Non trivial deformation structures in confined elastic membrane under stretching

Two dimensional elastic networks when stretched, deform plastically by producing pleats; system
spanning linear structures with width comparable to lattice spacing, where the network overlaps
on itself. When a similar elastic membrane is confined within rigid walls and allowed to have out
of plane fluctuations, similar unconventional deformation modes appear upon stretching. Within
these structures, which we call ripplocations, the height field becomes multivalued. These distinct
structures are separated by large free energy barriers from a phase with only smooth ripples, that
are always present at non-zero temperatures. To understand these structures and their interrelation,
we introduce an external field that couples to local non-affine fluctuations measured from the flat
reference. Using sequential umbrella sampling Monte Carlo involving sophisticated, non Boltzmann
sampling, we obtain conditions under which ripplocations are formed. We obtain a finite temperature
phase diagram in the strain-field plane. We also describe experimental signatures such as typical
stress strain curves for membranes by which transitions from rippled to ripplocated membranes may
be probed