  A new hyperelastic membrane material model is proposed for single layer blue
phosphorus ($\beta\text{-P}$), also known as blue phosphorene. The model is
fully nonlinear and captures the anisotropy of $\beta\text{-P}$ at large
strains. The material model is calibrated from density functional theory (DFT)
calculations considering a set of elementary deformation states. Those are pure
dilatation and uniaxial stretching along the armchair and zigzag directions.
The material model is compared and validated with additional DFT results and
existing DFT results from the literature, and the comparison shows good
agreement. The new material model can be directly used within computational
shell formulations that are for example based on rotation-free isogeometric
finite elements. This is demonstrated by simulations of the indentation and
vibration of single layer blue phosphorus sheets at micrometer scales. The
elasticity constants at small deformations are also reported.
