Page 164 - Introduction to Continuum Mechanics
P. 164
Kinematics of a Continuum 149
Thus, the area OABC, which was of unit area and having a normal in the direction of -63
becomes an area whose normal is in the direction of 62 and with a magnitude of Aj %•
It is easily verified that R corresponds to a 90° rotation about the ej, which is the axial
vector of the antisymmetric part of R
3.30 Components of Deformation Tensors in other Coordinates
The deformation gradient F transforms a differential material element dX. in the reference
configuration into a material element d\ in the current configuration in accordance with the
equation
where
describes the motion. If the same rectangular coordinate system is used for both the reference
and the current configurations, then since the set of base vectors (61,62,63) is the same at every
point, we have
That is
