  Bifurcation of an elastic structure crucially depends on the curvature of the
constraints against which the ends of the structure are prescribed to move, an
effect which deserves more attention than it has received so far. In fact, we
show theoretically and we provide definitive experimental verification that an
appropriate curvature of the constraint over which the end of a structure has
to slide strongly affects buckling loads and can induce: (i.) tensile buckling;
(ii.) decreasing- (softening), increasing- (hardening), or constant-load (null
stiffness) postcritical behaviour; (iii.) multiple bifurcations, determining
for instance two bifurcation loads (one tensile and one compressive) in a
single-degree-of-freedom elastic system. We show how to design a constraint
profile to obtain a desired postcritical behaviour and we provide the solution
for the elastica constrained to slide along a circle on one end, representing
the first example of an inflexional elastica developed from a buckling in
tension. These results have important practical implications in the design of
compliant mechanisms and may find applications in devices operating in
quasi-static or dynamic conditions.
