Fig. 4.

Force-displacement relation, countercurvature, and internal mechanics of filament bundles: the actuation force magnitude, , relative to the associated Euler bucking load (A), and the absolute countercurvature measured at the actuation point, , as a function of d (B), for a Euler–Bernoulli rod (black curve), and filament bundles with sliding resistances (blue curves) and (red curves) for (solid blue and red curves) and (dashed blue and red curves). Note that B outlines the counterbend and its sensitivity to different quantities in the -parameter space. Because is identically zero for the Euler–Bernoulli case, the black curve is omitted in B. (C) Horizontal and vertical load, Q and P, respectively, required to hold a filament bundle at a distance , as a function of μ and γ, depicted by the blue and orange contour lines. Note that the contours of Q and P conveniently form a mesh in -parameter space. (D) Curvature (solid curves) and interfilament sliding moment (dashed curves) as a function of s, for , , for three horizontal displacements d, as in Fig. 3. Darker blue curves are used for larger d, and black markers show the actuation point .