Page 144 - Introduction to Continuum Mechanics
P. 144
Kinematics of a Continuum 129
where U is the right stretch tensor. The tensor C is known as the right Cauehy-Green
deformation tensor (also known as the Green's deformation tensor). We note that if there is
no deformation, U = C = I.
Using Eq. (3.22.1), we have
The components of C have very simple geometric meanings which are described below.
Consider two material elements d^ = VdX^ and d^ = ¥dX^, we have
i.e.,
Thus, if dx = dsn, is the deformed vector of the material element dX = dS*i then Eq.
(3.23.4) gives
That is
similarly,
By considering two material elements dxP* = dS^i and dX^ = dS>$2 which deform
into dr ' = d$im and dsr ' = dsp where m and n are unit vectors having an angle of ft
between them, then Eq. (3.23.4) gives
That is
Similarly
