  We study the mechanics of a reversible decohesion (unzipping) of an elastic
layer subjected to quasi-static end-point loading. At the micro level the
system is simulated by an elastic chain of particles interacting with a rigid
foundation through breakable springs. Such system can be viewed as prototypical
for the description of a wide range of phenomena from peeling of polymeric
tapes, to rolling of cells, working of gecko's fibrillar structures and
denaturation of DNA. We construct a rigorous continuum limit of the discrete
model which captures both stable and metastable configurations and present a
detailed parametric study of the interplay between elastic and cohesive
interactions. We show that the model reproduces the experimentally observed
abrupt transition from an incremental evolution of the adhesion front to a
sudden complete decohesion of a macroscopic segment of the adhesion layer. As
the microscopic parameters vary the macroscopic response changes from
quasi-ductile to quasi-brittle, with corresponding decrease in the size of the
adhesion hysteresis. At the micro-scale this corresponds to a transition from a
`localized' to a `diffuse' structure of the decohesion front (domain wall). We
obtain an explicit expression for the critical debonding threshold in the limit
when the internal length scales are much smaller than the size of the system.
The achieved parametric control of the microscopic mechanism can be used in the
design of new biological inspired adhesion devices and machines.
