Limits of Lateral Expansion in Two-Dimensional Materials with Line Defects

The flexibility of two-dimensional (2D) materials enables static and dynamic ripples that are known to cause lateral contraction, shrinking of the material boundary. However, the limits of 2D materials' \emph{lateral expansion} are unknown. Therefore, here we discuss the limits of intrinsic lateral expansion of 2D materials that are modified by compressive line defects. Using thin sheet elasticity theory and sequential multiscale modeling, we find that the lateral expansion is inevitably limited by the onset of rippling. The maximum lateral expansion $\chi_{max}\approx 2.1\cdot t^2\sigma_d$, governed by the elastic thickness $t$ and the defect density $\sigma_d$, remains typically well below one percent. In addition to providing insight to the limits of 2D materials' mechanical limits and applications, the results highlight the potential of line defects in strain engineering, since for graphene they suggest giant pseudomagnetic fields that can exceed $1000$~T.