DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories (Ⅱ)-Micromorphic Continuum Theory and Couple Stress Theory[J]. Applied Mathematics and Mechanics, 2003, 24(10): 998-1004.
 Citation: DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories (Ⅱ)-Micromorphic Continuum Theory and Couple Stress Theory[J]. Applied Mathematics and Mechanics, 2003, 24(10): 998-1004.

Renewal of Basic Laws and Principles for Polar Continuum Theories (Ⅱ)-Micromorphic Continuum Theory and Couple Stress Theory

• Rev Recd Date: 2003-05-09
• Publish Date: 2003-10-15
• 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 microplar 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.
•  [1] 戴天民.重建极性连续统理论的基本定律和原理(Ⅰ)——微极连续统[J].应用数学和力学,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 sinple 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. Mechanicsofmicromorphicmaterials[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 JEngng 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-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 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] 戴天民.带有微结构的连续统中新的能量守恒定律和C-D不等式[J].应用数学和力学,2001,22(2):119-126. [16] 戴天民.广义连续统场论中新的功能及功率能率原理[J].应用数学和力学,2001,22(11):1111-1118. [17] A C爱林根,C B卡法达.微极场论[M].戴天民译.南京:江苏科学技术出版社,1982,17-23. [18] 戴天民.不带微结构的连续统中新的能量守恒定律和C-D不等式[J].应用数学和力学,2001,22(2):111-118.

Catalog

通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142