Nonlinear elastic behavior of 2D materials using molecular statics and comparisons with first principles calculations.

Classical molecular dynamics techniques are increasingly being employed to study the elastic behavior of materials at the atomic scale. It may be possible to use molecular dynamics in lieu of computationally expensive first principles calculations. However, it is not clear which, if any, of the available interatomic potentials is accurate for the comprehensive analysis of the finite elastic behavior of specific materials. Furthermore, there are some fundamental differences between density functional theory and molecular dynamics when simulating elastic processes. Density functional theory is based on solving the time-independent Schrödinger wave equation for a specific quantum state numerically through a self-consistent process to obtain the energies and stresses. In contrast, molecular dynamics simulations are based on computational time-domain integration of the classical equations of motion and may not necessarily be the best approach for evaluating the nonlinear elastic constants of a material since the results obtained depend on the timestep and deformation rate used in the simulation. To alleviate this issue, we introduce a computationally efficient molecular statics approach for simulating the nonlinear elastic response of a material wherein a unit cell is incrementally deformed to compute the variables of interest. The proposed molecular statics approach can be used to analyze 2D materials of arbitrary symmetries by sampling for the strain energy density along rays in strain space to determine the nonlinear elastic constants based on Murnaghan's hyperelastic constitutive model. The approach is verified by evaluating the nonlinear elastic constants of graphene and comparing the results with those obtained through density functional theory. Subsequently, we analyze black phosphorus, an orthorhombic material, since its comprehensive nonlinear elastic behavior has not been previously studied using molecular statics or dynamics. We compare the majority of the available interatomic potentials for black phosphorus to assess their accuracy in simulating its nonlinear elastic behavior. The nonlinear elastic response of black phosphorus is analyzed using the most accurate interatomic potential among those considered and the nonlinear elastic constants are compared with those obtained using density functional theory. It is found that while the molecular statics approach is computationally efficient for the nonlinear elastic analysis of 2D materials, the accuracy of the results depends on the interatomic potential used for the simulations. • Ray based methodology calculations using molecular statics. • Nonlinear elastic constants of graphene and black phosphorus. • Comparison of molecular statics and dynamics with density functional theory results. • General analysis of the interatomic potentials available for black phosphorus. • Limitations of molecular dynamics and some classical interatomic potentials. [ABSTRACT FROM AUTHOR]

Copyright of Physica E is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)