Elastic energy in the fiber

The deformed fiber shape is approximated by a circular arc with elastic energy E_e given by

$$E_e=\frac{\pi ER^4(\phi_p^2+\phi_y^2)}{8D}$$ (1)

where $\phi _p$ and $\phi_y$ are the ``pitch'' (normal to the substrate) and ``yaw'' (parallel to the substrate) fiber bending angles respectively.

A Surface Evolver script was written to move the fiber to its equilibrium position where solder capillary and fiber elastic forces balance. Run once every 30 Evolver iterations, this script was a Newton's method root finder which set equal the forces given by derivatives of equation 1 and the appendix. The derivative of capillary force with respect to $\phi _p$ and $\phi_y$ was calculated by a central difference method.