Infinitesimal Strains¶

In a 2D-DIC analysis, a two-dimensional displacement field $\bm{u}=\bm{u}(\bm{X},t)$ is measured. Here $\bm{X}$ denotes a position in the reference coordinate system. $t$ denotes the time, usually associated to the image ID in a sequence of images.

For any position $\bm{X}$ and any time $t$ the two-dimensional displacement gradient may be calculated as:

$\bm{H} = \frac{\bm{\partial u}}{\bm{\partial X}} = \begin{bmatrix} H_{11} & H_{12} \\ H_{21} & H_{22} \end{bmatrix}$

The infinitesimal strains are basically defined as the components of the displacement gradient matrix.

${\epsilon}_{11} = H_{11}$

${\epsilon}_{12} = {\epsilon}_{21} = \frac{1}{2}(H_{12} + H_{21})$

${\epsilon}_{22} = H_{22}$