Continuum Mechanics for Higher-Stage Micropolar Materials (3rd Report, Strain and Displacement)

Kazuyuki Shizawa, Seiichi Kobayashi, Kunihiro Takahashi

Research output: Contribution to journalArticlepeer-review


In the previous reports, the authors proposed the concept of a higher-stage micropolar continuum, and then formulated their kinematics and mechanical balance laws. In the present paper, strain tensors characterizing deformation of micropolar materials of stage-2 are newly defined on the basis of the kinematics presented in the 1st report. Some equations are derived, which express relations between material strain tensors and spactial ones, and between the strain rate tensors and the kinematical quantities (e.g., deformation rate tensor, angular velocity vector, etc.) defined in the 1st report. While, new displacement vectors and tensors which are peculiar to micropolar materials of stage-2 are defined, and the relations between strains and displacements are obtained. Furthermore, linearizing the strain-displacement relations, strain tensors defined here are discussed geometrically. The strain tensors are suitable for expressing the constitutive equation of bicouple stress which is the generalized bimoment in the theory of thin walls.

Original languageEnglish
Pages (from-to)892-899
Number of pages8
JournalTransactions of the Japan Society of Mechanical Engineers Series A
Issue number536
Publication statusPublished - 1991
Externally publishedYes


  • Continuum Mechanics
  • Deformation Rate
  • Displacement Vector
  • Elasticity
  • Finite Deformation Theory
  • Higher Stage
  • Microstructure
  • Polar Material
  • Strain Rate
  • Strain Tensor

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering


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