In this talk, we rigorously derive the Von-Karman continuum plate theory for 2D materials which captures the governing out-of-plane nonlinear deformations in the monolayered systems. We mathematically analyze the continuum approximation, prove the stability of the continuum energy allowing the out-of-plane deformations, and attain the comprehensive first order error estimates. We test the numerical examples of one-dimensional systems that confirm the theoretical results and propose a multiscale model for monolayered systems with point defects.

This is a joint work with Dr. Julian Braun from the University of Warwick, UK, and Dr. Derek Olson from Rensselaer Polytechnic Institute.