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Applied Mathematics and Mechanics

, Volume 24, Issue 12, pp 1375–1380 | Cite as

Renewal of basic laws and principles for polar continuum theories (VII) —Incremental rate type

  • Dai Tian-min
Article

Abstract

The purpose is to establish the rather complete equations of motion, boundary conditions and equation of energy rate of incremental rate type for micropolar continua. To this end the rather complete definitions for rates of deformation gradient and its inverse are made. The new relations between various stress and couple stress rate tensors are derived. Finally, the coupled equations of motion, boundary conditions and equation of energy rate of incremental rate type for continuum mechanics are obtained as a special case.

Key words

coupled equation of motion bundary condition energy rate incremental rate type micropolar continua 

Chinese Library Classification number

O33 

2000 Mathematics Subject Classification

74A35 74A60 

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References

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    KUANG Zhen-bang.Foundations of Nonlinear Continuum Mechanics[M]. Xi'an: Xi'an Jiaotong University Press, 1989. (in Chinese)Google Scholar
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    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 (English Edition), 2003,24(10):1126–1133.MathSciNetGoogle Scholar
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    DAI Tian-min. Renewal of basic laws and principles for polar continuum field theories (VI)-Conservation laws of mass and inertia[J].Applied Mathematics and Mechanics (English Edition), 2003,24(12):1369–1374.MathSciNetGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2003

Authors and Affiliations

  • Dai Tian-min
    • 1
  1. 1.Department of Mathematics & Center for the Application of MathematicsLiaoning UniversityShenyangP. R. China

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