Random Theory of Deformation of Structured Media

  • D. R. Axelrad
Part of the International Centre for Mechanical Sciences book series (CISM, volume 71)


In the last decade several theories have been proposed with the aim of modifying or extending classical continuum theory so that the deformation process of structured media can be described. The first theory considering the presence of a microstructure known as the theory of “oriented media” is due to E. and F. Cosserat[1]. In this theory the deformation is described in terms of a position vector of an arbitrary point in the medium with respect to a fixed reference frame and a vector called “director” associated with the position vector. The concept of using directors in continuum mechanics goes back to Duhem[2]. The fundamental aspects of the deformation kinematics of such media were treated comprehensively by Truesdell and Toupin[3]. Following the Cosserat approach, Mindlin[4] proposed a theory of elastic media possessing a microstructure in which a physical point or “unit cell” was considered deformable. This theory can be reduced in the case of a homogeneous deformation to a model suggested by Ericksen and Truesdell[5], which is based on the concept of a Cosserat continuum. Another theory extending the classical formulation is the “couple stress theory” treated in detail by Toupin[6]. This approach was later completed by Eringen and Suhubi[7].


Constitutive Relation Couple Stress Theory Structure Medium Cosserat Continuum Fixed Reference Frame 


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© Springer-Verlag Wien 1971

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