Renewal of basic laws and principles for polar continuum theories. I: Micropolar continua. (English) Zbl 1145.74308
Summary: Based on the restudies of existing polar continuum theories rather complete systems of basic balance laws and equations for micropolar continuum theory are presented. In these new systems not only the additional angular momentum, surface moment and body moment produced by the linear momentum, surface force and body force, respectively, but also the additional velocity produced by the angular velocity are considered. The new coupled balance laws of linear momentum, angular momentum and energy are reestablished. From them the new coupled local and nonlocal balance equations are naturally derived. Via contrast it can be clearly seen that the new results are believed to be rather general and complete.
References:
| [1] | DAI Tain-min. New conservation laws of energy and C-D inequalities in continua with microstructure [J].Applied Mathematics and Mechanics (English Edition), 2001,22(2):135–143. · Zbl 1046.74003 · doi:10.1007/BF02437878 |
| [2] | DAI Tain-min. New principles of work and energy as well as power and energy rate for continuum field theories [J].Applied Mathematics and Mechanics (English Edition), 2001,22(11):1231–1239. · Zbl 1064.74012 · doi:10.1007/BF02437846 |
| [3] | DAI Tian-min. New laws and principles for continuum mechanics-Part I: Balance laws and equations [A]. In: CHIEN Wei-zang Ed.Proceedings of the 4th International Conference on Nonlinear Mechniacs [C]. Shanghai: Shanghai University Press, 2002, 206–209. |
| [4] | DAI Tian-min. On basic laws and principles for continuum field theories[A]. In: CHIEN Wei-zang Ed.Proceedings of the 4th International Conference on Nonlinear Mechniacs[C]. Shanghai: Shanghai University Press, 2002, 29–41. |
| [5] | Eringen A C, Kafadar C B.Continuum Physics. Vol II [M]. New York and London: Academic Press, 1975. |
| [6] | Eringen A C.Microcontinuum Field Theories[M]. New York: Springer-Verlag, 1999. · Zbl 0953.74002 |
| [7] | Stojanovic R. On the principle of virtual work in the theory of oriented elastic media[J].Z Angew Math Mech, 1973,53:T79-T82. · Zbl 0265.73006 |
| [8] | Wang J, Dhaliwa R S. On some theorems in the nonlocal theory of micropolar elasticity[J].Int J Solids Structures, 1993,30(10):1331–1338. · Zbl 0773.73005 · doi:10.1016/0020-7683(93)90215-S |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
