Nonlinear elasticity of monolayer zinc oxide honeycomb structures: A first-principles study

We present the second- and third-order elastic constants and discuss the nonlinear elasticity for monolayer zinc oxide (ZnO) with honeycomb structure. Density functional theory (DFT) within generalized-gradient-approximation (GGA) combining with the method of homogeneous deformation is employed. The predictions for the elastic constants are obtained from the nonlinear least-squares polynomial fit to the calculated strain-energy relations from first-principles total-energy calculations. In comparison with the linear approach, the nonlinear effects really matter for strain larger than approximately 3.0%. We discuss how internal relaxation acts on the elastic properties, and internal relaxation displacements for the corresponding applied strain are obtained. Our results show that internal relaxation is important for the values of elastic constants, and especially influence the third-order elastic constants. Finally, we discuss force–displacement behavior and the breaking strength of monolayer ZnO within a framework of nonlinear stress–strain relationship. Monolayer ZnO exhibits very high ductility, in our study exceeding 20% ductility in tension, and the elastic response will exhibit highly nonlinear while the third-order effects really matter.

Research Highlights
► Second- and third-order elastic constants of two-dimensional honeycomb structures of zinc oxide have been obtained by using First-principles calculations.
► The internal relaxation importantly influences on the nonlinear elastic properties.
► The nonlinear effects really matter for strain larger than approximately 3.0%.
► The nonlinear stress–strain relationship shows that monolayer ZnO exhibits very high ductility.