where the differential is with respect to the spatial coordinate system.
This can be decomposed into3. Kinematics of Deformation
Section C
Review to Section 3.12 to 3.17
where the differential is with respect to the spatial coordinate system.
This can be decomposed into
where
are the rate of deformation tensor and spin tensor respectively.
2.
Rate of deformation gives the rate of change of differential element
whereas the spin tensor gives the
rate of rotation of
(see example 3.13.1).
3.
The dual vector of spin vector is
called the angular velocity. While
spin causes only pure rotation, rate of deformation contributes to
in all non-eigen orientations..
4. For any displacement field compatibility is satisfied, while for a specified strain fields need to invoke compatibility equations.
5.
Since compatibility conditions involves second derivatives of strain with
respect to
, if the strain field is a linear function of space then compatibility is
automatically satisfied. (see equations 3.6.7 to 3.6.12, examples 3.16.1 to
3.16.3)
See solved problems on problem 3-22
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