A velocity field
that only produces pure strain should satisfy
(no volume dilatation) and also no rotation is allowed. This implies that velocity field components have to satisfy
and
As a result, the velocity field is of the form
and
where
and
are constants. As an example of a vector field that only causes pure strain to a material element of the flow, consider the case where the constants
and
assume the values
and
.
Non-zero values of the constants
and
would have given a translation component to the velocity field. To illustrate the effect of this velocity field to a material contour, the user can use the vector field manipulation application. Type
in the text box Input
and type
in the text box Input
. Then input in the display area, by mouse clicking, a square contour. Then change the value of time in the text box Input t, and then click the Draw button. As a result the contour suffers pure strain by the vector field. Repeat it as many times you want.