  The amount of rippling in graphene sheets is related to the interactions with
the substrate or with the suspending structure. Here, we report on an
irreversibility in the response to forces that act on suspended graphene
sheets. This may explain why one always observes a ripple structure on
suspended graphene. We show that a compression-relaxation mechanism produces
static ripples on graphene sheets and determine a peculiar temperature $T_c$,
such that for $T<T_c$ the free-energy of the rippled graphene is smaller than
that of roughened graphene. We also show that $T_c$ depends on the structural
parameters and increases with increasing sample size.
