Summary
In the first part of the paper we discuss an equation of balance of generalized moment of momentum proposed earlier; we show that internal forces necessarily play a rôle in it; we put in evidence the formal structure of some theories of polar continua. In the second part we show that most cases of oriented materials studied so far can be interpreted as subcases of a general type, when appropriate kinematical constraints are introduced; this unifying point of view allows a clear classification of subcases. It becomes also possible to obtain, in a standard way, balance equations which are pure, in the sense that they do not involve internal reactions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. D. Mindlin,Micro-structure in linear elasticity, Arch. Rational Mech. Anal.,16 (1964), pp. 51–78.
J. L. Ericksen,Conservation laws for liquid crystals, Trans. Soc. Rheol.,5 (1961), pp. 23–34.
A. C. Eringen,Mechanics of micromorphic continua, in Proc. IUTAM Symp., Freudenstadt and Stuttgart, 1967, pp. 18–35, E. Kröner Ed., Springer (1968).
R. S. Rivlin,Generalized mechanics of continuous media, in Proc. IUTAM Symp., Freudenstadt and Stuttgart, 1967, pp. 1–17, E. Kröner Ed., Springer (1968).
G. Capriz -P. Podio Guidugli,Discrete and continuous bodies with affine structure. Ann. Mat. Pura Appl., (4)111 (1976), pp. 195–217.
R. A. Toupin,Theories of elasticity with couple-stress, Arch. Rational Mech. Anal.,17 (1964), pp. 85–112.
M. E. Gurtin -P. Podio Guidugli,The thermodynamics of constrained materials, Arch. Rational Mech. Anal.,51 (1973), pp. 192–208.
G. Grioli, Elasticità asimmetrica, Ann. Matem. Pura Appl., (4),50 (1960), pp. 387–417.
R. A. Toupin,Elastic materials with couple-stresses, Arch. Rational Mech. Anal.,11 (1962), pp. 385–414.
C. Truesdell - W. Noll,The non-linear field theories of mechanics, Handbuch der Physik, III/3, S. Flügge Ed., Springer (1965).
C. Truesdell - R. A. Toupin,The classical field theories, Handbuch der Physik, III/1, S. Flügge Ed., Springer (1960).
R. Stojanovitch - S. Djuritch,On the measures of strain in the theory of the elastic generalized Cosserat continuum, in Symp. Math. I, INAM, Roma, 1968, pp. 211–228, Oderisi and Academic Press (1969).
M. E. Gurtin - P. Podio Guidugli,The linear theory of constrained elastic materials, (unpublished).
R. D. Mindlin -H. F. Tiersten,Effects of couple-stresses in linear elasticity, Arch. Rational Mech. Anal.,11 (1962), pp. 415–448.
Author information
Authors and Affiliations
Additional information
Entrata in Redazione il 2 agosto 1976.
Rights and permissions
About this article
Cite this article
Capriz, G., Podio Guidugli, P. Formal structure and classification of theories of oriented materials. Annali di Matematica 115, 17–39 (1977). https://doi.org/10.1007/BF02414710
Issue Date:
DOI: https://doi.org/10.1007/BF02414710