Fig. 1.

Schematic of a triangular element deformed from un-deformed configuration ${\Omega }_0$ to deformed configuration ${\Omega }_1$ via deformation tensor ${\hspace{0.17em}}_0^{1}F$. The covariant surface base vectors $G_1$ and $G_2$ as well as $g_1$ and $g_2$ are not necessarily orthogonal but they are expressed in terms of their components in an orthogonal coordinate system (i.e., ($e_1,e_2,e_3$)) to take advantage of $3\times 3$ matrix algebra.