  Randomly crumpled sheets have shape memory. In order to understand the basis
of this form of memory, we simulate triangular lattices of springs whose
lengths are altered to create a topography with multiple potential energy
minima. We then deform these lattices into different shapes and investigate
their ability to retain the imposed shape when the energy is relaxed. The
lattices are able to retain a range of curvatures. Under moderate forcing from
a state of local equilibrium, the lattices deform by several percent but return
to their retained shape when the forces are removed. By increasing the forcing
until an irreversible motion occurs, we find that the transitions between
remembered shapes show co-operativity among several springs. For fixed lattice
structures, the shape memory tends to decrease as the lattice is enlarged; we
propose ways to counter this decrease by modifying the lattice geometry. We
survey the energy landscape by displacing individual nodes. An extensive
fraction of these nodes proves to be bistable; they retain their displaced
position when the energy is relaxed. Bending the lattice to a stable curved
state alters the pattern of bistable nodes. We discuss this shapeability in the
context of other forms of material memory and contrast it with the shapeability
of plastic deformation. We outline the prospects for making real materials
based on these principles.
