Page 156 - Introduction to Continuum Mechanics

Kinematics of a Continuum 141

3.26 Eulerian Strain Tensor

Let

T *
where B = FF , then the tensor e is known as the Eulerian Strain Tensor. We note that if
there if no deformation, then B~ = I and e* = 0.
* —i
The geometric meaning of the components of e and B are described below:
From

we have

where F is the inverse of F. In rectangular Cartesian coordinates, Eq. (3.26.3) reads

Thus,

where X( = ^-(^ lTr 2^3,0 is the inverse function of or,- = x^XiJC'bX^fy.

In other words, when rectangular Cartesian coordinates are used for both the reference and
the current configuration,

Now,

i.e.,