MICROPOLAR CONTINUUM MECHANICS IS MORE PROFOUND THAN CLASSICAL CONTINUUM MECHANICS

摘要/Abstract

摘要： This paper expounds the characteristic features of the micropolar continuum theory by developing micropolar continuum models for the static, dynamic and buckling analysis of beam-like or plate-like lattices with rigid joints, by analysing the Newton-micropolar stratified fluid model for blood and by producing experimental proofs demonstrating the micropolar property for human compact bone. In particular, it explains from the point of view of application that the micropolar continuum mechanics is a theory more profound than classical continuum mechanics. Presented in this paper is also a description of some recent advances in applications.

关键词: generalized Ginzburg-Landau equation, inhomogeneous initial-boundary value problem, weak solution, global existence

Abstract: This paper expounds the characteristic features of the micropolar continuum theory by developing micropolar continuum models for the static, dynamic and buckling analysis of beam-like or plate-like lattices with rigid joints, by analysing the Newton-micropolar stratified fluid model for blood and by producing experimental proofs demonstrating the micropolar property for human compact bone. In particular, it explains from the point of view of application that the micropolar continuum mechanics is a theory more profound than classical continuum mechanics. Presented in this paper is also a description of some recent advances in applications.

Key words: generalized Ginzburg-Landau equation, inhomogeneous initial-boundary value problem, weak solution, global existence

陆章基. MICROPOLAR CONTINUUM MECHANICS IS MORE PROFOUND THAN CLASSICAL CONTINUUM MECHANICS[J]. Applied Mathematics and Mechanics (English Edition), 1987, 8(10): 939-946.

Lu Zhang-ji . MICROPOLAR CONTINUUM MECHANICS IS MORE PROFOUND THAN CLASSICAL CONTINUUM MECHANICS[J]. Applied Mathematics and Mechanics (English Edition), 1987, 8(10): 939-946.

参考文献

[1] Eringen, A.C., Theory of micropolar elasticity, Chap. 7 of Fracture (ed. Liebowitz. H.), V. 2(1968), 621-729.
[2] Eringen, A.C., Theory of micropolar fluids, J. Math. Mech., 16 (1966), 1-18.
[3] Stokes, V.K., Couple stresses in fluids, Phy. Fluids, 19 (1966), 1709-1716.
[4] Kang, C.K. and A.C. Eringen, The effect of microstructure on the rheological properties of blood, Bull. Math. Biol., 38 (1976), 135-159.
[5] Noor, A.K. and M.P. Nemeth, Micropolar beam models for lattice grids with rigid joints.Comp. Meth. Appl. Mech. Eng., 21 (1980), 249-263.
[6] Noor, A.K. and M.P. Nemeth, Analysis of spatial beamlike lattices with rigid joints. Comp.Meth.Appl. Mech. Eng.,24 (1980), 35-59.
[7] Bazant, Z.P. and M. Christensen. Analogy between micropolar continuum and grid frameworks under initial stress, Int.J.Solids Stru.,8(1972),327-346.
[8] Kanatani,K.I.,A micropolar continuum model for vibrating gird frameworks. Int.J. Engng.Sci.,17(1979),409-418.
[9] Chaturani, P. and V.S. Upadhya, On micropolar fluid model for blood flow through narrow tubes, Biorheology, 16 (1979),419-428.
[10] Brunn,P.,The velocity slip of polar fluids, Rheol.Acta. 14 (1975). 1039-1054.
[11] Qiu Zu-gan and Lu Zhang-Ji, Lubrication theory for micropolar fluids and its application to a journal bearing with finlte length.Applied Mathematics and Mechanics,8,7(1987). 655-665.
[12] Lu Zhang-ji, The micropolar two-fluid model and pulastile blood flow through fine tube.Proceedings of the International Conference on Nonlinear Mechanics, Shanghai (1985).757-761.
[13] Lu Zhang-ji, Flow analysis of micropolar fluid through a circular tube with stenoses and effects of peripheral layer, Proceedings of the First National Congress on Rheology, Changsha,China (1985). (in Chinese)
[14] Lu Zhang-ji, Dispersion of soluble matter in laminar flow of micropolar fluid through a circular tube,Exploration of Nature,5.2(1986),43-48.(in Chinese)
[15] Tandon,P.N.,J.K.Misra and K.K.Srivastava,Microstructural and peripheral-layer viscosity effects on peristaltic transport of seminal fluid,Biorheology,19(1982),707-715.
[16] Yang.J.F.C.and R.S.Lakes.Experimental study of micropolar and couple stress elasticity in compact bone in bending,J.Biomech.,15(1982) 91-98.
[17] Yoon.H.S.and J.L.Katz.Is bone a Cosserat solid?J.Mater.Sci.,18(1983),1297-1305.
[18] Kolpashchikov,V.L.,N.P.Migun and P.P.Prokhorenko,Experimental determination of material micropolar fluids constants,Int.J.Engng.Sci.,21(1983),405-411.
[19] Ariman.T.,M.A.Turk and N.D.Sylvester.Microcontinuum fluid mechanics-a review,Int.J.Engng.Sci.,11(1973),905-930.
[20] Ariman,T.,M.A:Turk and N.D.Sylvester,Applications of microcontinuum fluid mechanics,Int.J.Engng.Sci.,12(1974),273-294.
[21] Eringen,A.C.and C.B.Kafadar,Polar Field Theories,Continuum Physics(ed.Eringen,A.C.),V.4,Part Ⅰ(1976),1-74.
[22] Lu Zhang-ji,Recent developments of application of micropolar fluid theory-biomechanics and liquid lubrication.Proceedings of the First National Congress on Rheology,Changsha,China(1985).(in Chinese)
[23] Fringen A.C.,Nonlocal Polar Field Theories,Continuum Physics(ed.Eringen,A.C.),V.4.Part Ⅲ(1976),205-264．