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

DAI Tian-min

Volume 24 Issue 10

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 2003 > 24(10): 998-1004

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:

PDF( 293 KB)

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

DAI Tian-min

Department of Mathematics & Center for the Application of Mathematics, Liaoning University, Shenyang 110036, P.R.China

Received Date: 2002-04-11
Rev Recd Date: 2003-05-09
Publish Date: 2003-10-15

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 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.
- micromorphic continuum,
- couple stress theory,
- coupled,
- basic balance law,
- balance equatio

FullText(HTML)

References(18)

References

[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.

Relative Articles

[1]	ZHANG Manzhe, GU Shuitao, FENG Zhiqiang. Bidirectional Evolutionary Topology Optimization for Stress Minimization Based on the Modified Couple Stress Elasticity[J]. Applied Mathematics and Mechanics, 2025, 46(1): 12-28. doi: 10.21656/1000-0887.450038
[2]	LÜ Xin, KE Liaoliang, SU Jie. An Axisymmetric Contact Problem of Piezoelectric Materials Based on the Couple Stress Theory[J]. Applied Mathematics and Mechanics, 2024, 45(10): 1268-1278. doi: 10.21656/1000-0887.450190
[3]	XUE Jianghong, HE Zanhang, XIA Fei, LI Zerong, JIN Fusong, YANG Peng. Size-Dependent Effects of Micro-Nano Mindlin Plates Based on the Couple Stress Theory[J]. Applied Mathematics and Mechanics, 2022, 43(7): 740-751. doi: 10.21656/1000-0887.420171
[4]	ZHOU Bo, ZHENG Xueyao, KANG Zetian, XUE Shifeng. A Timoshenko Micro-Beam Model and Its Size Effects Based on the Modified Couple Stress Theory[J]. Applied Mathematics and Mechanics, 2019, 40(12): 1321-1334. doi: 10.21656/1000-0887.400056
[5]	GUO Yong, XIE Jianhua. Research on the Flutter of Micro-Scale Cantilever Pipes——A Finite-Dimensional Analysis[J]. Applied Mathematics and Mechanics, 2018, 39(2): 199-214. doi: 10.21656/1000-0887.370400
[6]	DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅺ)——Consistency Problems[J]. Applied Mathematics and Mechanics, 2007, 28(2): 147-155.
[7]	DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅹ)—Master Balance Law[J]. Applied Mathematics and Mechanics, 2006, 27(2): 151-158.
[8]	DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories (Ⅸ)-Thermomechanics[J]. Applied Mathematics and Mechanics, 2005, 26(6): 653-658.
[9]	DAI Tian-min. Renewal of Basic Laws and Principlesfor Polar Continuum Theories (Ⅷ)——Principle of Total Work and Energy[J]. Applied Mathematics and Mechanics, 2005, 26(3): 287-292.
[10]	DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅲ)-Noether’s Theorem[J]. Applied Mathematics and Mechanics, 2003, 24(10): 1005-1011.
[11]	DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅳ)-Surface Couservation Laws[J]. Applied Mathematics and Mechanics, 2003, 24(11): 1101-1107.
[12]	DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅴ)-Polar Thermomechanical Continua[J]. Applied Mathematics and Mechanics, 2003, 24(11): 1108-1113.
[13]	DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅶ)——Incremental Rate Type[J]. Applied Mathematics and Mechanics, 2003, 24(12): 1217-1222.
[14]	DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅵ)——Conservation Laws of Mass and Inertia[J]. Applied Mathematics and Mechanics, 2003, 24(12): 1211-1216.
[15]	DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅰ)-Micropolar Continua[J]. Applied Mathematics and Mechanics, 2003, 24(10): 991-997.
[16]	DAI Tian-min. Restudy of Coupled Field Theories for Micropolar Continua (Ⅱ)──Thermopiezoelectricity and Magnetothermoelasticity[J]. Applied Mathematics and Mechanics, 2002, 23(3): 229-238.
[17]	DAI Tian-min. Restudy of Coupled Field Theories for Micropolar Continua(I)─Micropolar Thermoelasticity[J]. Applied Mathematics and Mechanics, 2002, 23(2): 111-118.
[18]	Dai Tianmin. Equations of Motion and Boundary Conditions of Incremental Rate Type for Polar Continua[J]. Applied Mathematics and Mechanics, 2000, 21(3): 221-225.
[19]	Tai Tien-min. On a Theory of Micropolar Protoelastic Material Bodies and Constitutive Equations for Nonlocal Micropolar Elastic Continua[J]. Applied Mathematics and Mechanics, 1981, 2(2): 167-172.
[20]	Tai Tien-min. Constitutive Theories for Nonlocal Micropolar Continua with Implicity and with Multiple Interactions[J]. Applied Mathematics and Mechanics, 1981, 2(4): 347-352.