Table 1.

Validation of the Elastica3D Model Against a Finite Element Solution in ABAQUS and/or Against the Analytic Solution

	sapplied(mm)	Fapplied(mN)	Error	Error (percent whisker arc length)
Cylindrical whiskers: Error is the distance between the contact point location (rcp, θcp, φcp) computed by using Elastica3D and computed via the analytic solution.
Figure 1a, case 1	13.9	2.4	0.31 mm	0.88
Figure 1a, case 2	31.4	6.0	0.36 mm	1.03
Figure 1a, case 3	10.0	8.1	0.41 mm	1.2
Compare cylindrical and tapered whiskers: Error is the distance between the contact point location (rcp, θcp, φcp) computed by using Elastica3D and computed by using FEM.
Cylindrical (no figure)	22.7	0.1	38.4 μm	0.11
Tapered (no figure)	22.7	0.1	26.6 μm	0.076
Tapered whisker with intrinsic curvature: Error is the distance between the contact point location (rcp, θcp, φcp) computed by using Elastica3D and computed by using FEM.
Figure 1c	34.5	0.4	40.8 μm	0.087

For the cases identified in the first column, we applied the same force (F_applied) at the same location along the whisker arc length (s_applied) to Elastica3D and the FEM model. Top rows: In the case of cylindrical whiskers, where the FEM solution matched the analytic solution, the errors remained below 1.5% of the whisker arc length. Middle rows: Errors between the FEM solution and Elastica3D were smaller for tapered whiskers than cylindrical whiskers when the same load was applied at the same arc length. Bottom row: Errors remained small for tapered whiskers with intrinsic curvature.

3D, three-dimensional; FEM, finite element model.