  Recently fabricated two dimensional (2D) phosphorene crystal structures have
demonstrated great potential in applications of electronics. Mechanical strain
was demonstrated to be able to significantly modify the electronic properties
of phosphorene and few-layer black phosphorus. In this work, we employed first
principles density functional theory calculations to explore the mechanical
properties of phosphorene, including ideal tensile strength and critical
strain. It was found that a monolayer phosphorene can sustain tensile strain up
to 27% and 30% in the zigzag and armchair directions, respectively. This
enormous strain limit of phosphorene results from its unique puckered crystal
structure. We found that the tensile strain applied in the armchair direction
stretches the pucker of phosphorene, rather than significantly extending the
P-P bond lengths. The compromised dihedral angles dramatically reduce the
required strain energy. Compared to other 2D materials such as graphene,
phosphorene demonstrates superior flexibility with an order of magnitude
smaller Young modulus. This is especially useful in practical
large-magnitude-strain engineering. Furthermore, the anisotropic nature of
phosphorene was also explored. We derived a general model to calculate the
Young modulus along different directions for a 2D system.
