Pure Strain.

A velocity field $\vec{v}$ that only produces pure strain should satisfy


\begin{displaymath}\nabla\cdot\vec{v} = 0
\end{displaymath}

(no volume dilatation) and also no rotation is allowed. This implies that velocity field components have to satisfy


\begin{displaymath}\frac{\partial V_{y}}{\partial x} = 0
\end{displaymath}

and


\begin{displaymath}\frac{\partial V_{x}}{\partial y} = 0.
\end{displaymath}

As a result, the velocity field is of the form


\begin{displaymath}V_{x} = Cx+C_{1}
\end{displaymath}

and


\begin{displaymath}V_{y} = -Cy+C_{2},
\end{displaymath}

where $C, C_{1}$ and $C_{2}$ 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 $C, C_{1}$ and $C_{2}$ assume the values $C = 1, C_{1} = 0$ and $C_{2} = 0$. Non-zero values of the constants $C_{1}$ and $C_{2}$ 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 $x$ in the text box Input $V_{x}$ and type $-y$ in the text box Input $V_{y}$. 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.



Karl P Burr
2003-07-07