas [1976], “A note on the physical foundation of the theory of multipolestresses”, Archives of Mechanics 28, 279–298.
A. Bressan [1962], “Metodo di assiomatizzazione in senso stretto della meccanica classica. Applicazione di esso ad alcuni problemi di assiomatizzazione non ancora completamente risolti”, Rendiconti Seminario Matematico Università di Padova 32, 55–212.
G. F. Capriz [1984], “Continui con microstruttura”, Bollettino U.M.I. (6) 3 A, 181–195.
G. F. Capriz [1985], “Continua with latent microstructure”, Archive for Rational Mechanics and Analysis 90, 43–56.
G. F. Capriz [1988], Continui con microstruttura, ETS Editrice, Pisa.
G. F. Capriz [1989], Continua with microstructure, Springer-Verlag, New York, etc.
G. F. Capriz & P. Podio-Guidugli [1976], “Discrete and continuous bodies with affine structure”, Annali di Matematica Pura e Appl., (IV) 111, 195–211.
G. F. Capriz & P. Podio-Guidugli [1981], “Materials with finite-dimensional structure”, Mechanics of Structured Media, A. P. S. Selvadurai, Ed., Proc. of the Int. Symposium on the Mechanical behavior of Structured Media, Ottawa, Elsevier Publishing Co., Amsterdam.
G. F. Capriz & P. Podio-Guidugli [1983], “Structured continua from a lagrangian point of view”, Annali di Matematica Pura e Appl. (IV) 135, 1–25.
G. F. Capriz, P. Podio-Guidugli & W. Williams [1982], “On balance equations for materials with affine structure”, Meccanica 17, 80–84.
C. F. Curtiss, R. B. Byrd & O. Hassager [1976], “Kinetic theory and rheology of macromolecular solutions”, Advances in Chemical Physics 35, 31–117.
J. S. Dahler & L. E. Scriven [1963], “Theory of structured continua. I”, Proceedings of the Royal Society of London A 275, 504–527.
A. C. Eringen [1966], “Mechanics of micromorphic materials”, pp. 131–138 of the Proceedings of the XI International Congress of Applied Mechanics, Springer-Verlag, Berlin.
A. C. Eringen [1967], “Theory of micropolar continua”, pp. 23–40 of the Proceedings of the IX Midwestern Mechanics Conference, Wiley, New York.
J. D. Goddard [1986], “Microstructural origins of continuum stress fields — A brief history and some unresolved issues”, Recent developments in structured continua (D. De Kee & P. N. Kaloni Ed.), Pitman Research Notes in Mathematics Series, Longman Scientific & Technical, Harlow.
A. E. Green & R. S. Rivlin [1964a], “Multipolar continuum mechanics”, Archive for Rational Mechanics and Analysis 17, 113–147.
A. M. Green & R. S. Rivlin [1964b], “On Cauchy's equations of motion”, Journal of Applied Mathematics and Physics (ZAMP) 15, 290–292.
J. H. Irving & J. G. Kirkwood [1960], “The statistical mechanical theory of transport processes, IV: the equations of hydrodynamics”, Journal of Chemical Physics 18, 817–829.
J. E. Marsden & T. J. R. Hughes [1983], Mathematical foundations of elasticity, Prentice-Hall, Englewood Cliffs, NJ.
A. I. Murdoch [1985], “A corpuscular approach to continuum mechanics: basic considerations”, Archive for Rational Mechanics and Analysis 88, 291–321.
A. I. Murdoch [1987], “On the relationship between balance relations for generalised continua and molecular behaviour”, International Journal of Engineering Science 25, 883–914.
W. Noll [1955], “Die Herleitung der Grundgleichungen der Thermomechanik der Kontinua aus der Statistischen Mechanik”, Journal of Rational Mechanics and Analysis 4, 627–646.
W. Noll [1963], “La mécanique classique, basée sur un axiome d'objectivité”, pp. 47–56 of La Méthode Axiomatique dans les Mécaniques Classiques et Modernes (Colloque International à Paris, 1959), Paris, Gauthier-Villars, reprinted in W. Noll, The foundations of Mechanics and Thermodynamics, Springer-Verlag, New York, etc., 1974.
M. Pitteri [1986], “Continuum equations of balance in classical statistical mechanics”, Archive for Rational Mechanics and Analysis 94, 291–305, and Corrigendum, Archive for Rational Mechanics and Analysis 100 (1988), 315–316.
M. Pitteri [1987], “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 & T. Ruggeri Eds.), Pitagora, Bologna.
M. Pitteri [1988], “On the equations of balance for mixtures constructed by means of classical statistical mechanics”, Meccanica 23, 3–10.
C. Truesdell [1977], A first course in rational continuum mechanics, Vol. 1, Academic Press, New York, etc.
C. Truesdell & R. A. Toupin [1960], “The classical field theories”, Handbuch der Physik III/1, S. Flügge ed., Springer-Verlag, Berlin, Heidelberg and New York.
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Dedicated to Bernard Coleman on the occasion of his 60th birthday
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Pitteri, M. On a statistical-kinetic model for generalized continua. Arch. Rational Mech. Anal. 111, 99–120 (1990). https://doi.org/10.1007/BF00375403
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DOI: https://doi.org/10.1007/BF00375403