Consider the hinge for
the lid of a box. The box, lid, and hinge
are to be molded as a single unit. The
hinge is a thin ligament that flexes elastically
as the box is closed, as shown in the
figure, but it carries no significant axial loads. Then the best material is the one that (for given ligament dimensions)
bends to the smallest radius without yielding or failing. When a ligament of
thickness t is bent elastically to a radius R, the surface strain is