A nonlinear hyperelasticity model for single layer blue phosphorus based on ab-initio calculations

Abstract

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.

References in corpus (7)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Semiconducting layered blue phosphorus: A computational study
• Phase coexistence and metal-insulator transition in few-layer phosphorene: A computational study
• A new rotation-free isogeometric thin shell formulation and a corresponding continuity constraint for patch boundaries
• A new shell formulation for graphene structures based on existing ab-initio data
• Modal analysis of graphene-based structures for large deformations, contact and material nonlinearities
• A new efficient hyperelastic finite element model for graphene and its application to carbon nanotubes and nanocones