  We show using computer simulations and mean field theory that a system of
particles in two dimensions, when confined laterally by a pair of parallel hard
walls within a quasi one dimensional channel, possesses several anomalous
structural and mechanical properties not observed in the bulk. Depending on the
density $\rho$ and the distance between the walls $L_y$, the system shows
structural characteristics analogous to a weakly modulated liquid, a strongly
modulated smectic, a triangular solid or a buckled phase. At fixed $\rho$, a
change in $L_y$ leads to many reentrant discontinuous transitions involving
changes in the number of layers parallel to the confining walls depending
crucially on the commensurability of inter-layer spacing with $L_y$. The solid
shows resistance to elongation but not to shear. When strained beyond the
elastic limit it fails undergoing plastic deformation but surprisingly, as the
strain is reversed, the material recovers completely and returns to its
original undeformed state. We obtain the phase diagram from mean field theory
and finite size simulations and discuss the effect of fluctuations.
