BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI

8 Ion Crăciun
with large molecules like polymers, because they have an internal structure
demanding that each point of them to enjoy of six degree of freedom. In a
remarkable monograph, the brothers E. and F. Cosserat (1909) gave a
systematic development of the mechanics of continuous media in which each
point has six degree of freedom of a rigid body. The orientation of a given
particle of such a medium can be represented mathematically by the values of
three mutually perpendicular unit vectors, called directors by Ericksen and
Truesdell (1958). Thus, the theory of oriented media has been appeared.
An exposition of the kinematics of oriented bodies, together with
references to other contributions on the subject up to 1960, is given in the
monograph by Truesdell and Toupin (1960)
Micropolar elasticity termed by Eringen (1966), or asymmetric elasticity,
after Nowacki (1986), as well as Cosserat elasticity theory are used to describe
deformation of elastic media with oriented particles. For engineering
applications it can model composites with rigid chopped fibres, elastic solids
with rigid granular inclusions, and other industrial materials.
However, in spite of its novelty, the theory of Cosserat brothers was not
appreciated for a long time. Only in the sixties the research development in the
area of the general theory of continuum helped the Cosserat theory to attract the
attention of researchers and it becames the starting point for a number of related
theories in mechanics and physics of oriented media.
Many papers written over the years in the area of mechanics have been
devoted to the media of Cosserat type. Due to its cognitive values, possible
complete experimental verification as well as technological applications, the
Cosserat theory is being developed in a great number of research centers in the
world (Poland, USA, Russia, Georgia, Germany, Great Britain, Sweden,
Romania, Canada, India, Italy, Japan, Holand). The first well-known and widely
appreciated monographs concerning the asymmetric elasticity theory have been
written in Poland. The most up-to-date monograph investigation devoted to
linear asymmetric elasticity theory is the book of W. Nowacki (1986). The work
of Nowacki contains a long list of references. A more extensive reference list
can be found in the recent monographs of Dyszlewicz (2004), and Ieşan (2004).
Thus, it has been created a new model of a continuum known today as the
Eringen-Nowacki model.
There are situations in practice when the causes acting on a micropolar
i t
elastic body depend on the time t by the function e − ω . A such dependence is
expressed in the form
i t
f% ( x
ω
, t) =Re[ f( x )e − ],
(1)
where ω is called the frequency of vibration, f % is a scalar or a vector field,
x=x1e1+ x2e2+
x3e3is
the position vector of a point of the body B referred to