strain tensor component

For small displacement a strain tensor component
$$\tag{1} \begin{array}{rcl} \varepsilon_{ab} & = & \displaystyle \frac{1}{2} \left( \frac{\partial u_a}{\partial x_b} + \frac{\partial u_b}{\partial x_a} + \frac{\partial u_a}{\partial x_b} \frac{\partial u_b}{\partial a} \right), \newline \newline & \approx & \displaystyle \frac{1}{2} \left( \frac{\partial u_a}{\partial b} + \frac{\partial u_b}{\partial a} \right), \end{array} $$
where $u_a$ is displacement in $a$ direction and $x_b$ coordinate in $b$ direction, e.g. $u_1 \equiv u_x$ and $x_3 \equiv z$.

Victor Giurgiutiu, "Chapter 2 - Fundamentals of aerospace composite materials", in Stress, Vibration, and Wave Analysis in Aerospace Composites, Academic Press, 2022, p 29-109, (), url https://doi.org/10.1016/B978-0-12-813308-8.00004-1 [].