  An energy-based model is developed to describe the periodic formation of
voids/saddle reefs in hinge zones of chevron folds. Such patterns have been
observed in a series of experiments on layers of paper, as well as in the
field. A simplified hinge region in a stack of elastic layers, with straight
limbs connected by convex segments, is constructed so that a void forms every m
layers and repeats periodically. Energy contributions include strain energy of
bending, and work done both against a confining overburden pressure and an
axial compressive load. The resulting total potential energy functional for the
system is minimized subject to the constraint of non-interpenetration of
layers, leading to representation as a nonlinear second-order free boundary
problem. Numerical solutions demonstrate that there can exist a minimum-energy
m-periodic solution with m equal to 1. Good agreement is found with experiments
on layers of paper.
