RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CON-TINUUM THEORIES (Ⅱ)—MICROMORPHIC CONTINUUM THEORY AND COUPLE STRESS THEORY

Abstract

Abstract: The purpose is to reestablish the balance laws of momentum, angular momentum and energy and to derive the corresponding local and nonlocal balance equations for micromorphic continuum mechanics and couple stress theory. The desired results for micromorphic continuum mechanics and couple stress theory are naturally obtained via direct transitions and reductions from the coupled conservation law of energy for micropolar continuum theory, respectively. The basic balance laws and equations for micromorphic continuum mechanics and couple stress theory are constituted by combining these results derived here and the traditional conservation laws and equations of mass and microinertia and the entropy inequality. The incomplete degrees of the former related continuum theories are clarified. Finally, some special cases are conveniently derived.

2010 MSC Number:

DAI Tian-min. RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CON-TINUUM THEORIES (Ⅱ)—MICROMORPHIC CONTINUUM THEORY AND COUPLE STRESS THEORY. Applied Mathematics and Mechanics (English Edition), 2003, 24(10): 1126-1133.

TrendMD

References

[1] DAI Tian-min . Renewal of basic laws and principles for polar continuum theories (Ⅰ)Micropolar continua[J]. Applied Mathematics and Mechanics (English Edition) , 2003,24(10):991-997.
[2] DAI Tian-min. On basic laws and principles for continuum field theories[A]. In: CHIEN Wei-zang Ed. Proceedings of the 4 th International Conference on Nonlinear Mechanics[C]. Shanghai:Shanghai University Press ,2002,29-41.
[3] Eringen A C, Suhubi E R. Nonlinear theory of simple microelastic solids-Ⅰ[J].Int J Engng Sci,1964,2:189-203.
[4] Eringen A C, Sububi E R. Nonlinear theory of simple microelastic solids-Ⅱ[J]. Int J Engng Sci,1964,2:389-404.
[5] Eringen A C. Mechanics of micromorphic materials[A]. In:Gortler H Ed. Proc 11th Int Congr Appl Mech[C]. Berlin: Springer-Verlag, 1966,131-138.
[6] Eringen A C. Microcontinuum Field Theories[M]. New York: Springer-Verlag, 1999.
[7] Soos E. Uniqueness theorems for homogeneous, isotropic, simple elastic and thermoelastic materials having a microstructure[J]. Int J Engng Sci, 1969,7:257-268.
[8] Eringen A C. Balance laws of micromorphic continua revisited[J].Int J Engng Sci, 1992,30(6):805-810.
[9] Mindlin R D, Tiersten H E. Effects of couple stresses in linear elasticity[J]. Arch Rat Mech Anal,1962,11:415-448.
[10] Toupin R A. Theories of elasticity with couple stresses[J]. Arch Rat Mech Anal, 1964,17: 85-112.
[11] Eringen A C. Linear theory of micropolar elasticity[J]. Journal of Mathematics and Mechanics,1996,15(6) :909-923.
[12] Eringen A C. Theory of micropolar fluids[J]. Journal of Mathematics and Mechanics, 1966,15(1):1-18.
[13] DAI Tian-nin. 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 Mechanics[C]. Shanghai: Shanghai University Press, 2002,206-209.
[14] Stojanovic R. On the principle of virtual work in the theory of oriented elastic media[J]. Z Angew Math Mech, 1973,53:T79-T82.
[15] DAI Tian-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.
[16] DAI Tian-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.
[17] Eringen A C. Continuumphysics[M]. Vol Ⅳ,New York:Academic Press,1976.
[18] DAI Tian-min. New conservation laws of energy and C-D inequalities in continua without microstructure[J]. Applied Mathematics and Mechanics (English Edition), 2001,22(2): 127-134.