Elastic anisotropy measure for two-dimensional crystals

Two-dimensional C5678: a promising carbon-based high-performance lithium-ion battery anode

“…Furthermore, C 5678 is an anisotropic two-dimensional material because its twodimensional elastic anisotropy index (0.68) is larger than that of graphene (0) and much close to that of black phosphorene (0.65). 39…”

High-performance phosphorene electromechanical actuators

“…2). The highly anisotropic electromechanical responses originate from the remarkable structural and mechanical anisotropies of phosphorene [23][24][25] . Furthermore, the charge-induced maximum actuation strain of phosphorene is remarkably larger than that of graphene, silicene, and even the maximum value reported of GO (28.2%) 20,21 , indicating that monolayer phosphorene exhibits an ultrahigh actuation performance.…”

“…Recently phosphorene arises after successful exfoliation from its bulk form (black phosphorus) 22 , and a lot of efforts have been made to investigate its structures, properties as well as applications. For example, phosphorene possesses remarkable in-plane mechanical anisotropy [23][24][25] , which is very different from the in-plane elastic isotropy of graphene 26 . Theoretical calculations demonstrated that the strains to failure (tensile stiffnesses) of phosphorene along the armchair and zigzag directions are as high as 30% (23 N/m) and 27% (92.3 N/m), respectively 23,24 .…”

Multiscale analysis of brittle failure in heterogeneous materials

“…From here, we aim to determine the scale from which the symmetry orders actually governs the elastic isotropy. To do so, the two-dimensional elastic anisotropy index a r -defined in [33] -is analysed at each material point for each observation scale. An explicit expression of a r as a function of C ij and S Cij can be written as follows: (with an error lower than 1% ) once l CG is larger than the characteristic length d of the microstructure.…”