With the aid of a referential description of the kinematics of a deformable continuum, explicit definitions are given for the materiality of vector fields and vector-lines, and necessary and sufficient conditions for materiality are derived. A number of examples are included.
Get full access to this article
View all access options for this article.
References
1.
[1] Truesdell, C. and Toupin, R. A.: The classical field theories, in Handbuch der Physik, Vol. III/1, pp. 226-858, C. Fligge, Springer, Berlin, 1960.
2.
[2] Prim, R. and Truesdell, C.: A derivation of Zorawski's criterion for permanent vector-lines. Proc. Amer Math. Soc., 1, 32-34 (1950).
3.
[3] Truesdell, C.: A First Course in Rational Continuum Mechanics, 2nd ed., Academic Press, San Diego, 1991.
4.
[4] Truesdell, C.: The Kinematics of Vorticity, Indiana University Press, Bloomington, 1954.
5.
[5] Casey, J. and Naghdi, P. M.: On the Lagrangian description of vorticity. Arch. Rational Mech. Anal., 115, 1-14 (1991).
