  When a flat elastic strip is compressed along its axis, it is bent in one of
two possible directions via spontaneous symmetry breaking and forms a
cylindrical arc, a phenomenon well known as Euler buckling. When this
cylindrical section is pushed in the other direction, the bending direction can
suddenly reverse. This instability is called snap-through buckling and is one
of the elementary shape transitions in a prestressed thin structure. Combining
experiments and theory, we study snap-buckling of an elastic strip with one end
hinged and the other end clamped. These asymmetric boundary constraints break
the intrinsic symmetry of the strip, generating rich exotic mechanical
behaviors including largely hysteretic but reproducible force responses and
switch-like discontinuous shape changes. We establish the set of exact
analytical solutions that fully explain all of our major experimental and
numerical findings. Asymmetric boundary conditions arise naturally in diverse
situations when a thin object is in contact with a solid surface at one end,
but their profound consequences for the buckling mechanics have been largely
overlooked to date. The idea of introducing asymmetry through boundary
conditions would yield new insight into complex and programmable
functionalities in material and industrial design.
